THE REPUBLIC OF TURKEY 
BAHCESEHIR UNIVERSITY 
 
 
 
 
 
 
PROACTIVE MAINTENANCE OF  THERMAL POWER 
PLANTS UNDER LIMITED OBSERVATIONS  
 
Master’s Thesis 
 
 
MO`TASEM ABUSHANAP 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
ISTANBUL, 2013  
 THE REPUBLIC OF TURKEY 
BAHCESEHIR UNIVERSITY 
 
GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES 
INDUSTRIAL ENGINEERING 
 
 
PROACTIVE MAINTENANCE OF  THERMAL 
POWER PLANTS UNDER LIMITED 
OBSERVATIONS  
Master’s Thesis 
 
 
 
MO`TASEM ABUSHANAP 
 
 
 
 
 
Supervisor: ASSIST.PROF. DEMET ÖZGÜR ÜNLÜAKIN 
 
 
 
 
 
 
 
 
ISTANBUL, 2013
 THE REPUBLIC OF TURKEY 
BAHCESEHIR  UNIVERSITY 
 
GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES 
INDUSTRIAL ENGINEERING 
 
Name of the thesis: Proactive Maintenance of  Thermal Power Plants Under 
 Limited Observations  
Name/Last Name of the Student: Mo`tasem Abushanap 
Date of the Defense of Thesis:5/6/2013 
 
The thesis has been approved by the Graduate School of  Natural and Applied 
Sciences. 
 
        
Assoc.Prof.Tunç BOZBURA 
                                                                                        Graduate School Director 
               
 
 
I certify that this thesis meets all the requirements as a thesis for the degree of 
Master of Science.    
 
      Assist. Prof. %DUÕú 6(/d8. 
                         Program Coordinator 
               
 
 
This is to certify that we have read this thesis and we find it fully adequate in scope, 
quality and content, as a thesis for the degree of Master of Science. 
    
Examining Comittee Members        Signature____  
 
Thesis Supervisor     ----------------------------------- 
Assist. Prof.  Demet ÖZGÜR ÜNLÜAKIN 
    
Member       ----------------------------------- 
Prof.7DQHU %ø/*ød 
 
Member       ----------------------------------- 
Assist. Prof. Ethem d$1$.2ö/8 
 
 
 ACKNOWLEDGEMENT 
 
First of all I would like to thank the mighty Allah for everything that I achieved. Then I 
ZDQW WR WKDQN P\ VXSHUYLVRU $VVLVW. 3URI. 'HPHW g]JU hQODNÕQ IRU EHLQJ SDWLHQW DQG IRU 
all the help she provided. Also I would like to thank Prof. Taner Bilgiç and Assist. Prof. 
(WKHP dDQDNR÷OX IRU DOO WKH DGYLFHV DQG notes they gave. And I appreciate the visit of Prof. 
0HKPHW %DUÕú g]HUGHP IRU WKH DGYLFHV KH SURYLGHG. Many thanks to my father and my 
mother for all the support they gave. Thanks to my Fiancée for standing and supporting me. 
And finally thanks to everyone who contributed in any way to this work.
 ABSTRACT 
 
 
PROACTIVE MAINTENANCE OF  THERMAL POWER PLANTS UNDER LIMITED 
OBSERVATIONS  
 
MO`TASEM ABUSHANAP 
 
INDUSTRIAL ENGINEERING 
 
THESIS SUPERVISOR: DEMET ÖZGÜR ÜNLÜAKIN 
 
 
JUNE 2013, 103 
 
In the past few decades, because of the technological revolution, interactions between the 
components of a system become more sophisticated which makes the maintenance decision 
making procedure a hard issue. At this point, effective problem diagnosis plays an 
important role in determining the right maintenance decisions. The objective of diagnosis is 
to analyze and determine the most likely causes of a problem. Hence the data or 
observations gathered so far helps the decision maker in effective diagnosis. On the other 
hand, monitoring and predicting system health is also important especially for dynamic 
systems where proactive maintenance is preferred instead of the reactive one. Improving 
system reliability by performing maintenance activities based on early diagnosis before a 
serious problem arises is essential in proactive maintenance.  
In this study, we consider the proactive maintenance decisions of thermal power plants 
consisting of interacting components under limited observations over a planning horizon. 
Maintenance activities are performed at any time by replacing either aging components or 
gauges in the system. The objective is to determine an optimum proactive maintenance plan 
in a discrete planning horizon. We use dynamic Bayesian networks (DBNs) for 
representation and to do fast inference. We propose two proactive maintenance 
methodologies and present their predicted maintenance plans. At any time when a 
replacement decision is made, three different diagnosis techniques, where two of them are 
from literature, are used. Computational analyses show that there exists no significance 
difference among the performances of these methods. The proposed methodologies can be 
easily adapted for proactive maintenance planning of other complex dynamic systems. 
Keywords: Thermal Power Plants, Dynamic Bayesian Network (DBN), Proactive 
Maintenance, Reliability 
 
 ÖZET 
 
 
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MO`TASEM ABUSHANAP 
 
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TEZ '$1,ù0$1,: DEMET ÖZGÜR ÜNLÜAKIN 
 
 
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Güvenilirlik 
 
 
 
 
 CONTENTS 
 
 
LIST OF FIGURES ........................................................................................................ IX 
LIST OF TABLES ............................................................................................................... X 
ABBREVIATIONS .......................................................................................................... XII 
1. INTRODUCTION ...................................................................................................... 1 
1. STEPS OF THE THESIS ..................................................................................... 4 
1. OUTLINE OF THE THESIS .............................................................................. 5 
2. LITERATURE REVIEW .......................................................................................... 6 
2.1 RELIABILITY AND MAINTENANCE ............................................................ 6 
2.2 BAYESIAN NETWORKS ................................................................................... 8 
2.3 DYNAMIC BAYESIAN NETWROKS .............................................................. 9 
2.4 RELIABILITY AND MAINTAINABILITY OF THERMAL POWER 
PLANTs ..................................................................................................................... 12 
3. BACKGROUND ....................................................................................................... 14 
3.1 RELIABILITY AND MAINTENANCE .......................................................... 14 
3.1.1 Reliability ............................................................................................... 14 
3.1.2 Maintenance ........................................................................................... 15 
3.1.2.1 Reactive Maintenance .............................................................. 16 
3.1.2.2 Preventive Maintenance ........................................................... 18 
3.1.2.3 Predictive Maintenance and Inspection .................................. 21 
3.1.2.4 Proactive Maintenance (Root Cause Maintenance) .............. 22 
3.1.2.5 Reliability Centered Maintenance ........................................... 24 
3.1.2.6 Diagnosis and Prognosis ........................................................... 29 
 3.2 PROBABILISTIC GRAPHICAL MODELS ................................................... 30 
3.2.1 Basic Terminologies .............................................................................. 31 
3.2.1.1 Conditional Probability ............................................................ 31 
3.2.1.2 Joint probability ........................................................................ 31 
3.2.1.3 Marginal probability ................................................................ 32 
3.2.1.4 Independent Events .................................................................. 32 
3.1.2.5 Transition Probability .............................................................. 32 
3.2.1.6 Bayes Rule ................................................................................. 33 
3.2.2 Decision Diagrams ................................................................................. 34 
3.2.2.1 Influence Diagrams ................................................................... 35 
3.2.2.2 Dynamic Decision Networks .................................................... 36 
3.2.3 Bayesian Networks ................................................................................ 36 
3.2.3.1 Static Bayesian Networks ......................................................... 36 
3.2.3.2 Dynamic Bayesian Networks ................................................... 39 
3.2.3.3 Inference in Dynamic Bayesian networks .............................. 40 
4. PROBLEM DEFINITION AND MODELING...................................................... 41 
4.1 THERMAL POWER PLANTs ......................................................................... 41 
4.1.1 Rankine Cycle ........................................................................................ 41 
4.1.2 Components in Rankine cycle .............................................................. 44 
4.1.3 Systems of Thermal Power Plants ....................................................... 45 
4.2 MODELING WITH DYNAMIC BAYESIAN NETWORKS ........................ 45 
4.2.1 Replaceable Nodes ................................................................................. 48 
4.2.2 Process Nodes......................................................................................... 48 
4.2.3 Observable Nodes .................................................................................. 49 
4.2.4 Non-aging (non-degrading) nodes: ...................................................... 50 
4.3 ESTABLISHING THE MODEL ...................................................................... 52 
4.3.1 Main replaceable components .............................................................. 52 
4.3.2 Gauge Components ............................................................................... 53 
4.3.3 Process Nodes......................................................................................... 56 
4.3.3.1 Hidden Processes ...................................................................... 56 
4.3.3.2 Observable processes ................................................................ 60 
4.3.4 Transition probabilities ........................................................................ 62 
 4.3.5 Independent variables ........................................................................... 63 
4.3.6 Domain of variables .............................................................................. 64 
5. METHODOLOGY ................................................................................................... 67 
5.1 ONE CRITICAL PROCESS ALGORITHM .................................................. 68 
5.1.1 Notation of SCP ..................................................................................... 68 
5.1.2 Algorithm of SCP .................................................................................. 69 
5.2 MULTIPLE CRITICAL PROCESSES ALGORITHM ................................. 71 
5.2.1 Notation of MCP.................................................................................... 74 
5.2.2 Algorithm of MCP ................................................................................. 75 
6. RESULTS AND EVALUATION ............................................................................ 77 
6.1 DESIGN OF EXPERIMENTS .......................................................................... 77 
6.2 ANALYSIS OF EXPERIMENTS ..................................................................... 87 
6.3 PREDICTED MAINTENANCE PLAN ........................................................... 91 
7. CONCLUSION ......................................................................................................... 94 
REFERENCES ................................................................................................................... 96 
 
 LIST OF FIGURES 
  
 
Figure 3.1: Taxonomy of maintenance strategies ............................................................. 16 
Figure 3.2: Categories of reactive maintenance ................................................................ 17 
Figure 3.3: Elements of preventive maintenance .............................................................. 19 
Figure 3.4: Proactive maintenance methods used to extend the life of components ........ 23 
Figure 3.5: Components of RCM ...................................................................................... 26 
Figure 3.6: Probabilistic Graphical representations .......................................................... 30 
Figure 3.7: Transition probability ..................................................................................... 33 
Figure 3.8: Influence Diagram .......................................................................................... 35 
Figure 3.9: Dynamic decision networks............................................................................ 36 
Figure 3.10: Bayesian Network......................................................................................... 37 
Figure 3.11: a- Diagnosis Reasoning, b-Prognosis (predictive) reasoning ....................... 38 
Figure 3.12: Dynamic Bayesian Networks (DBNs) .......................................................... 40 
Figure 4.1: Schematic representation of thermal power plant .......................................... 42 
Figure 4.2 Simple Rankine cycle ...................................................................................... 42 
Figure 4.3: process flow in thermal power plant using Rankine cycle ............................. 43 
Figure 4.4: Components of Rankine Cycle ....................................................................... 44 
 .................................................... 47 Figure 4.5: Bayesian Network for thermal power plant
Figure 4.6: Types of gauges used in the model ................................................................. 54 
Figure 4.7: Types of process nodes ................................................................................... 57 
 .................................... 66 Figure 4.8: Dynamic Bayesian Network for thermal power plant
Figure 5.1: Outline of the algorithms ................................................................................ 67 
Figure 5.2: Groups of MCP critical nodes ........................................................................ 73 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 LIST OF TABLES 
 
 
Table 1.1: Power plant types and their properities ................................................................ 3 
Table 3.1: Applications of maintenance stratigies ................................................................ 28 
Table 3.2: Differences between diagnosis and prognosis ..................................................... 29 
Table 3.3: Transition probability table .................................................................................. 33 
Table 4.1: Types of nodes in the Bayesian network of thermal power plant ........................ 51 
Table 4.2: Initial probabilities of main components ............................................................. 52 
Table 4.3: Initial probabilities of gauges............................................................................... 55 
Table 4.4: Causal probabilities of cold water........................................................................ 57 
Table 4.5: Causal probabilities of plate rotation ................................................................... 58 
Table 4.6: Causal probabilities of pressurized water ............................................................ 58 
Table 4.7: Causal probabilities of ignition ............................................................................ 58 
Table 4.8: Causal probabilities of heat .................................................................................. 58 
Table 4.9: Causal probabilities of pressurized steam ............................................................ 58 
Table 4.10: Causal probabilities of turbine rotation.............................................................. 59 
Table 4.11: Causal probabilities of pressure drop ................................................................. 59 
Table 4.12: Causal probabilities of electricity ...................................................................... 59 
Table 4.13: Causal probabilities of high voltage .................................................................. 59 
Table 4.14: Causal probabilities of temp1 ............................................................................ 60 
Table 4.15: Causal probabilities of temp2 ............................................................................ 60 
Table 4.16: Causal probabilities of press1 ............................................................................ 61 
Table 4.17: Causal probabilities of press2 ............................................................................ 61 
Table 4.18: Causal probabilities of press3 ............................................................................ 61 
Table 4.19: Causal probabilities of RPMM1 ........................................................................ 61 
Table 4.20: Causal probabilities of RPMM2 ........................................................................ 62 
Table 4.21: Causal probabilities of voltage........................................................................... 62 
Table 4.22: MTTF of aging components and their reliabilities ............................................ 63 
Table 4.23: Evaluating the working probabilities of variables under various evidences ...... 64 
Table 4.24: Domain of variables ........................................................................................... 65 
Table 5.1: Observable nodes and their related gauges .......................................................... 69 
Table 6.1: SCP evaluation data at 0.5 threshold ................................................................... 79 
Table 6.2: FEM evaluation data at 0.5 threshold .................................................................. 80 
Table 6.3: FEL evaluation data at 0.5 threshold ................................................................... 81 
Table 6.4: MCP evaluation data at 0.5 threshold .................................................................. 82 
Table 6.5: SCP evaluation data at 0.75 threshold ................................................................. 83 
Table 6.6: FEM evaluation data at 0.75 threshold ................................................................ 84 
Table 6.7: FELevaluation data at 0.75 threshold .................................................................. 85 
Table 6.8: MCP evaluation data at 0.75 threshold ................................................................ 86 
Table 6.9: Summary of data evaluated by SCP, FEM and FEL at threshold of 0.5 and 
0.75 ........................................................................................................................................ 88 
Table 6.10: ANOVA test results for main replaceable components at threshold of 0.5 ....... 89 
Table 6.11: ANOVA test results for main replaceable components at threshold of 0.75 ..... 89 
Table 6.12: ANOVA test results gauges at threshold of 0.5. ................................................ 89 
 Table 6.13: ANOVA test results for gauges at threshold of 0.75 ......................................... 89 
Table 6.14: Summary of MCP data evaluation at threshold 0.5 and 0.75 ............................ 90 
Table 6.15: Predicted maintenance schedule using SCP,FEM and FEL aat threshold of 
0.5 .......................................................................................................................................... 91 
Table 6.16: Predicted maintenance schedule using SCP,FEM and FEL at threshold of 
0.75 ........................................................................................................................................ 92 
Table 6.14: Predicted maintenance schedule using MCP at threshold of 0.5 and 0.75 ........ 93  
 ABBREVIATIONS 
 
 
BN  : Bayesian Network  
HBN  : Hybrid Bayesian Network     
FT  : Fault Tree 
DD  : Decision Diagram 
DAG  : Direct Acyclic Graph   
DBN  : Dynamic Bayesian Network       
DFT  : Dynamic Fault Tree   
DDD  : Dynamic Decision Diagram    
GMM  : Gaussian Mixture Models     
TTF  : Time To Failure     
MDP  : Markov Decision Process 
FMEA  : Fault Mode and Effect Analysis   
MTTF  : Mean Time to Failure       
RCM  : Reliability Centered Maintenance    
TBN  : Temporal Bayesian Network       
CTBN  : Continuous Temporal Bayesian Network    
RBN  : Recursive Bayesian Network       
DDN  : Dynamic Decision Network 
HMM  : Hidden Markov Model   
MC  : Markov Chain       
DOOBN  : Dynamic Object Oriented Bayesian Network   
HDBN  : Hybrid Dynamic Bayesian Network     
PM  : Preventive Maintenance     
PT and I  : Predictive Maintenance and Inspection     
PGM  : Probabilistic Graphical Model 
HVAC  : Heating, Ventilation and Air Conditioning   
US  : United State     
NASA  : National Aeronautics and Space Administration    
 BDD  : Binary Decision Diagram      
DDD  : Data Decision Diagram     
ID  : Influence Diagram        
Dis  : Distributor 
SP  : Spark Plug   
BAT  : Battery       
R  : Radio    
ES  : Engine Start       
AE  : Age Exploration     
PG  : Pressure Gauge        
TempG  : Temperature Gauge 
Press  : Pressure       
Temp  : Temperature    
RPM  : Tachometer (Revolution per Minute)     
RPMM  : Tachometer reading    
RAMS  : Reliability, Availability, Maintainability and Supportability 
CBM  : Condition Based Maintenance 
RBM  : Risk Based Maintenance 
CNC  : Computerized Numerical Control 
RTF  : Run To Failure 
RCFA  : Root Cause Failure Analysis 
SCP  : Single Critical Process 
MCP  : Multiple Critical Process 
FEM  : Fault Effect Myopic 
FEL  : Fault Effect  Look-ahead 
İ  : Evidence 
Pr  : Pressure 
F  : Force 
A  : Area 
Lc  : Critical component threshold 
Lr  : Main component threshold 
 P  : Probability. 
Oit  : state of observable node i in time t. 
Git  : state of gauge component j in time t. 
St  : state of critical process in time t. 
Ckt  : state of main component k in time t. 
X'  : Average. 
ı  : Standard deviation. 
 
 1. INTRODUCTION 
In the past decades, as the complexity of systems gets more and more, the need of 
methodologies to control the complex systems became a main field of study for researches 
in order to let decision maker analyze the situations accurately, and manage them.  
Many methodologies have been applied and experienced for static systems. Such as 
Bayesian networks (BNs), fault tree (FT) and decision diagrams (DDs). Many of the 
mentioned methodologies rely on the combination between probability theory and graph 
representation theory. In these, generally directed acyclic graphs (DAGs) are used to 
represent the system by the use of nodes and arrows, where nodes represent the variables in 
the system, and arrows define the relation between the nodes via conditional and 
transitional probabilities. 
In real life, most of the systems are dynamic, so the mentioned methodologies have been 
extended to take time into consideration. The extended methodologies are: Dynamic 
Bayesian networks (DBNs), Dynamic decision networks (DDNs), Dynamic fault tree 
(DFT).  The main difference between static and dynamic systems is that in a dynamic 
system the concept of aging or degradation of components generally takes place. In other 
words, the states of the variables may change from one state to others according to 
probability distribution in time. A battery working state in a car or pressure gauge sensor 
working state in air conditioning systems can be given as examples of such systems. 
Maintenance is a very important aspect of controlling the system. It is one of the aspects 
that get a very high intention while systems become more complex. Many methodologies 
and strategies have been suggested and applied in many fields. The main maintenance 
activities are categorized in the way the action is taken. E.g. we have the reactive 
maintenance that is being applied only and only if a problem happens. Preventive 
maintenance is applied according to a schedule provided by the designer in order to make 
the component reach its designed life (planned maintenance). Predictive maintenance and 
inspections (PT and I) is applied where observations are collected and then analyzed to 
determine the states of the other variable. Proactive maintenance is a maintenance strategy 
2 
 
combines time based and condition based maintenance strategies together to minimize the 
probability of system breakdown. Reliability centered maintenance is applied by combining 
the above activities in order to maximize the reliability of the system, and minimizing the 
total down time by scheduling maintenance activities at earlier time.  
Energy conversion plants are the plants where electricity is produced by converting the 
energy from heat or potential energy into electricity. Energy conversion plants or electricity 
production plants are very complex systems involving many components interacting with 
each other, and affecting each other. In such plants, since satisfying the demand at the right 
time is critical, down time must be at minimum level. Or in other words, availability of the 
plants must be at maximum level. All types of maintenance activities (replace/ repair/ 
inspection) must be done together to achieve a minimum level of downtime of the plant. 
There are plenty of power generation plants. They can be classified according to the energy 
conversion principles used as follows: 
1- Thermal power plants or Fossil fuel power plants. (E.g. Steam power plants, 
gas turbines). 
2- Nuclear power plants. (Use nuclear energy generated in the reactor instead of 
fuel). 
3- Geothermal power plants. (Use geothermal energy instead of fuel). 
4- Hydraulic power plants. (E.g. Dams that use the potential energy of water). 
The main characteristics of each one of the mentioned four power plants are shown in 
Table 1.1. 
Thermal power plants are very old power generation plants. They first appeared in the 
industrial revolution in Europe at the late of 18th century. At that time, thermal power plants 
were using reciprocating engines. After a few years, turbines were invented, and they were 
considered as an alternative for the reciprocating engine, because of the following reasons: 
turbines provided higher speeds. They are compact machinery. They provided stable speed 
regulation allowing synchronizing between turbine operations and the operation of 
generators. 
3 
 
Thermal power plants are complex systems, with thousands of components and systems 
related to each other and affected by each other. Thermal power plants usually use reactive, 
preventive and inspection maintenance activities to control the processes and systems, and 
to determine the schedule of the maintenance of the plant. These schedules help to increase 
the availability of the plant. Normally the availability of the thermal power plants ranges 
from 70-90%. The reliability improvement mainly depends on the preventive maintenance 
by providing better designs. Most of the work done about thermal power plants uses 
preventive and reactive maintenance strategies. 
Table 1.1 Power plant types and their properties 
 Thermal 
Power Plant 
Hydraulic 
Power Plant  
Geothermal 
Power Plant 
Nuclear Power 
Plant 
Fuel Coal-Gas-
Diesel 
Flowing water Heat from Lava 
gaps 
Radioactive 
elements (U, 
Pa, etc.) 
Transportation 
of fuel 
Trucks(easy) Hydraulic 
Gates 
Heat transfer to 
water in the 
pipes 
Hard and need 
complex 
technology 
Location Could be 
placed any 
where 
On rivers/dams Next to the 
areas that 
contains Lava 
gaps 
Near water 
sources 
Environment Green house 
emission-global 
warming 
Disturbs fish 
habitant 
Green house 
emission-global 
warming (but 
less than 
thermal power 
plants) 
Nuclear waste 
Efficiency 30-55% 
(depends on the 
cycle) 
80-94 % ( 
turbine 
efficiency)  
20-40% ( 
depends on the 
temperature) 
33%  
Energy share  70% 7% - 19% 
 
Table 1.1, shows a comparison between different types of power plants using different 
factors which are fuel, transportation of the fuel, location, environment effect, efficiency 
and energy share. Data is collected from the US energy information administration data 
sheets for the energy shares and efficiency of nuclear power plant. The efficiency of the 
4 
 
turbine in hydraulic power plants is collected from (Saadat 2011). Lastly the efficiency of 
geothermal power plant is collected from REPP-CREST: geothermal resources. 
Thermal power plants are the most widely used in power generation. This can be referred to 
many reasons, such as: 
1- Relatively cheap fuel costs. 
2- High efficiency (36-40 % for thermal power plant and 30 % for nuclear). 
3- Less location constraints. 
4- Availability of fuel is higher than other plants. 
In this thesis, we study scheduling of maintenance activities of thermal power plants in a 
given planning horizon. A thermal power plant is a facility that produces electrical energy 
from thermal energy. Normally it is operating 24 hours a day. In order to deal with this 
situation, we have to use predictive and preventive maintenance methodologies to prevent 
failure and minimize the down time. We propose a proactive maintenance methodology 
under limited observations in time with a predefined threshold policy. We use dynamic 
Bayesian networks (DBNs) to infer the observations and to calculate the reliability of the 
components of the system, and compare it with a predefined threshold. 
 
1. STEPS OF THE THESIS 
The thesis has preceeded in the following steps: 
1- Problem selection and definition. Maintenance scheduling of thermal power 
plant is selected as the problem. 
2- Problem representation. The problem is represented using Bayesian networks 
and dynamic Bayesian networks. 
3- Data collection. Initial reliabilities of components are collected. 
4- Model development. Model is developed using Bayes Net Tool Box (Murphy 
2002), and relations between components are defined. 
5- Model verification: Model is verified using GENIE. 
5 
 
6- Development of solution methodologies. A proactive maintenance scheduling 
plans are developed. 
7- Computational study. Using the solutions proposed results are collected. 
8- Results and evaluation. The collected results are discussed and compared to 
other methodologies. 
1. OUTLINE OF THE THESIS 
In Chapter 2, literature review about the work done through maintenance, reliability, 
Bayesian networks, and dynamic Bayesian networks, and main aims and methodologies are 
mentioned. 
In Chapter 3, definitions of main concepts used in the thesis are provided. The main 
concepts are: Reliability, Maintenance, maintenance types, probabilistic graphical methods, 
conditional probability, joint and marginal probabilities, reasoning types, Bayes rule, 
Bayesian networks, dynamic Bayesian networks and dynamic decision networks. 
In Chapter 4, problem definition of the topic is provided. Definition of thermal power plant, 
its main components, and assumptions made, interrelation between components and full 
description of each are provided. 
In Chapter 5, the proposed methodology is presented.  This contains explanation of the 
method, steps used in the solution, algorithms used in the proposed methodology. 
In Chapter 6, experimental design and computational results of the proposed method are 
presented and comments on the method performance are provided. 
In chapter 7, gives the conclusions and future study directions of the thesis. 
6 
 
2. LITERATURE REVIEW 
The last decades witnessed a very wide interest in maintenance and troubleshooting of 
complex systems. Because the industry introduced a very complex systems with highly 
interacting components. Some aspects like reliability and availability are defined to 
measure the level of success of complex systems. Reliability means the probability of the 
desired system or component to work in their desired way. Availability is period of time in 
which the system is working in the desired way. 
This chapter covers review on the following subjects: Literature review over reliability and 
maintenance strategies, literature review over Bayesian networks (BNs), literature review 
over dynamic Bayesian networks (DBNs), and literature review over reliability and 
maintenance of thermal power plants. 
2.1 RELIABILITY AND MAINTENANCE 
Reliability and maintenance are two essential concepts for all types of industry. Many 
strategies and approaches are suggested. The following review mentions some of the work 
done over reliability and maintenance. 
 
Chockie and Bjorkelo (1992) examine four organizations to evaluate system and 
component aging degradation. Four key elements of an effective maintenance program 
identified as the selection of critical components in the system, development and 
understanding of system aging through analysis of performance, development of suitable 
preventive (time-based) and predictive (condition-based) maintenance tasks to manage 
aging, also the feedback mechanism for continuous improvements.  
 
Lapa et al. (2000) aim to improve availability of nuclear power plant using an optimization 
of preventive maintenance plan. The optimization uses genetic algorithm and probabilistic 
safety. Genetic model holds unconstraint optimization that permits the variation in 
maintenance plans. 
Koca and Bilgic (2004) propose a new approach to perform troubleshooting with dependent 
actions. By defining dependent sets. Performance of this approach heuristic is tested against 
7 
 
other approaches, and they show that optimal troubleshooting sequence can be achieved. 
The methodology is made up on a fact that "efficiency of action is its priority ", but the 
methodology only observes 'dependent sets' not the whole system.  
 
Jesus et al. (2009) propose a method for evaluating the reliability and availability for gas 
turbines in electrical power stations. The method seemed to be suitable for interrelated 
components in systems. Since the method based on reliability concepts, it permits the 
identification of critical components for maintenance and defines quantitavly the system 
reliability and availability. They propose to use reliability centered maintenance to improve 
the reliability of the system and decrease unexpected failures of critical components. 
Failure mode and effect analysis (FMEA), mean time to failure (MTTF) and functional tree 
are used and applied to two gas turbines of type F series. 
Gomes and Gudwin (no date) present aspects related to the elaborating and implementation 
of an intelligent system, that works on predictive maintenance system (condition based 
maintenance) of hydro-electric power plant. The presented system (SIMPREAL) based on 
reliability centered maintenance (RCM). System contains two parts: First is the server part 
where the server collects data from sensors. Second is the client where java applet runs, and 
it is responsible for the presentation of a synoptic of the system to the user. 
Gupta (2011) develops a simulation model for evaluating the performance of a standard 
feed water system of thermal power plant using birth/death markov processes, and 
probabilistic approach. Model is built by drawing the transition diagram that is translated 
into differential equations. These differential equations can be solved recursively using 
probabilistic approach, to predict the steady state availability. Then build the simulation 
model. Availability matrix is made up after the simulation model is built up, and then plots 
of failure/repair rates are plotted of all subsystems. 
Özgür-hQODNÕQ and Bilgiç (2012) propose a methodology for reliability centered 
maintenance scheduling. They aim to minimize number of replacements by maintaining the 
system reliability over a predetermined value. The problem is represented with DBNs. Four 
approaches are used for selecting the components to replace. The approaches are: Fault 
8 
 
effect myopic approach, fault effect look-ahead approach, replacements effect myopic 
approach and replacement effect look-ahead approach. 
 
2.2 BAYESIAN NETWORKS  
Many methods are developed to measure the reliability of a system such as Fault tree (FT), 
Bayesian Networks (BNs), where BNs, gain the interest because of its ability to represent 
complex systems in a compact and easy way. Variables are represented with nodes, and the 
interrelation between the variables is represented with an arc between them. BNs are 
combinations between graph and probability theory. The arcs between the variables carry 
the conditional probability between the connected variables. Here is a review of some 
works done over BNs: 
Heckerman et al. (1995) introduce a new approach to decision theoretical troubleshooting 
approach. Aim to determine troubleshooting plans under uncertainty that provides 
observations and repairing actions. The approach is tested in printing machines, automobile 
startup problems, photocopier feeder system and gas turbines. Results obtained show that 
the generated plans are close to the optimal ones. Monte Carlo technique is used to estimate 
troubleshooting costs, and interrelations between system components represented by BNs. 
Richiardi et al. (2005) use BNs to estimate the probability for verification errors (fails). 
Given the Gaussian mixture models (GMM) based speaker verification system output and 
additional information about acoustic noise, then reliability of the system can be evaluated.  
Bai (2005) develops an extended Markov Bayesian networks model, and propose an 
algorithm for solving complex software systems. The development process focuses on 
discrete time failure data. The model is developed in order to deal with the fact that many 
of the software systems often depend on specific operation applied.  Operational profile is 
defined as: "The profile that consists of all operations in the system, that the system is 
designed to perform and their probability of occurrence. It provides quantities 
characterization of how the system will operate in the field". 
9 
 
Kryszczuk et al. (2005) use Bayesian network to represent the decision and information in 
multimodal biometric system. Bayesian network is used to present a framework to predict 
and correct decision errors. Prediction and correction of decision errors are based on 
modality reliability measures. 
Boudali and Dugan (2006) aim to find alternative formalism for modeling and analyzing 
large dynamic systems, and to identify the problems and issues related to the available 
techniques (Dynamic Fault Tree (DFT), Bayesian Networks (BNs), Temporal Bayesian 
networks (TBN)). The proposed method is continuous time Bayesian networks (CTBN). 
The techniques are compared according to their: 
1. Modeling Power.  
2. Ease of determining the model. 
3. Computational Efficiency. 
Marquez et al. (2007) aim to solve any configuration of static and dynamic gates. Propose a 
methodology using general parametric or empirical time to failure (TTF) distributions. The 
method proposes a hybrid Bayesian network (HBN) model to solve the configuration 
between the gates without using numerical integration or simulation methods. 
Casini et al. (2011) introduce recursive Bayesian networks (RBNs), and apply it to 
mechanisms. RBN formalism maintains and provides an integrated modeling formalization 
for predicting explanations and control. The formalization can be applied to model cancer 
mechanisms where hierarchy is ubiquitous and vast amount of data is available. 
Murphy (2001) defines BNT (Bayes net tool box) as a designed open source package. BNT 
works in Matlab environment. It is used to deal with BNs and DBNs. BNT supports many 
probability distribution functions. It also supports both exact and approximate inferences.  
2.3 DYNAMIC BAYESIAN NETWROKS  
In real life, not all of the systems are static. Or in general we are also interested in not only 
on the current state of the system, but also in the future state of the system. Using age 
exploration and prognosis inspect and prediction principles, we deal with the dynamic 
10 
 
systems. Many methodologies are proposed, such as: Dynamic Fault Tree (DFT), dynamic 
decision networks (DDNs), hidden Markov Models (HMMs), and Dynamic Bayesian 
networks (DBNs) where Bayesian networks (BNs) are extended to a dynamic system by 
taking time into consideration using transition probabilities, that define the future reliability 
of the system or components. 
Kuenzer et al. (2001) evaluate 6 models to understand which one has the best fit for 
modeling the predictions of rule based interaction behavior for real domain. These models 
are: Hidden Markov Models, auto regressive hidden Markov model, factorial hidden 
Markov model, simple hierarchical hidden Markov model, Markov chain of order and tree 
structure hidden Markov model.  
Weber and Jouffe (2003) propose a method based on dynamic Bayesian networks (DBNs), 
that easily allows construction of dynamic Bayesian networks (DBNs) structure. For 
modeling the temporal evolution of complex systems, correspondence between Markov 
chain (MC), Fault tree (FT), and Dynamic Bayesian networks (DBNs), are presented and 
applied in order to estimate system reliability. 
Weber et al. (2004) use DBNs to model the dependability in complex systems with 
degradations and failure modes, countered by exogenous constraints. They propose a 
method allows modeling DBNs structures to be used in modeling temporal evolution of 
complex systems. 
Montami et al. (2005) propose to describe dynamic gates within the Dynamic Bayesian 
network (DBN), by translating all the basic dynamic gates into corresponding DBN model. 
The approach is tested on a complex example taken from the literature. the experimental 
results show how DBN can be safely used if a quantitative analysis of the system is 
required. the aproach is able to improve both the modeling and the analysis capabilities of 
classical fault tree FT approaches, by representing more general simplified dependencies 
and by performing general inference on the resulting dynamic model.  
BenSalem et al. (2006) represent a method for modeling and analyzing the reliability of 
interrelated components in a system, based on DBNs. The influence of time or exogenous 
11 
 
variables can be considered on the failure (degradation) of the system. The method allows 
designing DBN structure for modeling temporal evolution of complex system. The 
correspondence between Markov chains (MC) and DBNs is represented and applied to the 
system reliability. 
Weber and Jouffe (2006) present a methodology that can be used to develop dynamic 
Object Oriented Bayesian Networks (DOOBNs). The methodology aims to get a general 
reliability evaluation in manufacturing systems. The presented method allows easily built 
up DOOBNs structures, to model temporal behaviors of probabilities of complex system 
states. 
Özgür-hQODNÕQ and Bilgiç (2006) try to optimize maintenance activity of a system where 
components age with constant failure rate together with a budget constraint, and try to 
optimize it by developing a predictive maintenance plan using DBNs. They first represent 
the as an optimization problem where mathematical model is used. Because of the 
complexity of the solution, representation they propose DBN for fast inference under some 
simplifying assumptions. The objective is to minimize total maintenance cost in a planning 
horizon such that the reliability of the system never goes down a predetermined threshold 
value, and maintenance budget is never exceeded. For replacement decision making they 
propose two approaches: myopic and look ahead. 
Neil et al. (2009) describe the use of hybrid dynamic Bayesian networks (HDBNs) in order 
to model risk of operations in the financial institutions in terms of economic capital. 
Methodology models the losses resulting from international events or sudden accidental 
events, and characterizes them by their ability to evade controls and which ultimately lead 
to increasingly severe financial consequences. Their Model focuses on cause and effect of 
losses of events using DBNs. It is argued that BNs are natural choice and powerful tool for 
modeling operational problems. They present generalized approach using HDBNs that 
successfully represent and model dependencies. 
Özgür-hQODNÕQ and Bilgiç (2010) study dynamic systems having several components, 
where components can be partially observed via indirect signals. They model the problem 
as POMDP. The POMDP problem is aggregated in terms of states and actions so it can be 
12 
 
optimally solved. The policy of the aggregated POMDP is disaggregated by simulating 
with DBNs. 
Varuttamaseni et al. (2011) proposes dynamic Bayesian networks as an alternative of 
Markov chain. conditional dependencies in DBN simplifies the factorization function of 
joint probability. they analyze feed and bleed in nuclear power systems using DBN. the 
analysis leads to understand and evaluate the risks and their effects over nuclear power 
system. 
 
2.4 RELIABILITY AND MAINTAINABILITY OF THERMAL POWER PLANTS 
Because of the importance role that thermal power plant plays in the daily life of people, 
many works are done. Many approaches and strategies proposed. In this review, some of 
these works are mentioned. 
Sergaki and Kalaitzakis (2002) propose a data base model that ensures the representation of 
the fuzzy information, and also ensures the handling of this information. The model 
provides additionally the functionality that allows the user to set the accuracy degree for 
conditions involved in the operation (situation), and then prepare the maintenance plan of 
the system. This model is applied to a case study to a power plant  
Krishnasamy et al. (2005) propose a risk based maintenance (RBM) strategy to analyze and 
determine maintenance plan. In the strategy, four principles are used. The principles are: 
1- Scope identification (dividing the big system to smaller systems and 
subsystems, then analyzing each system and subsystem alone, while collecting data 
from each and define potential failure scenarios).  
2- Risk assessment (defines the results of each possible failure mode). 
3- Risk evaluation (used to decide about the risk if it is in the acceptable range or 
not). 
4- Maintenance plan (if the risk evaluation decided on is not to accept the risk then 
maintenance plan is scheduled). 
13 
 
The methodology applied successfully to Holy rood thermal power plant. 
Eti et al. (2007) try to integrate reliability, availability, maintainability and supportability 
(RAMS), with risk analysis, in order to increase the plant availability. And improve the 
reliability of the plant. They determine the maintenance schedule using preventive 
maintenance and inspection. Risk analysis is used to decide about the action needed. If the 
risk is not acceptable, maintenance activities are scheduled. 
Ibargüengoytia and Flores (2009) propose three methods using intelligent probabilistic 
methods to help operators of thermal over plants. Because thermal power plant system is a 
large, complex and influenced by unexpected events, together with uncertainty. They 
present planning and decision support system, and diagnosis. The diagnosis based on 
qualitative probabilistic methods. Decision support system uses influence diagrams to show 
the relations between components. The three methods are: 
1- Probabilistic model over qualitative changes of variable applications, which 
shows how probabilistic diagnosis can be carried out utilizing common expert 
criteria. 
2- Utilizes influence diagrams that uses probabilistic reasoning and decision 
theory technique. 
3- Planning a system uses formalism of Markov decision processes (MDPs), 
which provides a powerful frame work for solving sequential decision problems 
under uncertainty. 
Rusin and Wajacazek (2012) propose mathematical model of selection the time between 
maintenance activities that considers economic effects and risk levels regarded to operation 
of components. Model used to estimate time between over-hauls of steam turbines, that is 
been identified as one of the main component in the power system. The evaluation of the 
model is done under four scenarios consideration.  
 
14 
 
3. BACKGROUND 
In this chapter, definitions and explanation of the principles used in this thesis are given. 
Like Bayesian networks (BNs), dynamic Bayesian networks (DBNs), maintenance, 
reliability, Bayes theory, reliability centered maintenance (RCM), reactive maintenance, 
preventive maintenance (PM), and predictive maintenance and inspection (PT and I), 
proactive maintenance, and also it contains dynamic decision networks, probabilistic 
graphical methods (PGM). 
 
3.1 RELIABILITY AND MAINTENANCE 
Reliability and maintenance are very important concepts for system availability and to 
maintain the system in its working state. In the following section, definitions and related 
characteristics related to reliability and maintenance are given. 
3.1.1 Reliability 
There are many definitions of reliability in the literature, which are nearly similar. We will 
provide the basic ones; Reliability is the ability that a device will perform its required 
operations successfully and in the intended way without failure (Ushakov 2012). 
Reliability engineering provides the theoretical and practical tools required to determine the 
probability and capability of systems/components, to perform their intended jobs in the 
intended way, for a specified period of time, in a specified work environment without 
failure. Then the reliability of the systems/components can be specified and predicted 
(0LOXWLQRYLü and /XþDQLQ 2005). 
Reliability is an inherent feature of the design, which is concerned about the performance 
of the system or components in the fields. In the last years, many methodologies and 
suggestions based on reliability principle have been developed. The importance of 
reliability can be expressed as follows: whenever the system reliability in the acceptable 
ranges, that means no problem. But when it falls under the acceptable range, it requires a 
15 
 
corrective action. Since reliability can be predicted; it became a key factor in dynamic 
system states predictions. 
3.1.2 Maintenance 
Maintenance is the total of activities required to retain the system or restore it to the state 
necessary to fulfillment of the production function (C.W.Gits 1992).  
Maintenance and its principles have been a challenge in the field since the industrial 
revolution. It is applied impressively in the field, but it is still a big challenge due to lots of 
reasons and factors such as: size, cost, complexity (Dhillon 2002). 
Maintenance strategies change along with the underlying philosophies used. For example, 
the time of acting is an important factor. Shall we act after the problem occurs or before? 
The following strategies are applied in the field: 
1- Reactive maintenance(Run to failure RTF) 
2- Preventive maintenance (PM) or Time based maintenance. 
3- Predictive maintenance and Inspection (PT and I) or Condition based 
maintenance (CBM). 
4- Proactive maintenance or Root causes elimination maintenance. 
5- Reliability Centered Maintenance (RCM). 
 
Engineering maintenance is the activity of system or component maintenance that develops 
principles, concepts and technical data in conceptual way. Then these data and concepts can 
be used and maintained in the current operating state, to ensure the best effective 
maintenance support. Engineering maintenance uses a maintenance plan. This is a 
statement that contrasts management and technical procedure to be applied to maintain the 
system or component. Then maintainability aspect is defined as the probability that a failed 
item will be restored to the proper working conditions. Taxonomy of maintenance 
strategies is shown in Figure 3.1. 
In the following sections, detailed definitions are provided for each of the strategies 
mentioned above. 
16 
 
Figure 3.1: Taxonomy of maintenance strategies 
Source: Taxonomy of maintenance concepts (redrawn after Kothamasu et al. (2006)). 
 
3.1.2.1 Reactive Maintenance 
Reactive maintenance is run to failure maintenance (RTF). It is the traditional maintenance 
type which means we take no action until a problem takes place in the system. No action is 
been taken to maintain the system unless a failure is occurred. In some literature it is called 
corrective maintenance. It is used to correct system or component that does not perform in 
its desired way. 
 
 
Maintenance 
strategies 
Proactive 
Planned 
Predictive 
RCM 
Condition 
Based 
Preventive 
Constant 
Interval 
Age Based 
Imperfect 
Reactive/cor
rective 
unplanned 
Corrective 
Emergency 
17 
 
There are many types of reactive maintenance as shown in Figure 3.2, they are categorized 
as: 
a) Fault-Repair: in this category, systems/ components are restored to its 
operational state after the failure occurred. 
b) Salvage: Disposal and use of salvage material from non-repairable 
component/system. 
c) Rebuild: restores the component/system to as close as possible to its original 
state. 
d) Overhaul: uses 'inspect and repair only as appropriate', restores the 
component/system to its total serviceable state. 
e) Servicing: by providing services to components/systems after repairs such as 
welding or recharging. 
Figure 3.2: Categories of reactive maintenance 
 
 
 
 
 
 
 
 
 
 
 
Source: Categories of Reactive Maintenance. (Dhillon 2002) 
In order to apply the reactive maintenance strategy, the following steps are used: 
1- Fault recognition. 
2- Localization of the failure. 
3- Diagnosis and evaluating the failure. 
categories of 
reactive 
maintenance 
Fault-
Repair 
Overhaul 
Rebuild Salvage 
Servicing 
18 
 
4- Repair and take the required actions. 
5- Check out. 
 
This strategy has few advantages, which are as follows: 
a) Low Cost for maintenance actions. 
b) Minimum experienced staff. 
c) Also some disadvantages are related to this maintenance strategy: 
d) Increase cost due to unplanned downtime. 
e) Increased labor cost (over time when downtime occurs). 
f) Cost involved with repair or replacement. 
g) Possible secondary system or process damage from system failure. 
h) Insufficient use of staff resources. 
Reactive maintenance has the ability to be applied everywhere in every industry. Or in 
other words it can be applied whenever an unplanned downtime occurs in any system. 
3.1.2.2 Preventive Maintenance  
Preventive maintenance (PM) or Time-Based maintenance is a prescheduled maintenance; 
used to maintain the system in its working state, and helps the system reaches its designed 
life. Or in other words, it is the actions performed on a system based on a schedule that 
detect component aging (degradation) of a component or system with the aim of 
maintaining or extending the useful time of the system through controlling component 
aging (degradation) to an acceptable level. 
The Objectives of PM are concentrated on enhancing component productive life. And it 
allows reducing critical components breakdown. Also it allows Planning better 
maintenance schedules and plans that reduce the downtime. And it allows Minimizing 
production loses due to component failures (less down time means more production). 
PM strategy consists of seven elements that are integrated with each other to develop the 
maintenance plan as shown in Figure 3.3. These elements are: 
19 
 
a) Inspection: periodic observation to check and compare serviceability to its 
standard. 
b) Servicing: by the mean of providing services to the component/system, such as: 
OXEULFDWLRQ FOHDQLQJ«HWF. WKDW ZLOO KHOS WR SUHYHQW IDLOXUH RFFXUUHQFHV. 
c) Calibration: comparing component/system characteristics to its standards. 
d) Testing: periodic tests that are used to determine the degradation of 
component/system. 
e) Alignment: changes done to the component/system in order to optimize 
performance. 
f) Adjustment: adjusting component/system in order to optimize performance. 
g) Installation: replacements of the limited life components. 
Figure 3.3: Elements of preventive maintenance 
Source: Elements of PM. (Dhillon 2002) 
To apply PM strategy, the following steps must be followed: 
1- Identifying and choosing the areas: identify and choose the areas where PM is 
going to be applied. 
2- Identifying PM needs and requirements. 
3- Setup the frequency of the assignment. 
4- Prepare PM assignment. 
Elements 
of PM 
Servicing 
Installation 
Test 
Calibration Alignment 
Adjustment 
Inspection 
20 
 
5- Schedule PM on annual basis. 
6- Expand PM program as necessary. 
Preventive maintenance has many advantages, these advantages makes this strategy an 
important strategy in maintenance. These advantages are as follows: 
i. Cost effective. 
ii. Component/system performs at convenient environment. 
iii. Balanced work load. 
iv. Increase in production revenue. 
v. Flexibility allows for the adjustments of maintenance schedule. 
vi. Consistency in quality. 
vii. Increased component life time. 
viii. Energy saving. 
ix. Reduced system failure or downtime. 
x. Estimates that it has sufficient cost saving over reactive maintenance. 
The disadvantages of the preventive maintenance are: 
i. Failures still likely to occur. 
ii. Labor intensive. 
iii. Includes performance of unneeded maintenance. 
iv. Potential for incidental damage to components in conducting unneeded 
maintenance. 
Preventive maintenance is applied in many industry areas such as: 
i. US Marine. 
ii. Cars and automobile. 
iii. Lubricated systems. 
iv. Calibrated systems. 
v. Everywhere when failure pattern is known. 
vi. Battery inspections. 
21 
 
3.1.2.3 Predictive Maintenance and Inspection  
Predictive maintenance and Inspection (PT&I) or Condition-Based maintenance is the 
maintenance actions taken by applying inspection and diagnosis to the system and 
analyzing the system condition to decide on the actions needed. The diagnosis process is 
done by collecting measurements that detects system degradation (lower functional state). 
PT&I allow the elimination of failure due to aging, and allowing the system to be 
controlled prior significant deterioration in the component state. Results indicate current 
and future functional capabilities.  
The advantages of the predictive maintenance and Inspection are as follows: 
i. Increases components availability. 
ii. Increases components life. 
iii. Allows for preemptive corrective. 
iv. Decreases in system failure. 
v. Decrease in the cost of labor and components. 
vi. Better final product quality.  
vii. Improve the safety of workers and environment. 
viii. Improve workers morale. 
ix. Energy saving. 
x. Sufficient cost saving to preventive maintenance. 
 
The disadvantages of the predictive maintenance and Inspection are: 
i. Increase investment in diagnosis (observations) components. 
ii. Increase investment in staff training. 
iii. Saving potential not readily seen by the management. 
iv. Increase the need of expertise stuff. 
 
22 
 
Predictive maintenance and Inspection has been applied in different areas, where complex 
systems appear, such as: 
1. US navy. 
2. NASA technologies. 
3. Electrical Surveys. 
4. Mechanical Surveys. 
5. HVAC systems. 
6. Building Surveys. 
7. Energy industry. 
3.1.2.4 Proactive Maintenance (Root Cause Maintenance) 
Proactive Maintenance or root cause maintenance improves maintenance through better 
design installation, maintenance activities, workmanship and scheduling. It combines 
predictive maintenance and inspection with preventive maintenance. 
Proactive maintenance improves maintenance tasks by providing a better design, and 
improving workmanship, also by improving the installation procedure, and by providing a 
maintenance schedule, and by improving the maintenance procedure. 
There are many methods that proactive maintenance relies on in order to extend the life of 
components/systems as shown in Figure 3.4. These concepts are: 
a) Reliability engineering: contains redesign, modification and improvement of 
components/systems, and improvement of the repairs. 
b) Failed item analysis: inspecting and testing the failed component/system in 
order to define the causes of the failure. 
c) Root cause failure analysis (RCFA): determining basic (root) cause of the 
failure of the component/system. 
d) Specifications for new/rebuild component/system: recording the historical data 
involved in the functioning of the components/systems. 
e) Age exploration (AE): tries to determine degradation of components/systems 
using three factors: Technical content, Performance interval and Task categorizing.  
23 
 
f) Rebuild certification/authentication: to verify that all installation works 
properly. 
g) Recurrence control: it is related to the repetitive failures. 
h) Precision Rebuild and installation. By improving the design to improve the 
system. Also by improving the installation procedure. 
 
Figure 3.4: Proactive maintenance methods used to extend the life of components 
Source: Elements of Proactive maintenance (Dhillon 2002). 
 
Advantages of proactive maintenance are: 
i. Better component/system design by the use of root cause data. 
ii. High availability. 
iii. High reliability. 
iv. Data base generated from feedback. 
v. Optimized maintenance plan. 
vi. Continuous improvements. 
Proactive maintenance 
methods  
Age 
Exploration 
Root 
Cause 
Failure 
Analysis 
Specification 
of new/rebuilt 
component 
Rebuild 
Certification/ 
authentication 
Reliability 
engineering 
Reccurence 
control 
Precision 
rebuild and 
installation 
Failed Item 
analysis 
24 
 
vii. Long component/system life. 
Disadvantages of proactive maintenance are: 
i. Cost savings are not clearly seen by the management. 
ii. High demand of trained personnel. 
iii. Establishing cost. 
Proactive maintenance is applied in many areas such as: 
a) Controlling Lubricant fluids. 
b) Controlling Hydraulic fluids. 
c) Controlling Coolants. 
d) Controlling Air. 
e) Controlling Fuel. 
f) HVAC systems. 
3.1.2.5 Reliability Centered Maintenance  
Reliability centered maintenance (RCM), integrates Preventive Maintenance, Predictive 
Testing and Inspection, Reactive Maintenance, and Proactive Maintenance to increase the 
probability that a machine or component will function in the required manner over its 
design life-cycle, with a minimum amount of maintenance and downtime. It is defined as 
the process used to determine the maintenance requirements of any physical states of the 
system variables to operate in its desired way, by integrating PT&I actions with PM 
actions. It focuses PM activities on the most likely failure modes. 
Goals and objectives of RCM are as follows: 
1- To setup system with associated priorities, that can help PM to order the 
focusing action. 
2- To collect feedback that will be used in future improvement of the system. 
3- To setup PM tasks in a way that they can bring the system components to their 
working states when deterioration detected. 
4- The last goal is to achieve all goals at minimum cost. 
 
25 
 
RCM is a combination of many principles that are integrated with each other. RCM is 
driven by safety and economics. RCM is a function based strategy that focuses on the 
improvements of system functions. Design limitations are covered by RCM. RCM is a live 
system where the age of the system is an important factor. Unsatisfactory condition is 
defined as failure in RCM. RCM contains three maintenance strategies (failure finding, 
time based maintenance, condition based maintenance). These tasks must be effectively 
applied and must be applicable. 
 
Steps of applying RCM: 
1- Identify the important components with respect to maintenance. 
2- Collect accurate failure data. 
3- Setup Fault Tree analysis data. 
4- Use decision methods to decide about critical failure modes. 
5- Classify maintenance demands and requirements. 
6- Apply RCM decisions. 
7- Collect feedback and apply sustaining engineering to the system. 
RCM is made up from four components as shown in Figure 3.5. These components are 
Reactive Maintenance (corrective maintenance) that is applied whenever a failure takes 
place in the system. Preventive maintenance (time based maintenance) that is applied 
according to a predefined schedule. Predictive Testing and Inspection (Condition based), 
that is applied by inspecting the system components and collecting observations to decide 
about the conditions of the system. Proactive maintenance is applied through providing 
better designs and installations; using failure and root cause data. 
 
 
 
 
 
 
 
 
 
 
 
26 
 
Figure 3.5: Components of RCM 
 
Source: (Dhillon 2002) 
Advantages of Reliability centered maintenance are: 
i. The most efficient maintenance program. 
ii. Lower costs by eliminating unnecessary maintenance or overhauls. 
iii. Minimizes frequency of overhauls. 
iv. Reduces probability of sudden system failure. 
v. Able to focus maintenance activities on critical components. 
vi. Increases component/system reliability. 
vii. Incorporate root cause analysis. 
viii. Improve safety. 
ix. Improve production quality. 
x. Extend life of costly components/systems. 
xi. Increases component/system availability. 
xii. Generates database from feedback collection. 
 
Disadvantages of the reliability centered maintenance are: 
i. Can have a significant startup cost. 
ii. Trained stuff is needed. 
iii. Savings potential not readily seen by management. 
RCM 
components 
Preventive 
maintenance 
Proactive 
Maintenance 
Predictive technology 
and inspection 
Reactive 
maintenance 
27 
 
Reliability centered maintenance, has been applied to many industrial areas like: 
a) Aviation Industry. 
b) Spacecraft Industry. 
c) Nuclear Industry. 
d) US Military. 
e) Medical services. 
Application fields of the mentioned maintenance strategies are summarized in Table 3.1. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
28 
 
Table 3.1: Applications of maintenance strategies: 
Strategy Applications 
Reactive maintenance  Industry. 
 Factories. 
 Everywhere where unplanned failure takes place. 
Preventive maintenance  US Marine. 
 Cars and automobile. 
 Lubricated systems. 
 Calibrated systems. 
 Everywhere when failure pattern is known. 
 Battery inspections. 
Predictive maintenance  US Marine. 
 NASA technologies. 
 Electrical Surveys. 
 Mechanical Surveys. 
 HVAC systems. 
 Building Surveys. 
 Energy industry. 
Proactive maintenance  Controlling Lubricant fluids. 
 Controlling Hydraulic fluids. 
 Controlling Coolants. 
 Controlling Air. 
 Controlling Fuel. 
 HVAC systems. 
Reliability Centered 
Maintenance 
 Aviation Industry. 
 Spacecraft Industry. 
 Nuclear Industry. 
 US Military. 
 Medical services. 
29 
 
3.1.2.6 Diagnosis and Prognosis 
This principle comes from the health monitoring activities. The main difference between 
the two concepts is the aimed time. In diagnosis mainly it aims to define the states at the 
moment, while prognosis tries to identify the states in future. Table 3.2 states the 
differences between diagnosis and prognosis. 
Diagnosis; is the process of monitoring the system, collecting observation, and determining 
the current states of the related variables, using the available observations. It is an important 
action that can help to detect the fault once it happens. Then it takes the required actions to 
prevent or decrease the down time, and keep the system reliability on the acceptable range. 
It is used within the static systems. When an event happens, causes of it are searched. 
Prognosis; is the process of estimating and predicting the future states of the variables in 
the future time slices depending on the transition probability that describes aging 
(degradation) of the variables (components) in the system. It is an important action that 
helps to predict the maintenance schedule which will minimize the downtime, and also 
helps to maintain the reliability of the system. It is used within the dynamic systems such 
that we predict the future states according to the present ones. 
Table 3.2: Differences between Diagnosis and Prognosis 
 Diagnosis Prognosis 
Time Current. Future. 
Method Uses observation to determine the 
current states of the variables. 
Uses aging of the variable to estimate 
the future states of the variables. 
Use Within static system (at same time 
slice). 
With dynamic systems (different time 
slices). 
30 
 
3.2 PROBABILISTIC GRAPHICAL MODELS  
Probabilistic Graphical Models (PGMs) is a combination between graph and probability 
theory. It is a graphical representation of nodes and arrows. Nodes represent the variables. 
Arrows (links) represent the relationship between the linked nodes and they carry they 
information. It is a representation of the joint probability of many variables via the use of 
conditional probability (Figure 3.6). Probabilistic Graphical Methods are compact and user 
friendly tools to represent complex systems and do a complex decision making. 
Figure 3.6: Probabilistic Graphical representations 
Source: (Koller and Freidman) 
Probabilistic Graphical Methods (PGMs) gain importance in engineering because it 
combines the graph and probability theory. Graph theory is used for representation, while 
probability theory is use for decision making. 
Murphy (2002) classifies PGMs as: 
 Directed graphs: contains directions (arrows). 
Bayesian Networks (BNs): are directed graphs which express the casual relation 
between variables. They are popular in statistics. 
 Undirected graphs: contains only links with no directions. 
Markov random filed: is an undirected graph which is used to express soft constraints 
between the variables in the system. They are popular in physics and vision. 
 
31 
 
3.2.1 Basic Terminologies 
PGMs benefits from various terminologies in probability theory such as conditional 
probability, and independencies and Bayes theorem. In this section, description of basic 
terminologies is given. 
3.2.1.1 Conditional Probability 
Conditional probability in brief, is the probability of event A to occur relative to event is, 
mathematically: 
      =  
      
    
  3 %( •    (3.1) 
Conditional probability helps us by giving us a way to decide about the results of an 
experiments based on some partial information (evidence). Especially in sequential 
experiments when the probability of an event depends on another. 
3.2.1.2 Joint probability 
Joint probability is the probability that two events A and B happen at the same time 
(simultaneously).  
Suppose X and Y are the WZR UDQGRP YDULDEOHV RQ WKH VDPSOH VSDFH Ÿ RI DQ H[SHULPHQW 
then the joint probability of X and Y is: 
                  , joint probability is also expressed as        
or       . 
Joint probability is used to find out how likely that two or more event will happen at the 
same time. 
 
 
32 
 
3.2.1.3 Marginal probability 
Marginal probability is the probability of occurrence of a single event. 
Marginal probability calculated as: 
      ∑         For each possible value of x         (3.2) 
      ∑         For each possible value of y         (3.3) 
3.2.1.4 Independent Events 
Two events are independent if occurrence probability of one event GRHVQ¶W UHODWH WR the 
other event. 
An event is said to be independent if and only if  
   |                                                                                                           (3.4) 
   |                                                                                                           (3.5) 
3..5 Transition Probability 
Transition Probability is the probability of change in variable from one state to another 
when time changes from a time slice to the future time slice. It is used in the dynamical 
graphical systems, such as dynamic Bayesian networks and dynamic decision networks. 
For random variable Xn where n denotes the time slice, transition probability can be 
expressed as: 
                                                                                                    (3.9) 
For different possible state values i and j that Xn can take. 
Transition probability is a main concept in dynamic system since it explains the relation 
between the variable and itself in the next time slices. 
33 
 
Figure 3.7: Transition probability 
 
 
 
 
 
 
Table 3.4, Transition Probability Table 
 X1-Fail X1-Work 
X2-Fail 1 0.3 
X2-Work 0 0.7 
 
For a dynamic system given in Figure 3.7, transition probabilities are given in Table 3.4. In 
Figure 3.7, X1 is the variable X at time slice 1, while X2 is the same variable X at time slice 
2, the link between X1 & X2 is the information link that carries the transitional probabilities 
between X1 and X2. And from table 3.4 , it says that if X1 state is Fail, that means it will be 
fail for X2 with probability of 1, and if the state of X1 is work, then the probability that X2 
will work is 0.7. 
3.2.1.6 Bayes Rule 
Bayes rule aims to make a mathematical method that can be used to update the existing 
expectation using the new (updated) evidence. 
Bayes rule is mainly used for inference by using the conjunction of total probability method 
and the reverse conditional relation between events. 
Let                be disjoint events that form a partition in sample space Ÿ. $lso 
assume that          , then for any event B that         we get: 
X1
1 
R1 
X2 
R2 
t=1 t=2 
34 
 
    |     
            
    
                                                                        (3.10) 
    |   
            
        |            |              |   
                   (3.11) 
Where the first equality comes from the conditional probability and the second equality 
comes from the total probability theory. 
In experiments, we are interested in some number of causes that result in an effect, that we 
observe the effect and use it to infer to the cause. 
Let event's               denote the causes and event B denote the effect. Then the 
probability         is the conditional probability that the effect B will be observed given 
the cause   . Given that the effect B has been observed, then we can use this information as 
evidence to calculate (infer) the probability of the cause          . Here the probability 
         called a posterior probability and the probability       called a prior probability. 
3.2.2 Decision Diagrams  
Decision diagrams (DDs) is a generalized form of the decision tree. It is a directed acyclic 
graph (DAG) that represents the data structure (state spaces) of the complex systems, it 
contains two node types. These are: Chance nodes describe "AND". Choice nodes describe 
"OR". 
 And each graph has only one root. 
Two main types of these graphs are: Binary Decision Diagrams (BDDs) and Data Decision 
Diagrams (DDDs). 
 
 
 
35 
 
3.2.2.1 Influence Diagrams  
Influence Diagrams (IDs) are decision diagrams. In influence diagrams three types of nodes 
are used and two types of arrows are combined. 
Node types: 
1- 'HFLVLRQ QRGH UHSUHVHQWHG E\ D VTXDUH Ŷ. 
2- &KDQFH HYHQW UHSUHVHQWHG E\ D FLUFOH ż. 
3- Value node represented by a rounded rectangle. 
Arrows Types: 
1- Solid Arrow: if it points to a value or chance node. 
2- Dashed Arrow: if it points to a decision node. 
A typical ID is given in Figure 3.8. The node at the beginning of the arrow is called a 
predecessor. The node at the end of the arrow is called a successor. In IDs, No cycling is 
allowed since they are directed acyclic graphs (DAGs). And IDs are not flow charts. 
 
Figure 3.8: Influence Diagram 
 
 
 
 
 
 
 
 
 
Decision 
Node 
Chance 
Node 
Value Node 
36 
 
3.2.2.2 Dynamic Decision Networks  
A dynamic decision networks (DDNs) is an extension of the decision networks that 
represent how the system changes over time and models general sequential decision 
making. 
Dynamic sequencing of the decision is represented by the links; the single chance node X is 
the process node and determines the utility. The node O is the observation node that the 
evidence will be added to before each subsequent decision, the sequencing is represented 
by the information link. The networks are used to maximize the utility U, in the end of the 
time steps. A DDN example is given in Figure 3.9 where D is the decision node at each 
decision epoch. 
Figure 3.9: Dynamic decision networks 
 
 
 
 
 
Source: (Korb & Nicholson, 2004) 
3.2.3 Bayesian Networks 
Bayesian Networks BNs and dynamic Bayesian networks are very helpful to represent the 
dependencies between system components. In the following sections; definitions and 
characteristics of BNs and DBNs and how to infer in DBN are given.  
3.2.3.1 Static Bayesian Networks 
Bayesian networks (BNs) is directed acyclic graphs. In which the nodes define (represents) 
the variables of interest or components (e.g. pressure of a device, gender of a patient, 
occurrence of an event), and the arrows (links) represent (define) the informational or 
casual dependencies between the variables. The strength of dependency between the nodes 
   ௡       
       
           ௡      U 
ܦ  ௡ ܦ  ܦ    ܦ    
37 
 
(variables of interest) is represented by conditional probabilities that are attached to each 
link that links the parent-child nodes in the network. BNs gain importance since they are 
considered as compact representation of complex systems that can show the relation 
between the components of the system in a clear way (Pearl 1985).  
 A Bayesian network example is given in Figure 3.10. This is a simplified BN of well-
known automobile diagnosis problem. 
Figure 3.10: Bayesian Network 
 
A Bayesian Networks is a convenient and easy tool to classify the nodes as parent node, or 
child node. A parent node is a node with one or more arcs (links) originated from it and 
directed towards another node (child node). A child node is a node with one or more arcs 
(links) towards to itself coming from other nodes (parents). A node without a child is called 
a leaf node. The links in Bayesian networks carry the conditional probabilities that define 
the relation between the linked nodes. 
In the Figure 3.10, all of (Distributor, Spark plug and Battery) are parents. And both of 
Radio and Engine start are children and in the same time leaf nodes.  
BNs are directed acyclic graphs. They take Joint probability into consideration. They can 
deal with both discrete and continuous random variables. 
 
38 
 
BNs use the following properties: 
1- Evidential Reasoning using the given data as evidence. The rest of nodes are 
evaluated according to the available information using the joint probability as in 
equation 3.12. 
              ∏                                                                                 (3.12) 
Where  
i. Pai defines the conditional probability of Xi and it defines the child. 
ii. x1, x2 « [n define the set of predecessors of Xi (parent). 
2- Reasoning about actions is one of the most powerful properties of BNs. When 
any change or modification happens on the network, it can be easily modified, and 
reasoning about modification action can be achieved. 
There are many ways of reasoning in Bayesian networks (BNs), see Figure 3.11. 
1- Diagnosis: collecting observation to determine the current states. 
2- Prognosis (predictive): uses the current states as evidences to determine (predict) the 
future states. 
 
 
Figure 3.11: a- Diagnosis Reasoning, b-Prognosis (predictive) reasoning 
 
 
39 
 
3.2.3.2 Dynamic Bayesian Networks 
A dynamic Bayesian networks (DBN) is an extension of a Bayesian network, where the 
system states change through time. It is a compact representation that describes the system 
states and their changes through time. It decreases the combinational explosion effect while 
measuring the reliability of the system. DBNs can be considered as helpful tools to deal 
with variable (component) aging (degradation) by using transition probabilities (Murphy 
2002, Athi 2011, Weber 2003). 
An example of a DBN is given in Figure 3.12. This is a dynamic system generated from the 
static system given in Figure 3.10 where components Distributor, Spark plug and Battery 
age through time. 
As DBNs are compact structures of dynamic systems, they can be considered as tools that 
are able to deal with aging and maintenance activities. DBNs are applied in many filed such 
as robotics, data mining applications, speech recognition, digital forensics, protein 
sequencing and bioinformatics. 
DBNs are power full tools to predict the future reliability of systems. Especially in complex 
systems; with DBNs maintenance plan and prediction is easier. Hence the early predictions 
allow preparing to be ready on time (e.g. ask for spare parts earlier which will make the 
parts ready when needed).  
The easiest way to deal with dynamic Bayesian networks (DBNs), is to develop stationary 
Bayesian networks in each time slice, and define the relation and dependencies inside 
Bayesian network (BN), then connect the dynamic nodes with themselves in the next time 
slices. 
Where   
  is the ith node at time t,   
  can be         ,      
   represent the parents of   
 . 
 
40 
 
Figure 3.12: Dynamic Bayesian Networks (DBNs) 
 
3.2.3.3 Inference in Dynamic Bayesian networks  
Inference is a computational method for evaluating a query given in a probability model 
expressed by BN (D'Ambrosio 1999). Inference can be made to evaluate the state of any 
variable given the evidence of the state of other variables (Needham 2006). Inference Uses 
Bayes theorem and simplified by conditional independence. 
Inference can be either exact or approximate. Exact inference is used when the analytical 
form of the problem is available, and the computationally state is feasible. It can be used 
with directed acyclic graphs. 
Approximate inference is used when the analytical form of the problem is not available or 
when the time needed for the exact solution is very long. In approximate inference, 
intractability is important and there are three ways to handle it: Sampling by using Monte 
Carlo methods. Variation Methods are the simplest methods is the mean filed 
approximation method. Belief propagation (PB) entails the message passing algorithm to 
the initial form. 
41 
 
4. PROBLEM DEFINITION AND MODELING 
Thermal power plant is a complex system having man interrelated components. Fixing 
maintenance plans for thermal power plants needs solutions. Methodologies to schedule a 
proactive maintenance scheduls using DBNs are proposed. The methodologies aim to 
minimize the main component repairs in the planing horizon. We assume that the system 
has a discrete time horizon. The variables have a discrete sample space. And we assume no 
cycling affects the system. 
Thermal power plant is a facility responsible to produce electricity from thermal energy. It 
is a critical facility to people's life. 
4.1 THERMAL POWER PLANTS 
Thermal Power plant is facility that is responsible of electricity generation. It mainly 
converts the thermal energy gains from burning the fossil fuel in the boiler, to a pressurized 
steam that moves to the turbine. In turbine the energy is converted into mechanical energy. 
Once the blades of the turbines rotates the moving part of the generator (rotor) starts to 
rotate too. Once rotor rotates, electrical charges are generated on the stator (static part of 
the generator). Then these charges move to the transformers, where the high voltage current 
is made up, Figure 4.1 represents a schematic diagram of thermal power plant. 
4.1.1 Rankine Cycle 
In thermal power plants, many components and systems are interrelated in order to finalize 
the process. The process is mainly made up by the use of Rankine cycle. Figure 4.2 shows a 
simple Rankine cycle. 
The working principle of Rankine cycle is as follows: 
1- Cold water enters the pump. 
2-  The pump pressurizes the water. 
3-  The water flows to the boiler, where the heat is transferred from the ignition of 
fuel into the pressurized water, to produce a pressurized steam. 
 
42 
 
Figure 4.1: Schematic representation of thermal power plant 
Source: Wikipedia 
Figure 4.2 Simple Rankine cycle 
Source :( Flynn 2003) 
4-  The pressurized steam flows into the turbine. The turbine structure contains 
blades that are designed to increase the collision between the pressurized steam and 
the turbine blades. When the collision happens, it forces the turbine to flow over its 
pivot which is connected to the generator rotor. 
Boiler 
Condenser 
 Turbine Generator Pump 
43 
 
5- When the turbines pivot rotates, the rotor of the generator rotates too. The rotor 
is made up so it can generate a magnetic field.  The stator (static part of the generator) 
is made up from copper windings, so when the rotor rotates, electrical charges are 
produced in the stator winding. 
6-  Electrical charges then flows to the transformer that is responsible to produce 
the high voltage.  
7- Going back to the turbine, after the collision, pressure of the steam drops down. 
The steam flows to the condenser, which is mainly made up from long pipes that are 
used to cold the steam, and condense it to water again. Figure 4.3 represents the 
process flow in thermal power plants using Rankine cycle.  
Figure 4.3: process flow in thermal power plant using Rankine cycle 
 
 
 
44 
 
4.1.2 Components in Rankine cycle 
In Rankine cycle, there are five basic components related to the efficiency of the cycle, and 
related to the electricity generation. These are shown in Figure 4.4 in the order below: 
Turbine: a rotating machine, covered with blades and it is rotating around its pivot. 
Boiler: the combustion chamber, where the fuel is burned and chemical energy is 
transformed into heat. 
Condenser: a device combined from long pipes used to increase the heat transfer area, 
which leads to cool the moving fluid. 
Pump: Fluid machinery. A device used to increase the pressure of the flowing fluid. 
Generator: it is made up from rotor (magnet), stator (windings). Where these combination 
can generate electricity using magnetic fields. 
Figure 4.4: Components of Rankine Cycle 
 
 
 
 
 
 
 
 
45 
 
4.1.3 Systems of Thermal Power Plants 
In Rankine cycle, different systems are interacted together simultaneously to accomplish 
the jobs. These systems are: 
Pumping system: consists of the pumps used in the cycle, which are used to increase the 
pressure of the moving fluid. 
Boiler System: the system used to produce the heat energy from burning the fuel. 
Piping System: all the pipes used to connect the systems with each other. 
Turbine System: the system related to the turbine rotates, and extracting heat and pressure 
energy and converting them to mechanical energy. 
Generating System: the system responsible of generating electrical current by changing 
mechanical energy into electrical. 
Transforming System: the system responsible of transforming the electrical current 
generated in the generator, into high voltage current using electromagnetic induction. 
Condensing System: the system is responsible of condensing the low pressure steam to 
water, by extracting the heat energy from it. 
Controlling System: the system responsible of controlling the other systems, and consists 
of all sensors and gauges. 
4.2 MODELING WITH DYNAMIC BAYESIAN NETWORKS 
Thermal power plant is a very complex system. Analyzing it, is not an easy job, and to 
maintain its reliability as high as possible is the main aim of the personnel there, because it 
is a critical facility that many other facilities depend on, e.g. hospitals, airports, industry... 
etc.  
We propose to use dynamic Bayesian networks to model and analyze such a system. Both 
diagnosis and prognosis of the system at each period of time are possible with DBNs. The 
46 
 
data provided by the controlling system is used as evidence in the network, and then the 
states (reliability) of the other systems can be predicted using DBNs. 
Diagnosis can be performed within the static system at each period with the help of 
Bayesian network. Once conditional probabilities of the interrelated system are defined 
with DBN representation, evidence is collected via the data from the controlling system. 
Then using the evidence gathered so far the states (reliability) of the interrelated systems 
can be calculated. 
Prognosis can also be performed using Dynamic Bayesian networks. After identifying the 
transitional probabilities that define the aging of the systems (degradation), and using the 
evidence gathered so far the states (reliability) of the systems for the future periods can be 
predicted. 
In this work, we model the thermal power plant using DBNs; the static network of the 
problem represented with a BN is given in Figure 4.5. While building the model, some 
assumptions are made. These assumptions are: 
1- We assume no cycling affects the system. 
2- Maintenance activities are performed by either repairing or replacing 
components or gauges. All kinds of gauge calibration and repair activities are 
DVVXPHG WR EH SHUIHFW UHSDLU DFWLYLWLHV. 7KDW¶V ZK\ WKHVH DUH FDOOHG UHSODFHPHQWV 
since they bring the component or gauge to the perfect working condition. 
3- We assume a discrete time horizon. And we assume a discrete sample space for 
each node in the model. 
4- We assume the observations are collected at the beginning of each period. 
5- We assume each component can either works or fails in a period. Once a 
component or gauge is replaced in a period, its working probability is set to 1. 
We classify the nodes used in the BN model to represent thermal power plants according to 
their duties. These are replaceable nodes, process nodes, observable nodes and non-aging 
nodes. The detailed explanations of these nodes are given subsequently. 
47 
 
  
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48 
 
4.2.1 Replaceable Nodes 
The main replaceable nodes are: 
Pump: representing the pumping system. 
Condenser: representing the condensing. 
Generator: representing the generating system. 
Boiler: representing the boiler system. 
Transformer: representing the transformation system. 
Gauge nodes are the nodes where the measuring devices are located. Gauge nodes used to 
give readings to the observations nodes. They are directly connected to the hidden process 
we are interested in. In the BN representation, the following gauge types are used: 
Temperature gauges: two gauges are used. One is used after condensing process and the 
other one is used after boiling process. 
Pressure gauges: three pressure gauges used. One is used after pumping the water in order 
to generate pressurized water, the second one is used after the pressurized steam, and the 
last one is used after the turbine rotation to check the efficiency of the process. 
Tachometers: two tachometers used. One is used to check the pump rotation, and the other 
one is used to check the turbine rotation. 
Voltmeter: only one volt meter is used to check the voltage of the produced current. 
 
4.2.2 Process Nodes 
Process nodes are the nodes where two parent nodes acts together to produce a child. The 
child here is the process node. The following processes are defined as the result of the 
interaction between the parent components: 
49 
 
Cold water: is the result of the condenser. 
Plate rotation: is the result of the interaction between pump and electricity. 
Pressurized water: is the result of the interaction between cold water and plate rotation. 
Ignition: is the result of the interaction between boiler and fuel. 
Heat: is the result of ignition. 
Pressurized steam: is the result of the interaction between of pressurized water and heat. 
Turbine rotation: is the product of the interaction between pressurized steam and turbine. 
Pressure drop: is the result of turbine rotation that is happened to the steam. 
Electricity: is the result of the interaction between turbine rotation and generator. 
High voltage: is the result of the interaction between electricity and transformer. 
4.2.3 Observable Nodes 
Observable nodes are the nodes used to collect the readings from the gauge nodes. The 
following observable nodes are used to collect data from the gauges and sensors of the 
controlling system: 
Temp 1 is the temperature read on TempG1 (temperature gauge 1), after measuring the 
temperature of cold water process. 
Temp 2 is the temperature read on TempG2 (temperature gauge 2), after heat is produced 
from the ignition. 
press1 is the pressure read on PRESSURE GAUGE 1 (pressure gauge 1), after producing 
pressurized water from the interaction between plate rotation and cold water. 
press2 is the pressure read on PRESSURE GAUGE 2 (pressure gauge 2), after producing 
pressurized steam by the interaction between pressurized water and heat. 
50 
 
press3 is the pressure read on PRESSURE GAUGE 3 (pressure gauge 3), after the turbine 
rotation to check the pressure drop. 
RPMM1 is the tachometer RPM1 reading after the interaction between pump and 
electricity to produce plate rotation. 
RPMM2 is the tachometer RPM2 reading after interaction between turbine and pressurized 
steam that produces turbine rotation. 
Voltage is the reading on the volt meter, which measures the high voltage produced by the 
interaction between electricity and transformer. 
4.2.4 Non-aging (non-degrading) nodes: 
The non-DJLQJ FRPSRQHQWV DUH WKH FRPSRQHQWV ZKRVH UHOLDELOLW\ GRHVQ¶W FKDQJH WKURXJK 
time (time independent). In the model there are three non-aging components. These 
components are: 
Fuel: is the main input for the boiler. It contains the chemical energy required for the 
ignition. 
Pump electricity: is the electricity needed to make the pump work. 
Turbine: turbine is the heart of the facility, and generally turbines have a very long life 
time. Another factor to consider it as non-aging component is that when it stops the whole 
system stops. 
 
 
 
 
 
 
51 
 
Table 4.1 categorize the nodes into groups and specifies their duties, and the related nodes 
in each group. 
Table 4.1, Types of nodes in the Bayesian Network of thermal power plant model 
Group of 
nodes 
Nodes definitions Related nodes Duty of the node 
Observable 
nodes 
All sensor and 
gauges readings. 
Temp1 Temp2 Gives information 
about the process states. Press1 Press 2 
Press3 RPMM1 
RPMM2 Voltage 
Easy to 
replace and 
control nodes 
All gauges and 
sensors 
Temperature 
Gauge1 
Temperature 
Gauge 2 
The devices used to 
measure the process 
states. PRESSURE 
GAUGE 1 
PRESSURE 
GAUGE 2 
PRESSURE 
GAUGE 3 
RPM meter 1 
RPM meter 2 Volt meter 
Main 
replaceable 
nodes 
All  the aging 
components used to 
drive the plant 
Pump Condenser Produces the main 
inputs of the processes. Generator Boiler 
Transformer 
Process nodes All the children of 
the main 
components 
interactions, or the 
children of another 
processes. 
Pressurized 
water. 
Pressurized 
steam 
Nodes where processes 
happen. 
High voltage Cold water 
Plate rotation Heat 
Turbine 
rotation 
Pressure drop 
Electricity Ignition 
Non-aging 
components 
All the time 
independent 
components (their 
UHOLDELOLWLHV GRQ¶W 
change through 
time). 
Fuel Pump 
electricity 
Critical to other process 
nodes (needed to 
perform other 
processes). Turbine 
 
52 
 
4.3 ESTABLISHING THE MODEL 
The BN model is built on Matlab using BNT (Murphy 2002), and verified using GENIE 
package. The model consists of 34 nodes. Five of them are main replaceable components, 
and eight of them are gauges. There are eight observable nodes in the model, where each 
one of them is connected with one gauge. There are three non-degrading components in the 
model. Remaining nodes are divided into two groups; the first one is critical process group, 
where the second one is defined as regular process group. 
 
4.3.1 Main replaceable components 
The main replaceable components are the components having high repair cost and critical 
to the process of the plant. In the model we have five of the main replaceable components 
that are: pump, condenser, boiler, generator and transformer. 
In this thesis, turbine is considered as the soul of all processes and it is assumed that it is 
not replaceable. The initial probabilities of each of these components are defined depending 
on the efficiency of each, and also by collecting data related of each one. The initial 
probabilities of these components are shown in Table 4.2. The states of each component are 
defined as working (W) or not working (NW). 
Table 4.2: Initial probability of main components 
Component Working Probability Not Working Probability 
Pump 0.980 0.020 
Condenser 0.880 0.120 
Generator 0.950 0.050 
Boiler 0.988 0.012 
Transformer 0.950 0.050 
Turbine 1.000 0.000 
 
The initial probabilities are defined according to the components efficiencies. 
53 
 
Pumps really have high reliabilities. They are simply an electrical motor with impeller. 
Failure condition is mainly because of burning the electrical motor of the pump or after 
working for a long time and because of cavitation. 
Condenser in this thesis consists of the condenser itself and the pipes. The main task of 
condenser it to supply cold water, but friction of pipes which can generate heat, makes the 
task of the condenser less reliable. Failure modes are either burning of the condenser motor, 
or leakage in the pipes. 
Generators are highly reliable components. Their failure modes take place either when the 
bearing of the rotor fails or when the windings of the stator burn. 
Boilers are combustion chambers. They are highly reliable components. Their failure mode 
can be failure in the ignition system or leakage in the body. 
Transformers are highly reliable components. Their failure modes are generally burning of 
the winding of the poles. 
4.3.2 Gauge Components 
The gauge components are devices to measure the efficiency of the processes in the system. 
Temperature gauges pressure gauges; tachometers and voltmeters are the gauge 
components defined in the model. The main characteristics of these components are that 
they need to be calibrated from time to time, in order to get accurate readings. 
There are four types of gauges used in this model as shown in Figure 4.6. They are: 
Temperature gauges:  there are two of them, used to read temperature. 
Pressure gauges: there are three of them, used to read the pressure. 
Tachometer: there are two of them, used to read revolution per minute. 
Volt meter: there is one, used to read the voltage. 
 
54 
 
Figure 4.6: Types of gauges used in the model 
 
These components are used to control and check efficiency and reliability of each process.  
Failure modes of these gauges depend on the type of the gauge used. For example; there are 
many temperature reading device in the market. Like infrared temperature reading devices, 
anemometer measuring devices, and mercury temperature reading devices. The latter one is 
the most widely known temperature reading device. In thermal power plants, since when 
we want to read the temperature of a hot surface, the most logical one is to use infrared 
measurement devices. This device can fail either because of calibration error, or because of 
failure in the thermal sensors inside the device. 
For the pressure gauges, there are many types too. But the most famous one is the gauge 
having a spring inside. And it uses the formula Pr=F/A, where Pr is the pressure exerted on 
the spring, F is the force acting on the spring, A is the area where the force is exerted. As 
the pressure increases, the spring is compressed; accordingly the indicator reads the 
pressure. Failure modes related to this type are either failure in the spring inside or error in 
calibration of the indicator. 
Tachometers are devices that are attached to the rotating parts. There are many types of 
tachometers such as laser pointing or directly connected to the rotating part. When the 
rotating part starts to move, the tachometer starts to calculate the distance traveled through 
Gauges  
Temperature 
gauges 
Pressure gauges 
(PGs) 
Tachoometers 
(RPMs) 
Volt meter 
55 
 
time. Rotating parts normally have circular cross sections. By using circumference of the 
circle, we can calculate the speed of rotation as round per second (RPS) or round per 
minute (RPM). Failure modes of this type are either failure in the inside circuit of the 
device, or calibration error of speed or diameter. 
The last type of gauges used is voltmeter. Volt meter is used to read the voltage of the 
current. It is device where one pole is calibrated to earth voltage (0 V) and this voltage is 
used as a reference value. Then the second pole is attached to the current and the difference 
between the two poles is the reading. Failure modes of these gauges are either failure in the 
inside circuit or calibration error. 
The states of these components in the model are assume to be working (W) or not working 
(NW), and the initial probabilities related to these gauges are shown in Table 4.3. 
Table 4.3:  Initial probabilities of gauges 
Component Working probability Not working probability 
Temperature gauge 1 0.93 0.07 
Temperature gauge 2 0.93 0.07 
Pressure gauge 1 0.95 0.05 
Pressure gauge 2 0.95 0.05 
Pressure gauge 3 0.95 0.05 
RPM meter 1 0.90 0.10 
RPM meter 2 0.90 0.10 
Volt meter 0.90 0.10 
 
The initial probabilities of the gauges are given according to their efficiencies. 
The duties of the gauges used in the model are as follows: 
1- Temperature gauge 1 is used to read temperature of cold water. 
2- Temperature gauge 2 is used to read temperature of the steam comes from boiler. 
56 
 
3- Pressure gauge 1 is a pressure gauge used to read the pressure of the water after 
pumping it. 
4- Pressure gauge 2 is a pressure gauge used to read pressure of the steam. 
5- Pressure gauge 3 is a pressure gauge used to read the pressure drop after collision 
in the turbine. 
6- RPM meter 1 is a tachometer used to read the speed of the pump plate rotation. 
7- RPM meter 2 is a tachometer used to read the speed of turbine rotation. 
8- Volt meter is used to read the voltage results from the transformer. 
4.3.3 Process Nodes 
A Process node is a child of two parent nodes, where another two components interact 
together to perform the process (child). In the BN model, there are two types of processes. 
One consists of the hidden processes where we have no direct observations. The other 
consists of the observation processes of which we are able to directly observe the states. 
The process nodes defined in the model are shown in Figure 4.7. 
4.3.3.1 Hidden Processes 
+LGGHQ 3URFHVVHV DUH WKH SURFHVVHV ZKHUH ZH GRQ¶W KDYH DQ\ GLUHFW REVHUYDWLRQ RQ WKHP. 
Nevertheless there exists a causal relation between hidden process node and its parent 
nodes, which represents the interaction among these. So that their reliabilities can be 
predicted. They are representing the main processes in the plant. There are ten hidden 
processes in the model. Each process has two states: "A' means that the process is available 
whereas "NA" means that it is not available. 
 
 
 
 
 
 
 
 
 
 
 
57 
 
Figure 4.7: Types of process nodes 
 
 
The conditional probabilities of each of these hidden processes given the states of their 
parents are illustrated in Tables 4.4-4.13. 
 
Table 4.4: Conditional probabilities of cold water 
Condenser Not Working (NW) Working (W) 
Cold Water not available (NA) 0.99 0.20 
Cold Water available (A) 0.01 0.80 
 
E.g. the probability of Cold water to have "A" state when the state of the condenser is given 
as "W" is 0.8. 
 
 
Process Nodes 
Observable processes 
1- temp1 
2-temp2 
3- press1 
4- press2 
5- press3 
6- RPMM1 
7-RPMM2 
8- voltage 
Hidden Processes 
1- Cold Water 
2- Plate Rotation 
3- Ignition 
4- Heat 
5- Pressurize Water 
6- Pressurized Steam 
7- Turbine Rotation 
8- Pressure Drop 
9- Electricity 
10- High Voltage 
58 
 
Table 4.5: Conditional probabilities of plate rotation 
Pump Electricity NA A 
Pump NW W NW W 
Plate rotation NA 1.00 1.00 0.90 0.00 
Plate rotation A 0.00 0.00 0.10 1.00 
 
Table 4.6: Conditional probabilities of pressurized water  
Cold Water NA A 
Plate Rotation NA A NA A 
Pressurized Water NA 1.00 0.80 0.80 0.20 
Pressurized Water A 0.00 0.20 0.20 0.80 
 
Table 4.7: Conditional probabilities of ignition 
Fuel NA A 
Boiler NW W NW W 
Ignition NA 1.00 1.00 1.00 0.10 
Ignition A 0.00 0.00 0.00 0.90 
 
Table 4.8: Conditional probabilities of heat 
Ignition NA A 
Heat NA 1.00 0.00 
Heat A 0.00 1.00 
 
Table 4.9: Conditional probabilities of pressurized steam 
Pressurized water NA A 
Heat NW W NW W 
Pressurized steam NA 1.00 0.50 1.00 0.00 
Pressurized steam  A 0.00 0.50 0.00 1.00 
 
59 
 
Table 4.10: Conditional probabilities of turbine rotation 
Turbine NA A 
Pressurized Steam NW W NW W 
Turbine Rotation NA 1.00 0.99 0.10 0.00 
Turbine Rotation  A 0.00 0.01 0.90 1.00 
 
Table 4.11: Conditional probabilities of pressure drop 
Turbine Rotation NA A 
Pressure drop A 0.60 0.00 
Pressure drop NA 0.40 1.00 
 
Table 4.12: Conditional probabilities of electricity 
Turbine Rotation NA A 
Generator NW W NW W 
Electricity NA 1.00 0.80 0.80 0.00 
Electricity A 0.00 0.20 0.20 1.00 
 
Table 4.13: Conditional probabilities of high voltage 
Electricity NA A 
Transformer NW W NW W 
High Voltage NA 0.80 0.80 0.80 0.20 
High Voltage A 0.20 0.20 0.20 0.80 
 
For example, in Table 4.13, P(High Voltage=A| Electricity=NA and Transformer=W)=0.2. 
 
 
 
 
 
60 
 
4.3.3.2 Observable processes 
Observable processes are the nodes resulting from readings of the measurments of the 
hidden processes. Hence they give insights about the reliability and efficiency of the hidden 
process to which they are directly connected to. In the model there are eight observable 
nodes. The observable nodes are located so that each of them is the child node of a 
measuring device from one side, and of a hidden process from the other side. 
The states of each observable node are defined as follows: 
For temperature readings (Temp), there are three states (Hot, Medium, and Cold). 
For pressure readings (Press), there are three states (High, Medium, and Low). 
For the tachometer readings (RPMM), there are two states (Fast, Slow). 
For the voltage readings, there are two states (High, Low). 
The conditional probabilities of the observable nodes given the states of their parents are 
illustrated in Table 4.14-4.21.  
 
Table 4.14: Conditional probabilities of temp1. 
Temperature gauge 1 NW W 
Cold Water NW W NW W 
Hot 0.05 0.00 0.05 0.00 
Medium 0.95 0.10 0.95 0.05 
Cold 0.00 0.90 0.00 0.95 
 
Table 4.15: Conditional probabilities of temp2. 
Heat NA A 
Temperature gauge 2 NW W NW W 
Cold 1.00 0.90 0.80 0.00 
Medium 0.00 0.10 0.20 0.30 
Hot 0.00 0.00 0.00 0.70 
 
 
61 
 
 
Table 4.16: Conditional probabilities of press1. 
Pressurized water NA A 
PRESSURE GAUGE 1 NW W NW W 
Low 0.80 0.65 0.65 0.05 
Medium 0.15 0.30 0.30 0.05 
High 0.05 0.05 0.05 0.90 
 
Table 4.17: Conditional probabilities of press2. 
Pressurized water NA A 
PRESSURE GAUGE 2 NW W NW W 
Low 0.80 0.65 0.65 0.05 
Medium 0.15 0.30 0.30 0.05 
High 0.05 0.05 0.05 0.90 
 
 
Table 4.18: Conditional probabilities of press3. 
Pressure drop NA A 
PRESSURE GAUGE 3 NW W NW W 
High 0.05 0.05 0.05 0.05 
Medium 0.15 0.30 0.30 0.05 
Low 0.80 0.65 0.65 0.90 
 
Table 4.19: Conditional probabilities of RPMM1 
RPM meter 1 NW W 
Plate rotation NA A NA A 
Slow 1.00 0.95 1.00 0.05 
Fast 0.00 0.05 0.00 0.95 
 
62 
 
Table 4.20: Conditional probabilities of RPMM2 
RPM meter 2 NW W 
Turbine rotation NA A NA A 
Slow 1.00 0.80 0.90 0.00 
Fast 0.00 0.20 0.10 1.00 
 
Table 4.21: Conditional probabilities of voltage 
High voltage NA A 
Volt meter NW W NW W 
Low 1.00 0.80 0.80 0.00 
High 0.00 0.20 0.20 1.00 
 
 
4.3.4 Transition probabilities 
After defining the components and their related conditional probabilities, the model is built 
up using BNT, Murphy (2002). BNT is a tool box based on Bayes theory works in 
MATLAB environment. The model is coded in the static state first as shown in Figure 4.5 
and verified using GENIE package. 
Then the dynamic model is built up using BNT and verified with GENIE again. 
Transitional probabilities of aging components are determined using mean time to failure 
(MTTF) under the assumption of exponential distribution as shown in Table 4.22 . 
The equations used to determine reliability of aging components is as follow: 
Ȝ   
 
    
              (4.1) 
Reliability after 1 time period is given by: 
Reliability after 1 period =             (4.2) 
Reliability decrement due to aging = 1-           (4.3) 
 
 
 
63 
 
Table 4.22 Transition probabilities of aging components 
  MTTF Ȝ WORKING AGING 
PUMP 15 0.066667 0.9355 0.0645 
CONDNSER 18 0.055556 0.946 0.054 
GENERATOR 25 0.04 0.9608 0.0392 
BOILER 22 0.045455 0.9556 0.0444 
TRANSFORMER 14 0.071429 0.9311 0.0689 
TEMPG1 10 0.1 0.9048 0.0952 
TEMPG2 10 0.1 0.9048 0.0952 
PRESSURE 
GAUGE 1 8 0.125 0.8825 0.1175 
PRESSURE 
GAUGE 2 8 0.125 0.8825 0.1175 
PRESSURE 
GAUGE 3 10 0.1 0.9048 0.0952 
RPM1 12 0.083333 0.92 0.08 
RPM2 12 0.083333 0.92 0.08 
VOLTMETER 5 0.2 0.8187 0.1813 
 
In the model, it is assumed that only the main components and gauges are aging with a 
degradation level given in Table 4.22 . 
MTTF values are collected from different resources such as manufacturur data. 
After constructing  the temporal relations of the aging components, dynamic Bayesian 
network of the model is built. The DBN of the model built with GENIE is given in Figure 
4.8. Where the nodes with circled arcs are the aging components. 
 
4.3.5 Independent variables 
All gauge nodes and their corresponding hidden process nodes are independent from each 
other. Take for instance High voltage and volt meter. Given evidence on High voltage, 
working probability of Volt meter is not effected. Similarly given evidence on Volt meter, 
availability probability of High voltage is not effected. To show this, an inference test is 
applied to the subsection of nodes High voltage, volt meter and voltage in the model.  The 
test is applied by using different evidences and we observe the change in the nodes. The 
results of the test are shown in table 4.23. In table 4.23, given that High voltage is available, 
64 
 
the working probability of Volt meter is 0.9 and given that the high voltage is not available, 
the working probability of volt meter is still 0.9 as also in the no evidence case. Similar 
results are obtained for the availability of High voltage given evidence on Volt meter which 
is 0.8, again same as in the no evidence case 
Table 4.23: Evaluating the working probability of variables under various evidences 
Evidence Probability 
HV="A" VM="W" V="High" 
- 0.8 0.9 0.772 
HV="A" - 0.9 0.92 
HV="NA" - 0.9 0.18 
VM="W" 0.8 - 0.84 
VM="NW" 0.8 - 0.16 
V="High" 0.953 0.979 - 
V="Low" 0.281 0.632 - 
 
4.3.6 Domain of variables 
The domain of variables in the models changes according to the type of nodes. They are 
either working (W) or not working (NW) for components. And they are available (A) and 
not available (NA) for hidden processes. And the domain of 
slow/fast/medium/high/low/cold/hot is related to the observable processes. The domains of 
all variables are shown in table 4.24. 
 
 
 
 
 
 
65 
 
Table 4.24: Domain of variables 
Pump W, NW 
Condenser W, NW 
Generator W, NW 
Boiler W, NW 
Transformer W, NW 
Temperature gauge1 W, NW 
Temperature gauge 2 W, NW 
Pressure gauge 1 W, NW 
Pressure gauge 2 W, NW 
Pressure gauge 3 W, NW 
RPM1 W, NW 
RPM2 W, NW 
Volt meter W, NW 
Cold water A, NA 
Plate rotation A, NA 
Pressurize water A, NA 
Ignition A, NA 
Heat A, NA 
Pressurized steam A, NA 
Turbine rotation A, NA 
Pressure drop A, NA 
Electricity A, NA 
High voltage A, NA 
Temp 1 Hot, Medium, Cold 
Temp 2 Cold, Medium, Hot 
Press 1 Low, Medium, High 
Press 2 Low, Medium, High 
Press 3 High, Medium, Low 
RPMM1 Slow, Fast 
RPMM2 Slow, Fast 
Voltage Low, High 
Fuel A, NA 
Pump electricity A, NA 
Turbine W, NW 
66 
 
  
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5. METHODOLOGY 
Two algorithms are proposed in this thesis. First one is the "Single Critical Process" 
algorithm (SCP), while the other one is the "Multiple Critical Processes" algorithm (MCP). 
The two algorithms differ from each other in the detection of degradation, and also the 
selection of the replaceable components. 
The algorithms are based on collecting limited number of observations at each period. Then 
they check whether to do repair or not, based on the reliabilities of predefined critical 
processes. If the reliability of these critical processes fall under a predefined threshold, then 
the algorithms decide on the repair action needed. 
The outline of the algorithms is given in Figure 5.1. The first step is to simulate the 
observations by generating a random number, and comparing it to the cummulative 
probability of the observable nodes. If the simulated value is undesirable, then the related 
gauge is checked/repaierd. After gauge check/repair, observations are simulated again. 
Using these observations, reliability of critical process is infered. If the reliability falls 
below the threshold, repairs are done and observations are simulated again. Then reliability 
of the critical process is infered again. Otherwise, if the reliability isn't below the threshold, 
then it continous with the next period. 
Figure 5.1: Outline of the algorithms
 
68 
 
5.1 ONE CRITICAL PROCESS ALGORITHM 
Single critical process algorithm (SCP) uses one process as a critical process. Main repair 
decisions are taken according to this process by selecting the component with the minimum 
working reliability. 
The critical process here is the high voltage, which is the last process in the model. 
Decisions to be taken are those related to main component repairs. 
5.1.1 Notation of SCP 
The notations used while building the SCP model is given below. 
Sets and Indices 
I: observable node set, I= {temp 1, temp2, press1, press2, press3, RPMM1, RPMM2, 
voltage}. 
J: Gauge set, J= {Temperature Gauge 1, Temperature Gauge 2. Pressure Gauge1, Pressure 
Gauge 2, Pressure Gauge 3, RPM1, RPM2, Volt Meter}. 
K: replaceable main component set. K= {pump, condenser, boiler, generator, transformer} 
i: observable node,    . 
j: gauge component,    . 
k: replaceable main component,    . 
 Variables 
    : State of observable node i in time t 
    : State of gauge component j in time t 
   : State of critical process in time t 
    : State of main component k in time t 
69 
 
  : Evidence list 
    : Efficiency measure of component k in period t. 
Parameters 
Lc: threshold reliability for the critical process node. 
T: planning horizon. 
There exists a one to one relation between observable node      and gauge      which is 
given in table 5.1. 
Table 5.1: Observable nodes and their related gauges 
Observable node  
I 
Gauge 
j 
Temp1 Temperature gauge 1 
Temp2 Temperature gauge 2 
Press 1 Pressure gauge 1 
Press 2 Pressure gauge 2 
Press 3 Pressure gauge 3 
0RPMM1 RPM1 
RPMM2 RPM2 
Voltage Volt meter 
 
5.1.2 Algorithm of SCP 
Steps of the SCP algorithm are as follows: 
The algorithm works in the following steps 
1- Initialize t=1 
2- Simulate observations oit for each observable node    . 
A. If the simulated value is fast/high/hot; then continue with (3) 
70 
 
B. Else, replace the related gauge j and update evidence 
            
C. Simulate the observable node i using the updated evidence. 
3- Evidence is updated using the simulated observation. 
                 
4- Infer critical process reliability          |   
5- If          |        then continue with (7) 
6- Else, do th followings 
a- Initialize remaining main component list      
b- Calculate            
c- Select the component to replace with min       
                        
d- Update evidence                
e- Set the evidence of observable nodes free 
    |           
f- Simulate observations     For each observable node i 
g- Update evidence using the simulated observations 
                 
h- Update remaining main component list      |     
i- Infer critical process reliability 
j- If          |       , then continue with (6.b) 
7- Increase t,       
8- If     then stop 
9- Else continue with (2)  
Let       Is an efficiency measure of component k in period t when a repair is planned. It is 
the reliability of component k in period t. FEM is the fault effect myopic approach and the 
FEL is the fault effect look-ahead approach (Özgür-hQODNÕQ DQG %LOJLo 121).  
 Namely it is calculated as: 
    
             |   
71 
 
    
             |              
    
             |                  
The difference between the mentioned approaches is selection of the replaceable 
component. In SCP critical process reliability is evaluated and if it falls below the 
threshold, then the reliabilities of the replaceable component are evaluated, the replaceable 
component that has the minimum reliability is selected. In FEM the probability of the 
critical process is evaluated and if it falls below threshold, it is set to the evidence as not 
available "NA" in that period. And its effect is evaluated over the replaceable components. 
And the replaceable component with the minimum reliability is selected. In FEL the 
reliability of the critical process is evaluated, and then if it falls below the threshold it is set 
to the evidence from that period up to the planned horizon as not available "NA". And its 
effect is evaluated over the replaceable component, and then the one with the minimum 
reliability is selected. 
5.2 MULTIPLE CRITICAL PROCESSES ALGORITHM 
Multiple critical processes (MCP) logic, divides the system into many critical processes 
where the outputs of these critical processes is the main outputs of the system. Each critical 
process depends on a predefined number of main replaceable components. At each time 
period; the reliability of the critical processes are evaluated. The algorithm takes the critical 
process with the minimum reliability and checks whether it falls below the threshold or not. 
If it falls, then the repair decision is made according to the minimum working reliability of 
the replaceable components. In this model, there are three critical processes defined. 
Pressurized water, pressurized steam and high voltage. Pressurized water is the descended 
process of pump and condenser. If the working reliability of the pressurized water is not in 
the acceptable range, then the problem can be either from pump or condenser. The 
pressurize steam process is the descended of the boiler and pump and condenser. But since 
pump and condenser are already cover by pressurized water, then any problem in the 
working reliability is directly assigned to the boiler. Finally, the high voltage is the 
descended of all main replaceable components (pump, condenser, boiler, generator and 
transformer). And since pump and condenser are covered by pressurize water. And boiler is 
72 
 
covered by pressurized steam. Only generator and transformer are assigned to this process. 
The groups of MCP are shown in Figure 5.1. 
73 
 
  
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5.2.1 Notation of MCP 
Notations and parameters used in the MCP model are given below. 
Sets and Indices 
I: observable node set, I= {temp 1, temp2, press1, press2, press3, RPMM1, RPMM2, 
voltage}. 
J: Gauge set, J= {Temperature Gauge 1, Temperature Gauge 2. Pressure Gauge1, Pressure 
Gauge 2, Pressure Gauge 3, RPM1, RPM2, Volt Meter}. 
Kh: replaceable main component relate to critical process h. Kh= {pump, condenser, boiler, 
generator, transformer}. 
H: critical process set. H= {Pressurized water, Pressurized steam, High voltage}. 
   = {pump, condenser}. 
   = {boiler}. 
   = {generator, transformer}. 
i: observable node,    . 
j: gauge component,    . 
k: replaceable main component,     . 
h: critical process    . 
Variables 
    : state of observable node i in time t. 
    : state of gauge component j in time t. 
    : state of critical process h in time t. 
75 
 
    : State of main component k in time t. 
  : Evidence list. 
Parameters 
Lc: threshold reliability for the critical process node. 
Lr: threshold reliability for the replaceable component. 
T: planning horizon. 
5.2.2 Algorithm of MCP 
Steps for the MCP model are given below. 
The algorithm works in the following steps 
1- Initialize t=1 
2- Simulate observations Oit for each observable node i 
a. If the simulated value is fast/high/hot; then continue with (3) 
b. Else, replace the related gauge j and update evidence 
              
c. Simulate the observable node i using the updated evidence. 
3- Evidence is updated using the simulated observation. 
                  
4- Initialize remaining critical process list,      
5- Infer critical process reliability for each critical process h 
         |          
6- Select the process with minimum reliability  
                   |          
7- If         |      then continue with (11) 
8- Else do the followings 
a- Initialize remaining main component list        
b- Calculate reliability of related main components  
76 
 
         |         
c- Select the component with minimum reliability 
                    |          
d- Update evidence                
e- Set the evidence of observable nodes free 
    |           
f- Simulate observations     for each observable node i 
g- Update evidence using the simulated observations 
                 
h- Update remaining main component list      |     
i- Infer critical process reliability 
j- If           |     , then continue with (8.b) 
9- Else update remaining critical process list      |      
10- Continue with (5) 
11- Increase t,       
12- If     then stop 
13- Else, continue with (2(
77 
 
6. RESULTS AND EVALUATION 
The proposed approaches are executed in Matlab environment using BNT toolbox 
developed by Murphy. Results are collected for each approach. Each of SCP, FEM and 
FEL is executed for 20 replications; each replication contains a planning horizon of 50 
periods. Each approach is evaluated for two different thresholds. 
6.1 DESIGN OF EXPERIMENTS 
The problem in hand is to minimize total main replaceable components repairs over a 
predefined planning horizon in thermal power plants, to develop a proactive maintenance 
schedule. The planning horizon is determined such that each main replaceable component 
is replaced at least once. So the planning horizon is chosen to be 50 years which is a 
reasonable number for a long run maintenance planning of thermal power plants. Each 
period is taken as 1 year which is enough to see the immediate effect of main components 
repairs and gauge checks/repairs. The threshold reliability which is set as a constraint to be 
satisfied by the critical processes is taken to be initially 0.5. 
We like to compare the methods with each other statistically. For each method we take a 
replication number of 20 replications. Each replication contains a planning horizon of 50 
years. In the comparison we check the total number of main replaceable components in 
each replication and the total check/repairs of gauges in each replication. Then we make a 
sensitivity analysis for each method by evaluating it using threshold of 0.75. 
A comprehensive evaluation data for each method using threshold of 0.5, and replication 
number of 20 replications are given in Tables 6.1-6.4. In these tables a total number of 
main replaceable components repairs and the total number of gauge checks/repairs are 
given together with their mean DQG VWDQGDUG GHYLDWLRQ ı(. 
In the tables below, the seventh row shows the total repair number of main replaceable 
components in each replication. The sixteenth row shows the total repair number of gauges 
at each replication. The eighteenth row shows the total repair done at each replication (main 
replaceable components and gauges). The nighnteenth and tweenteenth rows show the time 
78 
 
ellapsed by each replication in seconds and minutes respectively. The 22nd column shows 
the mean of the 20th replications for each row. The 23rd colunm shows the standard 
deviation of each row.  
The total number of repairs for main replaceable components and also for gauges differ 
significantly in each replication because of the observations simulated according to the 
UDQGRP QXPEHU JHQHUDWLRQ SURFHGXUH. 7KDW¶V Zhy the mean and standard deviations of 20 
replications give us a general idea about the performances of  the methods. According to 
the mean total number of repairs of main replaceable components given in tables 6.1-6.3, it 
may be concluded that SCP and FEM  are doing less repairs than FEL. Also for the mean 
total number of repairs of gauges, it may be concluded that SCP is doing less total gauge 
checks/repairs that the other two. But one has to make statistical analysis in order to say 
wether these differences are significant or not. That is why we perform one way ANOVA 
test  for main replaceable components and also for gauges in the next section. 
MCP model is doing much more repairs than the other methods. MCP keeps the reliability 
of all critical processes over the threshold, so once a critical process falls below the 
threshold repairs take place. 
 
79 
 
 
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A comprehensive evaluation data for each method using threshold of 0.75, and replication 
number of 20 replications are given in Tables 6.5-6.9. In these tables a total number of 
main replaceable components repairs and the total number of gauge checks/repairs are 
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6.2 ANALYSIS OF EXPERIMENTS 
 
After data evaluation of the approaches, a comparison is done over them using ANOVA. 
The test is applied over SCP, FEM and FEL since all of these approaches depends on only 
one critical process to decide on repairs. The tests are done over thresholds of 0.5 and 0.75 
for the total number of main replaceable components repairs in each replication. Also the 
tests are done on the total number of gauge checks/ repairs in each replication using 
thresholds of 0.5 and 0.75. A summary of the data evaluated for each method is given in 
Table 6.9. 
In tables 6.10-6.13, ANOVA test results are given. From these test results, since the P-
values in all one factor ANOVA tables are so high, we can say that performances of the 
methods according to the total number of repairs of main replaceable components and 
gauges are not significantly different from each other at the selected threshold values of 0.5 
and 0.75.  
Multi critical processes algorithm is different from single critical process algorithm in 
structure. Because in each period it ensures that three critical processes are functioning over 
the threshold while single critical process algorithm, which is performed by SCP, FEM and 
FEL approaches, checks only one critical process. So it is not reasonable to compare MCP 
method with SCP, FEM and FEL methods. 7KDW¶V ZK\ ZH WUHDW 0&3 PHWKRG VHSDUDWHO\. A 
summary of MCP data evaluation for 10 replications at thresholds 0.5 and 0.75 respectively 
is given in Table 6.14.  
According to table 6.14, the mean number of repairs of main replaceable components given 
in MCP method is 11.8 which are obviously greater than the single process algorithms. 
When the threshold is increased to 0.75, this number further increases to 26, which is again 
obviously higher than the related results of single critical process algorithms.
88 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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Table 6.10: ANOVA test results for main replaceable components at threshold of 0.5. 
SOURCE DF SS MS F P 
METHOD 2 4.03 2.02 0.24 0.785 
ERROR 57 473.70 8.31   
TOTAL 59 477.73    
 
Table 6.11: ANOVA test results for main replaceable components at threshold of 0.75. 
SOURCE DF SS MS F P 
METHOD 2 0.6 0.3 0.03 0.968 
ERROR 27 248.2 9.19   
TOTAL 29 448.8    
 
Table 6.12: ANOVA test results for gauges at threshold of 0.5. 
 
Table 6.13: ANOVA test results for gauges at threshold of 0.75. 
  
SOURCE DF SS MS F P 
METHOD 2 139 69 0.55 0.581 
ERROR 57 7214 127   
TOTAL 59 7353    
SOURCE DF SS MS F P 
METHOD 2 23 11 0.11 0.898 
ERROR 57 5948 104   
TOTAL 59 5971    
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6.3 PREDICTED MAINTENANCE PLAN 
Tables 6.15-6.17, shows the predicted average repairs for each main replaceable component 
and each gauge. The average is collected from 20 repetitions for each method. Table 6.15, 
shows the predicted average repairs for SCP, FEM and FEL at 0.5 thresholds. Table 6.16, 
shows the predicted average repairs for SCP, FEM and FEL at 0.75 thresholds. Table 6.17 
shows the predicted repairs for MCP at threshold of 0.5 and 0.75 for 10 repetitions. 
Table 6.15: Predicted maintenance schedule using SCP, FEM, FEL at threshold of 0.5  
Component SCP FEM FEL 
Pump 4.05 3.45 4.15 
Condenser 0.05 0.10 0.20 
Generator 0.30 0.45 0.50 
Boiler 0.55 0.75 0.40 
Transformer 1.60 1.80 1.85 
Temperature gauge 1 8.75 8.60 9.70 
Temperature gauge 2 27.70 28.40 28.15 
Pressure gauge 1 28.25 29.45 28.50 
Pressure gauge 2 31.25 31.35 31.80 
Pressure gauge 3 8.30 8.05 8.25 
RPM1 38.75 39.25 39.70 
RPM2 6.90 7.30 7.20 
Volt meter 18.45 19.15 18.30 
 
 
 
 
 
92 
 
Table 6.16: Predicted maintenance schedule using SCP, FEM, FEL at threshold of 
0.75  
Component SCP FEM FEL 
Pump 4.9 4.5 4.3 
Condenser 0.1 0.1 0.1 
Generator 0.3 0.2 0.7 
Boiler 0.7 0.8 0.3 
Transformer 1.8 2.2 2.4 
Temperature gauge 1 8.7 8.7 8.8 
Temperature gauge 2 27.2 27.7 26.0 
Pressure gauge 1 29.7 28.6 28.5 
Pressure gauge 2 29.6 31.4 33.2 
Pressure gauge 3 8.6 8.1 8.7 
RPM1 39.4 39.1 39.6 
RPM2 6.8 6.9 6.9 
Volt meter 19.4 19.0 19.0 
 
 
 
 
 
 
 
 
 
93 
 
Table 6.17: Predicted maintenance schedule using MCP at thresholds of 0.5 and 0.75 
Component 0.5 threshold 0.75 threshold 
Pump 4.10 8.00 
Condenser 0.50 1.20 
Generator 0.40 1.40 
Boiler 5.20 12.90 
Transformer 1.60 2.50 
Temperature gauge 1 8.90 11.00 
Temperature gauge 2 22.10 24.20 
Pressure gauge 1 28.00 28.90 
Pressure gauge 2 31.20 31.00 
Pressure gauge 3 7.90 8.00 
RPM1 42.10 37.10 
RPM2 7.00 9.30 
Volt meter 19.50 20.50 
 
 
 
 
 
 
 
 
94 
 
7. CONCLUSION 
Thermal power plants are very complex systems involving many interrelated components 
and subsystems. Developing maintenance plans of such systems is also a sophisticated 
procedure. In the literature generally preventive and reactive maintenance methods are 
proposed for developing maintenance scheduling of thermal power plants. Also there are 
some studies using RCM approach which are applied to only subsystems or components of 
WKHUPDO SRZHU SODQWV VXFK DV WXUELQH ERLOHU«HWF. So this study distinguishes from the 
literature since proactive maintenance of the whole thermal power plant system is modeled 
with all of necessary subsystems and components.  
In this study, we propose methodologies (SCP and MCP) to develop a proactive 
maintenance schedule for thermal power plants, which aim to minimize total number of 
repairs. The methodologies are modeled using DBN and coded in Matlab using BNT 
toolbox. The reliabilities of critical processes are inferred. Then repair decisions are made 
according to a comparison done using the inferred critical process reliability and a 
predefine threshold value. We compare performances of these methods with other 
component selection approaches (FEM and FEL) available in the literature. The results 
show that SCP and FEM are doing fewer repairs than FEL while MCP is doing much more 
repairs than the other methodologies. Then we compare the results of SCP, FEM and FEL 
statistically using ANOVA tests. The results show that since the P-value in one factor 
ANOVA table is so high, we can conclude that performances of the methods are not 
significantly different from each other. The ANOVA test is done over the total number of 
main components repairs and on the total number of gauge checks/repairs. 
In this work, minimizing total number of repairs is the main objective. However repair 
costs can be added to the model to minimize the total repair cost for future study. In the 
MCP model, total number of repairs is higher than the other methods. For future study, 
threshold reliability for also replaceable components can be added to the MCP model that 
will allow checking the reliability of main components after the check of the critical 
processes. In this way, performance of the method can be improved. There are a few other 
95 
 
component selection approaches proposed in the literature. Those can also be used in the 
comparison of performances. 
 
 
96 
 
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