Multi-state System Reliability Analysis and Optimization for Engineers and Industrial Managers / Edition 1

by Anatoly Lisnianski, Ilia Frenkel, Yi Ding

Overview

Multi-state System Reliability Analysis and Optimization for Engineers and Industrial Managers presents a comprehensive, up-to-date description of multi-state system (MSS) reliability as a natural extension of classical binary-state reliability. It presents all essential theoretical achievements in the field, but is also practically oriented. New theoretical issues are described, including: • combined Markov and semi-Markov processes methods, and universal generating function techniques; • statistical data processing for MSSs; • reliability analysis of aging MSSs; • methods for cost-reliability and cost-availability analysis of MSSs; and • main definitions and concepts of fuzzy MSS. Multi-state System Reliability Analysis and Optimization for Engineers and Industrial Managers also discusses life cycle cost analysis and practical optimal decision making for real world MSSs. Numerous examples are included in each section in order to illustrate mathematical tools. Besides these examples, real world MSSs (such as power generating and transmission systems, air-conditioning systems, production systems, etc.) are considered as case studies. Multi-state System Reliability Analysis and Optimization for Engineers and Industrial Managers also describes basic concepts of MSS, MSS reliability measures and tools for MSS reliability assessment and optimization. It is a self-contained study resource and does not require prior knowledge from its readers, making the book attractive for researchers as well as for practical engineers and industrial managers.

Product Details

ISBN-13:	9781849963190
Publisher:	Springer London
Publication date:	08/06/2010
Edition description:	2010
Pages:	393
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

About the Author

Anatoly Lisnianski is the author and co-author of more than 80 scientific papers, one book and 3 book chapters. He has more than 30 years of experience in the fields of reliability, maintainability and risk analysis, both in industry and academia. Dr Lisnianski received his MSc degree in Electrical Engineering from the State University of Information Technology, Precision Mechanics and Optics, Sankt-Petersburg, Russia, in 1975 and his PhD degree in Reliability from the Federal Scientific & Production Centre "Aurora" in Sankt-Petersburg, Russia, where he was working from 1975 till 1989. Since 1991 he has been an expert engineer in the Planning, Development & Technology Division, Reliability Department, of The Israel Electric Corporation Ltd. He is also a scientific supervisor of the Centre for Reliability and Risk Management in the Sami Shamoon College of Engineering, Beer Sheva, Israel and senior lecturer at Haifa University.

Ilia Frenkel is the author and co-author of more than 30 scientific publications. He has more than 35 years of experience in academia and industry in the fields of operational research, reliability and statistical quality control. Dr Frenkel received his MSc degree in Applied Mathematics from Voronezh State University, Russia, and his PhD degree in Operational Research and Computer Science, Institute of Economy, Ukrainian Academy of Science, formerly USSR. From 1988 till 1991 he was Department Chair and Associate Professor in the Applied Mathematics and Computers Department in the Volgograd Civil Engineering Institute, Russia. Now he is senior lecturer and director of the Centre for Reliability and Risk Management in the Sami Shamoon College of Engineering, Beer Sheva, Israel. He is a member of the editorial boards of scientific and professional journals.

Yi Ding received his BEng from Shanghai Jiaotong University, China, and his PhD from Nanyang Technological University, Singapore, both in Electrical Engineering. From 2005 to 2006, he worked as a post-doctoral research fellow in the Centre for Reliability and Risk Management of SCE - Shamoon College of Engineering, Beer Sheva, Israel. From 2007 to 2008, he was a postdoctoral research fellow in the University of Alberta, Canada. Currently, he is a member of the academic staff at Nanyang Technological University. His research interests include: electric power systems reliability and security; restructured power systems management and policy; engineering systems reliability; and evolutionary programming and fuzzy modeling. His research papers have been published in several international journals, such as: IEEE Trans. on Power Systems, Fuzzy Sets & Systems, Reliability Engineering & System Safety, and IEE Proc.-Gener. Transm. Distrib.

Table of Contents

1 Multi-state Systems in Nature and in Engineering 1

1.1 Multi-state Systems in the Real World: General Concepts 1

1.2 Main Definitions and Properties 8

1.2.1 Generic Multi-state System Model 8

1.2.2 Main Properties of Multi-state Systems 13

1.3 Multi-state System Reliability and Its Measures 16

1.3.1 Acceptable and Unacceptable States. Failure Criteria 16

1.3.2 Relevancy and Coherency in Multi-state System Reliability Context 17

1.3.3 Multi-state Systems Reliability Measures 18

References 27

2 Modern Stochastic Process Methods for Multi-state System Reliability Assessment 29

2.1 General Concepts of Stochastic Process Theory 30

2.2 Markov Models: Discrete-time Markov Chains 34

2.2.1 Basic Definitions and Properties 34

2.2.2 Computation of n-step Transition Probabilities and State Probabilities 36

2.3 Markov Models: Continuous-time Markov Chains 40

2.3.1 Basic Definitions and Properties 40

2.3.2 Markov Models for the Evaluating Reliability of Multi-state Elements 48

2.3.3 Markov Models for Evaluating the Reliability of Multi-state Systems 66

2.4 Markov Reward Models 79

2.4.1 Basic Definition and Model Description 79

2.4.2 Computation of Multi-state System Reliability Measures Using Markov Reward Models 84

2.5 Semi-Markov Models 99

2.5.1 Embedded Markov Chain and Definition of Semi-Markov Process 100

2.5.2 Evaluation of Reliability Indices Based on Semi-Markov Processes 105

References 113

3 Statistical Analysis of Reliability Data for Multi-state Systems 117

3.1 Basic Concepts of Statistical Estimation Theory 117

3.1.1 Properties of Estimators 118

3.1.2 Main Estimation Methods 120

3.2 Classical Parametric Estimation for Binary-state System 127

3.2.1 Basic Considerations 127

3.2.2 Exponential Distribution Point Estimation 128

3.2.3 Interval Estimation for Exponential Distribution 131

3.3 Estimation of Transition Intensities for via Output Performance Observations 132

3.3.1 Multi-state Markov Model and Observed Reliability Data. Problem Formulation 132

3.3.2 Method Description 135

3.3.3 Algorithm for Point Estimation of Transition Intensities for Multi-state Systems 138

3.3.4 Interval Estimation of Transition Intensities for Multi-state System 139

References 142

4 Universal Generating Function Method 143

4.1 Mathematical Fundamentals 143

4.1.1 Generating Functions 144

4.1.2 Moment Generating Functions and the z-transform 148

4.1.3 Universal Generating Operator and Universal Generating Function 152

4.1.4 Generalized Universal Generating Operator 155

4.1.5 Universal Generating Function Associated with Stochastic Processes 158

4.2 Universal Generating Function Technique 159

4.2.1 Like-term Collection and Recursive Procedure 159

4.2.2 Evaluating Multi-state System Reliability Indices Using Universal Generating Functions 162

4.2.3 Properties of Composition Operators 167

4.2.4 Universal Generating Function of Subsystems with Elements Connected in Series 170

4.2.5 Universal Generating Function of Subsystems with Elements Connected in Parallel 172

4.2.6 Universal Generating Function of Series-parallel Systems 175

4.2.6 Universal Generating Function of Systems with Bridge Structure 178

4.3 Importance and Sensitivity Analysis Using Universal Generating Function 183

4.4 Estimating Boundary Points for Continuous-state System Reliability Measures 188

4.4.1 Discrete Approximation 189

4.4.2 Boundary Point Estimation 193

References 198

5 Combined Universal Generating Function and Stochastic Process Method 201

5.1 Method Description 202

5.1.1 Performance Stochastic Process for Multi-state Element 202

5.1.2 Multi-state System Reliability Evaluation 207

5.2 Redundancy Analysis for Multi-state Systems 214

5.2.1 Introduction 214

5.2.2 Problem Formulation 216

5.2.3 Model Description 218

5.2.4 Algorithm for Universal Generating Function Computation for Entire Multi-state System 226

5.2.5 Reliability Measures Computation for Entire Multi-state System 228

5.3 Case Studies 228

References 234

6 Reliability-associated Cost Assessment and Management Decisions for Multi-state Systems 237

6.1 Basic Life Cycle Cost Concept 238

6.2 Reliability-associated Cost and Practical Cost-reliability Analysis 242

6.2.1 Case Study 1: Air Conditioning System 243

6.2.2 Case Study 2: Feed Water Pumps for Power Generating Unit 257

6.3 Practical Cost-reliability Optimization Problems for Multi-state Systems 265

6.3.1 Multi-state System Structure Optimization 265

6.3.2 Single-stage Expansion of Multi-state Systems 270

References 272

7 Aging Multi-state Systems 273

7.1 Markov Model and Markov Reward Model for Increasing Failure Rate Function 273

7.1.1 Case Study: Multi-state Power Generating Unit 275

7.2 Numerical Methods for Reliability Computation for Aging Multi-state System 281

7.2.1 Bound Approximation of Increasing Failure Rate Function 283

7.2.2 Availability Bounds for Increasing Failure Rate Function 285

7.2.3 Total Expected Reward Bounds for Increasing Failure Rate Function 287

7.3 Reliability-associated Cost Assessment for Aging Multi-state System 291

7.3.1 Case Study: Maintenance Investigation for Aging Air Conditioning System 293

7.4 Optimal Corrective Maintenance Contract Planning for Aging Multi-state System 299

7.4.1 Algorithm for Availability and Total Expected Cost Bound Estimation 301

7.4.2 Optimization Technique Using Genetic Algorithms 302

7.4.3 Case Study: Optimal Corrective Maintenance Contract for Aging Air Conditioning System 303

7.5 Optimal Preventive Replacement Policy for Aging Multi-state Systems 310

7.5.1 Problem Formulation 311

7.5.2 Implementing the Genetic Algorithm 313

7.5.3 Case Study: Optimal Preventive Maintenance for Aging Water Desalination System 315

References 318

8 Fuzzy Multi-state System: General Definition and Reliability Assessment 321

8.1 Introduction 321

8.2 Key Definitions and Concepts of a Fuzzy Multi-state System 323

8.3 Reliability Evaluation of Fuzzy Multi-state Systems 336

8.3.1 Fuzzy Universal Generating Functions: Definitions and Properties 336

8.3.2 Availability Assessment for Fuzzy Multi-state Systems 337

8.3.3 Fuzzy Universal Generating Function for Series-parallel Fuzzy Multi-state Systems 338

8.3.4 Illustrative Examples 343

References 346

Appendix A Heuristic Algorithms as a General Optimization Technique 347

A.1 Introduction 347

A.2 Parameter Determination Problems 355

A.3 Partition and Allocation Problems 356

A.4 Mixed Partition and Parameter Determination Problems 359

A.5 Sequencing Problems 360

A.6 Determination of Solution Fitness 362

A.7 Basic Genetic Algorithm Procedures and Reliability Application 364

References 365

Appendix B Parameter Estimation and Hypothesis Testing for Non-homogeneous Poisson Process 367

B.1 Homogeneous Poisson Process 367

B.2 Non-homogeneous Poisson Process 368

B.2.1 General Description of Non-homogeneous Poisson Process 368

B.2.2 Hypothesis Testing 370

B.2.3 Computer-intensive Procedure for Testing the Non-homogeneous Poisson Process Hypothesis 372

References 375

Appendix C MATLAB® Codes for Examples and Case Study Calculation 377

C.1 Using MATLAB® ODE Solvers 377

C.2 MATLAB® Code for Example 2.2 377

C.3 MATLAB® Code for Example 2.3 378

C.4 MATLAB® Code for Example 2.4 379

C.5 MATLAB® Code for Air Conditioning System (Case Study 6.2.1) 381

C.5.1 Calculating Average Availability 381

C.5.2 Calculating Total Number of System Failures 383

C.5.3 Calculating Mean Time lo System Failure 384

C.5.4 Calculating Probability of Failure-free Operation 386

C.6 MATLAB® Code for Multi-state Power Generation Unit (Case Study 7.1.1) 387

C.6.1 Calculating Average Availability 387

C.6.2 Calculating Total Number of System Failures 388

C.6.3 Calculating Reliability Function 388

References 389

Index 391

Editorial Reviews

MATLAB codes provided in the appendix of the book enhance its usefulness for a serious minded researcher who likes to go in depth into the study of MSS.

The book is a stand alone resource and does not require any prior knowledge on the part of a reader. This feature is likely to be appreciated by beginners who are being initiated to MSS reliability analysis. This feature will be particularly useful to the practicing engineers and managers who do not have time to look around and search all the supporting resources. The reviewer feels that this book would also be found useful for researchers, students and teachers.

Krishna B. Misra, International Journal of Performability Engineering

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