Lisnianski / Frenkel / Ding Multi-state System Reliability Analysis and Optimization for Engineers and Industrial Managers

1. Auflage 2010
ISBN: 978-1-84996-320-6
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 393 Seiten

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.

Autoren/Hrsg.

Lisnianski, Anatoly

Frenkel, Ilia

Ding, Yi

Inhaltsverzeichnis

1;Preface;6
2;Contents;10
3;1 Multi-state Systems in Nature and in Engineering;15
3.1;1.1 Multi-state Systems in the Real World: General Concepts;15
3.2;1.2 Main Definitions and Properties;22
3.2.1;1.2.1 Generic Multi-state System Model;22
3.2.2;1.2.2 Main Properties of Multi-state Systems;27
3.2.2.1;1.2.2.1 Relevancy of System Elements;27
3.2.2.2;1.2.2.2 Coherency;28
3.2.2.3;1.2.2.3 Homogeneity;29
3.3;1.3 Multi-state System Reliability and Its Measures;30
3.3.1;1.3.1 Acceptable and Unacceptable States. Failure Criteria;30
3.3.2;1.3.2 Relevancy and Coherency in Multi-state System Reliability Context;31
3.3.3;1.3.3 Multi-state System Reliability Measures;32
3.4;References;41
4;2 Modern Stochastic Process Methods for Multi-state System Reliability Assessment;43
4.1;2.1 General Concepts of Stochastic Process Theory;44
4.2;2.2 Markov Models: Discrete-time Markov Chains;48
4.2.1;2.2.1 Basic Definitions and Properties;48
4.2.2;2.2.2 Computation of n-step Transition Probabilities and State Probabilities;50
4.3;2.3 Markov Models: Continuous-time Markov Chains;54
4.3.1;2.3.1 Basic Definitions and Properties;54
4.3.2;2.3.2 Markov Models for Evaluating the Reliability of Multi-state Elements;62
4.3.2.1;2.3.2.1 Non-repairable Multi-state Element;62
4.3.2.2;2.3.2.2 Repairable Multi-state Elements;71
4.3.3;2.3.3 Markov Models for Evaluating the Reliability of Multi-state Systems;80
4.4;2.4 Markov Reward Models;93
4.4.1;2.4.1 Basic Definition and Model Description;93
4.4.2;2.4.2 Computation of Multi-state System Reliability Measures Using Markov Reward Models;98
4.4.2.1;2.4.2.1 Multi-state System with Variable Demand;98
4.4.2.2;2.4.2.2 Combined Performance-demand Model;100
4.4.2.3;2.4.2.3 Reward Determination for Computation of Multi-state System Reliability Indices;104
4.5;2.5 Semi-Markov Models;113
4.5.1;2.5.1 Embedded Markov Chain and Definition of Semi-Markov Process;114
4.5.2;2.5.2 Evaluation of Reliability Indices Based on Semi-Markov Processes;119
4.6;References;127
5;3 Statistical Analysis of Reliability Data for Multi-state Systems;130
5.1;3.1 Basic Concepts of Statistical Estimation Theory;130
5.1.1;3.1.1 Properties of Estimators;131
5.1.2;3.1.2 Main Estimation Methods;133
5.1.2.1;3.1.2.1 Point Estimation;133
5.1.2.2;3.1.2.2 Interval Estimation;138
5.2;3.2 Classical Parametric Estimation for Binary-state System;140
5.2.1;3.2.1 Basic Considerations;140
5.2.2;3.2.2 Exponential Distribution Point Estimation;141
5.2.3;3.2.3 Interval Estimation for Exponential Distribution;144
5.3;3.3 Estimation of Transition Intensities via Output Performance Observations;145
5.3.1;3.3.1 Multi-state Markov Model and Observed Reliability Data. Problem Formulation;145
5.3.2;3.3.2 Method Description;148
5.3.3;3.3.3 Algorithm for Point Estimation of Transition Intensities for Multi-state System;151
5.3.4;3.3.4 Interval Estimation of Transitions Intensities for Multi-state System;152
5.4;References;155
6;4 Universal Generating Function Method;156
6.1;4.1 Mathematical Fundamentals;156
6.1.1;4.1.1 Generating Functions;157
6.1.2;4.1.2 Moment Generating Functions and the z-transform;161
6.1.3;4.1.3 Universal Generating Operator and Universal Generating Function;165
6.1.4;4.1.4 Generalized Universal Generating Operator;168
6.1.5;4.1.5 Universal Generating Function Associated with Stochastic Processes;171
6.2;4.2 Universal Generating Function Technique;172
6.2.1;4.2.1 Like-terms Collection and Recursive Procedure;172
6.2.2;4.2.2 Evaluating Multi-state System Reliability Indices Using Universal Generating Function;175
6.2.3;4.2.3 Properties of Composition Operators;180
6.2.4;4.2.4 Universal Generating Function of Subsystems with Elements Connected in Series;183
6.2.5;4.2.5 Universal Generating Function of Subsystems with Elements Connected in Parallel;185
6.2.6;4.2.6 Universal Generating Function of Series-parallel Systems;188
6.2.7;4.2.6 Universal Generating Function of Systems with Bridge Structure;191
6.2.7.1;4.2.6.1 Flow Transmission Multi-state System;192
6.2.7.2;4.2.6.2 Task Processing Multi-state System;193
6.3;4.3 Importance and Sensitivity Analysis Using Universal Generating Function;196
6.4;4.4 Estimating Boundary Points for Continuous-state System Reliability Measures;201
6.4.1;4.4.1 Discrete Approximation;202
6.4.2;4.4.2 Boundary Point Estimation;206
6.5;References;211
7;5 Combined Universal Generating Function and Stochastic Process Method;214
7.1;5.1 Method Description;215
7.1.1;5.1.1 Performance Stochastic Process for Multi-state Element;215
7.1.1.1;5.1.1.1 Markov Model for Multi-state Element;216
7.1.1.2;5.1.1.2 Semi-Markov Model for Multi-state Element;217
7.1.2;5.1.2 Multi-state System Reliability Evaluation;220
7.2;5.2 Redundancy Analysis for Multi-state Systems;227
7.2.1;5.2.1 Introduction;227
7.2.2;5.2.2 Problem Formulation;229
7.2.3;5.2.3 Model Description;231
7.2.3.1;5.2.3.1 Model for Multi-state Element;231
7.2.3.2;5.2.3.2 Model for Main Multi-state System and Its Demand;233
7.2.3.3;5.2.3.3 Model for Reserve Multi-state System and Its Demand;235
7.2.3.4;5.2.3.4 Model for Reserve System Obligation and Connecting System;237
7.2.3.5;5.2.3.5 Model for Entire Multi-state System;239
7.2.4;5.2.4 Algorithm for Universal Generating Function Computation for Entire Multi-state System;239
7.2.5;5.2.5 Reliability Measures Computation for Entire Multi-state System;241
7.3;5.3 Case Studies;241
7.4;References;247
8;6 Reliability-associated Cost Assessment and Management Decisions for Multi-state Systems;249
8.1;6.1 Basic Life Cycle Cost Concept;250
8.2;6.2 Reliability-associated Cost and Practical Cost-reliability Analysis;254
8.2.1;6.2.1 Case Study 1: Air Conditioning System;255
8.2.2;6.2.2 Case Study 2: Feed Water Pumps for Power Generating Unit;269
8.3;6.3 Practical Cost-reliability Optimization Problems for Multi-state Systems;277
8.3.1;6.3.1 Multi-state System Structure Optimization;277
8.3.1.1;6.3.1.1 Problem Formulation;278
8.3.1.2;6.3.1.2. Implementing the Genetic Algorithm;278
8.3.2;6.3.2 Single-stage Expansion of Multi-state Systems;282
8.4;References;284
9;7 Aging Multi-state Systems;285
9.1;7.1 Markov Model and Markov Reward Model for Increasing Failure Rate Function;285
9.1.1;7.1.1 Case Study: Multi-state Power Generating Unit;287
9.2;7.2 Numerical Methods for Reliability Computation for Aging Multi-state System;293
9.2.1;7.2.1 Bound Approximation of Increasing Failure Rate Function;295
9.2.2;7.2.2 Availability Bounds for Increasing Failure Rate Function;297
9.2.3;7.2.3 Total Expected Reward Bounds for Increasing Failure Rate Function;299
9.3;7.3 Reliability-associated Cost Assessment for Aging Multi-state System;303
9.3.1;7.3.1 Case Study: Maintenance Investigation for Aging Air Conditioning System;305
9.4;7.4 Optimal Corrective Maintenance Contract Planning for Aging Multi-state System;311
9.4.1;7.4.1 Algorithm for Availability and Total Expected Cost Bound Estimation;313
9.4.2;7.4.2 Optimization Technique Using Genetic Algorithms;314
9.4.3;7.4.3 Case Study: Optimal Corrective Maintenance Contract for Aging Air Conditioning System;315
9.4.3.1;7.4.3.1 System Description and Data;315
9.5;7.5 Optimal Preventive Replacement Policy for Aging Multi-state Systems;322
9.5.1;7.5.1 Problem Formulation;323
9.5.2;7.5.2 Implementing the Genetic Algorithm;326
9.5.3;7.5.3 Case Study: Optimal Preventive Maintenance for Aging Water Desalination System;327
9.6;References;330
10;8 Fuzzy Multi-state System: General Definition and Reliability Assessment;332
10.1;8.1 Introduction;332
10.2;8.2 Key Definitions and Concepts of a Fuzzy Multi-state System;333
10.3;8.3 Reliability Evaluation of Fuzzy Multi-state Systems;347
10.3.1;8.3.1 Fuzzy Universal Generating Function: Definitions and Properties;347
10.3.2;8.3.2 Availability Assessment for Fuzzy Multi-state Systems;348
10.3.3;8.3.3 Fuzzy Universal Generating Function for Series-parallel Fuzzy Multi-state Systems;349
10.3.4;8.3.4 Illustrative Examples;354
10.4;References;357
11;Appendix A - Heuristic Algorithms as a General Optimization Technique;358
11.1;A.1 Introduction;358
11.2;A.2 Parameter Determination Problems;366
11.3;A.3 Partition and Allocation Problems;367
11.4;A.4 Mixed Partition and Parameter Determination Problems;370
11.5;A.5 Sequencing Problems;371
11.6;A.6 Determination of Solution Fitness;373
11.7;A.7 Basic Genetic Algorithm Procedures and Reliability Application;375
11.8;References;376
12;Appendix B - Parameter Estimation and Hypothesis Testingfor Non-homogeneous Poisson Process;378
12.1;B.1 Homogeneous Poisson Process;378
12.2;B.2 Non-homogeneous Poisson Process;379
12.2.1;B.2.1 General Description of Non-homogeneous Poisson Process;379
12.2.2;B.2.2 Hypothesis Testing;381
12.2.3;B.2.3 Computer-intensive Procedure for Testing the Non-homogeneous Poisson Process Hypothesis;383
12.3;References;386
13;Appendix C - MATLAB® Codes for Examples and Case Study Calculation;388
13.1;C.1 Using MATLAB® ODE Solvers;388
13.2;C.2 MATLAB® Code for Example 2.2;388
13.3;C.3 MATLAB® Code for Example 2.3;389
13.4;C.4 MATLAB® Code for Example 2.4;390
13.5;C.5 MATLAB® Code for Air Conditioning System (Case Study 6.2.1);392
13.5.1;C.5.1 Calculating Average Availability;392
13.5.2;C.5.2 Calculating Total Number of System Failures;394
13.5.3;C.5.3 Calculating Mean Time to System Failure;395
13.5.4;C.5.4 Calculating Probability of Failure-free Operation;397
13.6;C.6 MATLAB® Code for Multi-state Power Generation Unit (Case Study 7.1.1);398
13.6.1;C.6.1 Calculating Average Availability;398
13.6.2;C.6.2 Calculating Total Number of System Failures;399
13.6.3;C.6.3 Calculating Reliability Function;399
13.7;References;400
14;Index;401