Lisnianski / Frenkel / Karagrigoriou Recent Advances in Multi-state Systems Reliability

Theory and Applications
1. Auflage 2018
ISBN: 978-3-319-63423-4
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 378 Seiten

Reihe: Springer Series in Reliability Engineering

This book addresses a modern topic in reliability: multi-state and continuous-state system reliability, which has been intensively developed in recent years. It offers an up-to-date overview of the latest developments in reliability theory for multi-state systems, engineering applications to a variety of technical problems, and case studies that will be of interest to reliability engineers and industrial managers. It also covers corresponding theoretical issues, as well as case studies illustrating the applications of the corresponding theoretical advances. The book is divided into two parts: Modern Mathematical Methods for Multi-state System Reliability Analysis (Part 1), and Applications and Case Studies (Part 2), which examines real-world multi-state systems. It will greatly benefit scientists and researchers working in reliability, as well as practitioners and managers with an interest in reliability and performability analysis. It can also be used as a textbook or as a supporting text for postgraduate courses in Industrial Engineering, Electrical Engineering, Mechanical Engineering, Applied Mathematics, and Operations Research.

Anatoly Lisnianski is an engineering expert at the Reliability Department of the Israel Electric Corporation Ltd., an adjunct senior lecturer at Haifa University, and scientific supervisor of the Centre for Reliability and Risk Management at Shamoon College of Engineering, Israel. He received his MSc degree (1975) in Electrical Engineering from the University of Information Technology, Precision Mechanics and Optics, St. Petersburg, and his PhD degree (1984) in Reliability from the Federal Scientific & Production Centre 'Aurora' in St. Petersburg, where he served as a senior researcher until 1989. Since 1991 he has been working at the Israel Electric Corporation, Haifa, Israel, where he has specialized in reliability and applied probability. He is a Senior Member of the IEEE and Member of the Israel Society of Quality and Israel Statistical Association. He is the author or co-author of more than 150 research papers in the field of reliability and applied probability and co-author of two books. Alex Karagrigoriou is a Professor of Probability and Statistics and Director of Graduate Studies in Statistics and Actuarial-Financial Mathematics at the Department of Mathematics of the University of the Aegean, Greece. He studied at the University of Maryland, USA (MA, 1988, PhD, 1992), worked at the United States Department of Agriculture (USDA) and the Institute of Statistical Sciences, Taiwan, and taught at the Universities of Maryland, Athens, Aegean, Cyprus and Hellenic Open University. His research activities cover areas such as statistical modeling, model selection criteria, biostatistics, information theory, time series analysis, stochastic modeling, economic demography, finance and reliability theory. He has published over 100 research articles and has extensive experience in the design and execution of research projects involving the statistical analysis of medical, biomedical, technological, socioeconomic and economic data. Ilia Frenkel is the Chair of the Center for Reliability and Risk Management and a Senior Lecturer at the Industrial Engineering and Management Department, Shamoon College of Engineering, Israel. He received his MSc in Applied Mathematics from Voronezh State University, Russia, and his PhD in Operational Research and Computer Science from the Institute of Economy, Ukrainian Academy of Science, former USSR. He has more than 40 years of academic and teaching experience at universities and institutions in Russia and Israel. He has specialized in applied statistics and reliability with applications to preventive maintenance. He is an Editor and a member of the editorial board for numerous scientific and professional journals. He has published one book and more than 50 scientific articles and book chapters in the fields of reliability, applied statistics, and production and operation management.

Autoren/Hrsg.

Lisnianski, Anatoly

Frenkel, Ilia

Karagrigoriou, Alex

Inhaltsverzeichnis

1;Preface;6
1.1;Part I Modern Mathematical Methods for Multi-state System Reliability Analysis;7
1.2;Part II Applications and Case Studies;8
2;Contents;11
3;Contributors;13
4;Modern Mathematical Methods for Multi-state System Reliability Analysis;16
5;Reliability of a Network with Heterogeneous Components;17
5.1;1 Introduction;17
5.2;2 The Principal Model: Two Types of Components;19
5.2.1;2.1 Network Description;19
5.2.2;2.2 One Type of Components;19
5.2.3;2.3 Two Types of Components;21
5.2.4;2.4 Counting (k,r)-failure Vectors;22
5.2.5;2.5 Counting the Number C(k,r) of (k,r)-failure Sets;24
5.2.6;2.6 Simulation Algorithm for Estimating F(k,r);25
5.3;3 Reliability of a Transportation Network;26
5.3.1;3.1 Description of the Network. Reliable Nodes, Unreliable Edges;26
5.3.2;3.2 Unreliable Nodes;28
5.4;4 "03F13F4 g(k,r)"03F13F4 Matrix and ``Shock Process'' Trajectories;29
5.5;5 More Than Two Types of Components---Concluding Remarks;31
5.6;References;31
6;2 Reliability Analysis of Complex Multi-state System with Common Cause Failure Based on DS Evidence Theory and Bayesian Network;33
6.1;Abstract;33
6.2;1 Introduction;34
6.3;2 Multi-state Bayesian Network Under Evidence Theory;35
6.3.1;2.1 The Node Definition of Multi-state Bayesian Network Under Evidence Theory;35
6.3.2;2.2 The Multi-state Bayesian Network Reasoning Under Evidence Theory;36
6.4;3 Reliability Modeling of System with Multiple CCFGs;38
6.4.1;3.1 A Modified ? Factor Model for CCFGs;38
6.4.2;3.2 Model Limitation and Solution;41
6.4.3;3.3 The Bayesian Network Node with CCFGs;42
6.5;4 Reliability Analysis of Feeding Control System for CNC HDHLs with Multiple CCFGs;43
6.5.1;4.1 Fault Tree Modeling of Feeding Control System;43
6.5.2;4.2 The BN Modeling and CCFGs Fusion;44
6.5.3;4.3 Reliability Analysis of Feeding Control System by Using DSET Based BN;46
6.6;5 Conclusions;50
6.7;Acknowledgements;51
6.8;References;51
7;3 A D-MMAP to Model a Complex Multi-state System with Loss of Units;53
7.1;Abstract;53
7.2;1 Introduction;53
7.3;2 The System and the Model;55
7.3.1;2.1 The State Space;57
7.3.2;2.2 Analyzing Events;58
7.4;3 The Markovian Arrival Process with Marked Arrivals;61
7.5;4 The Transient Distribution;63
7.6;5 Measures;64
7.6.1;5.1 Availability;64
7.6.2;5.2 Reliability;64
7.6.3;5.3 Mean Sojourn Times;64
7.6.4;5.4 Mean Number of Events;66
7.7;6 A Numerical Example;66
7.8;7 Conclusions;69
7.9;Acknowledgements;69
7.10;Appendix;69
7.11;References;72
8;Modeling and Inference for Multi-state Systems;73
8.1;1 Introduction;73
8.2;2 A Special Case of Semi-Markov Multi-state Systems;74
8.3;3 Parametric Specification of the System;77
8.4;4 Maximum Likelihood Estimation;79
8.5;5 Concluding Remarks;82
8.6;References;83
9;Optimizing Availability and Performance of a Two-Unit Redundant Multi-state Deteriorating System;85
9.1;1 Introduction;85
9.2;2 Description of a Two-Unit System with Maintenance;87
9.2.1;2.1 Two-Unit System with Minimal and Major Maintenance;88
9.2.2;2.2 Two-Unit System with Minimal or Major Maintenance Only;90
9.3;3 Model Assumption and Sojourn Time Distributions;91
9.4;4 Semi-Markov Modelling;92
9.5;5 Asymptotic Dependability and Performance Measures;94
9.5.1;5.1 Asymptotic Availability;94
9.5.2;5.2 Expected Downtime Cost;94
9.5.3;5.3 Expected Cost Due to Maintenance and Unavailability;95
9.6;6 Optimization Problems;97
9.6.1;6.1 Maximization of the Asymptotic Availability;97
9.6.2;6.2 Minimization of the Overall Cost;97
9.6.3;6.3 Multi-objective Optimization Using Weighted Sum Approach;98
9.7;7 Numerical example;98
9.8;8 Conclusions and Future Work;109
9.9;References;118
10;Phase-Type Models and Their Extension to Competing Risks;120
10.1;1 Introduction;120
10.2;2 Phase-Type Distributions;121
10.2.1;2.1 Model Specification;122
10.3;3 Classical Competing Risks;123
10.3.1;3.1 Distributional Properties of Competing Risks;123
10.3.2;3.2 The Identifiability Problem of Competing Risks;124
10.4;4 Phase-Type Models for Competing Risks;124
10.4.1;4.1 Model Specification for Phase-Type Based Competing Risks;124
10.5;5 Statistical Inference in Coxian Phase-Type Models;126
10.5.1;5.1 Coxian Survival Models;126
10.5.2;5.2 Model 1: Coxian Competing Risks Model with K=2 Transient States and m=2 Absorbing States;126
10.5.3;5.3 Parametric Identifiability of Model 1;128
10.5.4;5.4 Identifiability of Coxian Phase-Type Models;129
10.5.5;5.5 Case Study: Pneumonia on Admission to Intensive Care Unit (;130
10.6;6 Statistical Inference for General Phase-Type Distributions;131
10.7;References;132
11;7 A Study on Repairable Series Systems with Markov Repairable Units;134
11.1;Abstract;134
11.2;1 Introduction;135
11.3;2 Model Assumptions;137
11.4;3 General Repairable Series System;141
11.5;4 General Repairable Series System with Neglected Failures;143
11.6;5 Phased-Mission Repairable Series System;146
11.7;6 Phased-Mission Repairable Series System with Neglected Failures;154
11.8;7 Numerical Examples;158
11.9;8 Conclusions;169
11.10;Acknowledgements;169
11.11;References;169
12;8 Dynamic Performance of Series Parallel Multi-state Systems with Standby Subsystems or Repairable Binary Elements;171
12.1;Abstract;171
12.2;1 Introduction;173
12.3;2 System Model and Performance Metrics;174
12.3.1;2.1 Generic Model of Series Parallel MSSs;175
12.3.2;2.2 MSS Dynamic Performance Metrics;175
12.4;3 Obtaining Performance DSCTP for Individual Components;177
12.4.1;3.1 Performance DSCTP for Warm Standby Components;177
12.4.2;3.2 Performance DSCTP for Repairable Binary Elements;178
12.5;4 Examples of Component Performance Evaluation;180
12.5.1;4.1 Warm Standby Components;180
12.5.2;4.2 Repairable Binary Element;181
12.6;5 Obtaining Performance DSCTP for Entire MSS5;183
12.6.1;5.1 UGF (U-Function) Technique;183
12.6.2;5.2 Generalized RBD Method for Multi-state Series-Parallel System;184
12.7;6 Examples of System Performance Evaluation;185
12.7.1;6.1 Systems with Warm Standby Components;185
12.7.2;6.2 Systems with Repairable Binary Elements;186
12.8;7 Summary;188
12.9;References;189
13;Optimal Imperfect Maintenance in a Multi-state System;191
13.1;1 Introduction;191
13.2;2 Modeling the System and Maintenance Policy;193
13.3;3 Cost Optimization Problem;193
13.4;4 Discrete Lifetime Distributions;196
13.4.1;4.1 The Discrete Modified Weibull Distribution;196
13.4.2;4.2 The Discrete Reduced Modified Weibull Distribution;197
13.5;5 Example for Cost Optimal Maintenance;199
13.6;6 Conclusion;204
13.7;References;204
14;10 Reliability Evaluation of Non-repairable Multi-state Systems Considering Survival-Death Markov Processes;206
14.1;Abstract;206
14.2;1 Introduction;207
14.3;2 Multi-state Models and Markov Processes for Non-repairable Components;208
14.3.1;2.1 Model I for Non-repairable Components;210
14.3.2;2.2 Model II for Non-repairable Components;212
14.4;3 Dynamic Reliability Evaluation for Non-repairable Multi-state Systems;213
14.5;4 System Studies;215
14.5.1;4.1 Example 1;215
14.5.2;4.2 Example 2;217
14.5.3;4.3 Example 3;219
14.6;5 Conclusions;222
14.7;Acknowledgements;222
14.8;References;222
15;11 Reliability Assessment of Systems with Dependent Degradation Processes Based on Piecewise-Deterministic Markov Process;224
15.1;Abstract;224
15.2;1 Introduction;225
15.3;2 Dynamic Reliability Models for Systems with Degradation Dependence;226
15.3.1;2.1 Degradation Models;226
15.3.1.1;2.1.1 PBMs;227
15.3.1.2;2.1.2 MSMs;227
15.3.2;2.2 Degradation Model of the System Considering Dependence;228
15.4;3 System Reliability Estimation Method;230
15.5;4 Case Study;232
15.6;5 Conclusion;235
15.7;References;235
16;12 Trade-Off Between Redundancy, Protection, and Imperfect False Targets in Defending Parallel Systems;237
16.1;Abstract;237
16.2;1 Introduction;238
16.3;2 Literature Review;239
16.4;3 Defense of Parallel Systems with Redundancy, Protection, and Imperfect False Targets;241
16.5;4 Conclusions and Future Research;246
16.6;Acknowledgements;247
16.7;References;247
17;13 Optimal Testing Resources Allocation for Improving Reliability Assessment of Non-repairable Multi-state Systems;250
17.1;Abstract;250
17.2;1 Introduction;250
17.3;2 Review of Bayesian Reliability Assessment for MSS;252
17.3.1;2.1 Bayesian Parameter Inference for Multi-state Components;254
17.3.2;2.2 Bayesian Reliability Assessment for Multi-state Systems;257
17.4;3 Optimal Testing Resources Allocation Strategy;258
17.4.1;3.1 Evaluating Performance of Candidate Allocation Schemes;260
17.4.2;3.2 Kriging Model;262
17.4.3;3.3 Optimization Model and Algorithm;264
17.5;4 Illustrative Examples;265
17.5.1;4.1 Example 1;266
17.5.2;4.2 Example 2;269
17.6;5 Conclusion;271
17.7;Acknowledgements;272
17.8;References;272
18;14 Topological Analysis of Multi-state Systems Based on Direct Partial Logic Derivatives;274
18.1;Abstract;274
18.2;1 Introduction;274
18.3;2 Structure Function;275
18.3.1;2.1 Modular Decomposition;276
18.3.2;2.2 Series and Parallel Systems;277
18.4;3 Topological Analysis of Multi-state Systems;278
18.4.1;3.1 Structural Importance Measures;280
18.4.2;3.2 Logical Differential Calculus;281
18.4.2.1;3.2.1 Chain Rule;282
18.5;4 Hand Calculation Example;284
18.6;5 Conclusion;288
18.7;Acknowledgements;289
18.8;References;289
19;Applications and Case Studies;291
20;15 Short-Term Reliability Analysis of Power Plants with Several Combined Cycle Units;292
20.1;Abstract;292
20.2;1 Introduction;293
20.3;2 Lz-Transform Method and Its Application to Reliability Analysis of Power Plant Consisting of Number CCGT Generating Units;295
20.3.1;2.1 A Multi-state Markov Model for a Combined Cycle Generating Unit and Lz-Transform for Its Output Generating Capacity Process;295
20.3.2;2.2 Reliability Analysis for Power System Consisting of Number Combine Cycle Generating Units;299
20.4;3 Numerical Example;301
20.5;4 Summary;305
20.6;References;305
21;16 Reliability Analysis of a Modified IEEE 6BUS RBTS Multi-state System;307
21.1;Abstract;307
21.2;1 Introduction;307
21.3;2 System Analysis—Original System;313
21.4;3 Modified System—Application of the Model;314
21.5;4 Conclusions;323
21.6;References;323
22;17 Lz-Transform Approach for Fault Tolerance Assessment of Various Traction Drives Topologies of Hybrid-Electric Helicopter;326
22.1;Abstract;326
22.2;1 Introduction;326
22.3;2 Comparative Analysis of Two Traction Drive Topologies of Hybrid-Electric Helicopter;328
22.3.1;2.1 Common Description;328
22.3.2;2.2 Operational Scenarios for Various Traction Drive Topologies;329
22.3.2.1;2.2.1 Serial Topology;329
22.3.2.2;2.2.2 Combined Topology;330
22.4;3 Brief Description of the Lz-Transform Method;330
22.5;4 Multi-state Modeling of the Multi Power Source Traction Drive;331
22.5.1;4.1 Systems’ Description;331
22.5.2;4.2 Elements’ Description;333
22.5.2.1;4.2.1 Elements with 2 States;333
22.5.2.2;4.2.2 Element with 3 States;334
22.5.2.3;4.2.3 Element with 4 States;335
22.5.3;4.3 Lz-Transform for Serial Topology System;336
22.5.3.1;4.3.1 Sub-System 1 (SS1s);336
22.5.3.2;4.3.2 Sub-System 2 (SS2s);336
22.5.3.3;4.3.3 Serial Topology System (STS);337
22.5.3.4;4.3.4 Serial Topology System with Energy Storage (STS-ESs);337
22.5.4;4.4 Lz-Transform for Combined Topology System;338
22.5.4.1;4.4.1 Sub-System 1 (SS1c);338
22.5.4.2;4.4.2 Sub-System 2 (SS2);339
22.5.4.3;4.4.3 Sub-System 3 (SS3);339
22.5.4.4;4.4.4 Combined Topology System (CTS);340
22.5.4.5;4.4.5 Combined Topology System with Energy Storage (CTS-ESc);340
22.6;5 Availability and Mean Power Performance Calculation;341
22.7;6 Conclusion;345
22.8;References;346
23;18 Patient Diagnostic State Evolution During Hospitalization: Developing a Model for Measuring Clinical Diagnostic Dynamics;348
23.1;Abstract;348
23.2;1 Introduction;348
23.3;2 Some Basic Definitions;350
23.4;3 The Distance Between Two Diagnoses as a Measure of Their Dissimilarity;350
23.5;4 Some Facts Concerning the Similarities and Differences Between Two Consecutives Diagnoses in Hospital;352
23.6;5 How to Measure Divergence Between Two Sets of Diagnoses;353
23.7;6 Example of Segregation Index Calculations;354
23.8;7 Applying Proposed Measures to Patients Which Passed Only One Ward;356
23.9;8 Brief Summary and Future Research;358
23.10;References;359
24;19 Automated Development of the Markovian Chains to Assess the Availability and Performance of Multi-state Multiprocessor System;360
24.1;Abstract;360
24.2;1 Introduction;361
24.2.1;1.1 Motivation and Approach;361
24.2.2;1.2 Related Works Analysis;361
24.3;2 Description of the Multi-state Multiprocessor System;363
24.4;3 Technique for Automated Development of the Markov Model of the Multi-state Multiprocessor System;364
24.4.1;3.1 Procedures for Behaviour Description of the Multi-state Multiprocessor System;365
24.4.2;3.2 Basic Events;365
24.4.3;3.3 Components of Vector States;365
24.4.4;3.4 Parameters of the Markov Model;366
24.4.5;3.5 Structural-Automated Model for Multi-state Multiprocessor System;366
24.5;4 Availability and Performance Analysis. Markov Model Development;372
24.5.1;4.1 Simulation Results;375
24.6;5 Conclusion;377
24.7;References;378