Stochastic Reliability Modeling, Optimization and Applications

Reliability theory and applications become major concerns of engineers and managers engaged in making high quality products and designing highly reliable systems. This book aims to survey new research topics in reliability theory and useful applied techniques in reliability engineering. Our research group in Nagoya, Japan has continued to study reliability theory and applications for more than twenty years, and has presented and published many good papers at international conferences and in journals. This book focuses mainly on how to apply the results of reliability theory to practical models. Theoretical results of coherent, inspection, and damage systems are summarized methodically, using the techniques of stochastic processes. There exist optimization problems in computer and management sciences and engineering. It is shown that such problems as computer, information and network systems are solved by using the techniques of reliability. Furthermore, some useful techniques applied to the analysis of stochastic models in management science and plants are shown. The reader will learn new topics and techniques, and how to apply reliability models to actual ones. The book will serve as an essential guide to a subject of study for graduate students and researchers and as a useful guide for reliability engineers engaged not only in maintenance work but also in management and computer works. Cover......Page 1 S-Title......Page 2 Title......Page 4 ISBN-13 978-981-4277-43-3......Page 5 Preface......Page 6 List of Contributors......Page 10 Contents......Page 12 1 Introduction......Page 18 Notations......Page 20 2 Coherent Systems......Page 21 3 k-out-of-n systems......Page 28 4 Modules of Coherent Systems......Page 32 5 Probabilistic Aspect of Coherent Systems......Page 36 6 Hazard Transform of Multistate Coherent Systems......Page 40 7 Concluding Remarks......Page 47 References......Page 48 1 Introduction......Page 50 2.1 Shock Arrival......Page 53 2.2 Cumulative Damage......Page 54 2.3 Cumulative Damage Model......Page 55 3 Failure Interaction Models......Page 56 3.1 Age and Damage Limit Model......Page 57 3.2 Numerical Examples......Page 59 3.3 Shock Number and Damage Limit (N; k) Model......Page 60 3.4 Numerical Examples......Page 62 3.5 Age and Shock Number Model......Page 64 3.6 Numerical examples......Page 65 3.7 Conclusions......Page 66 4 Oppotunistic Replacement Model......Page 67 4.1 Age Model......Page 68 4.2 Numerical examples......Page 70 4.3 Damage Limit Model......Page 72 4.4 Numerical Examples......Page 74 4.5 Conclusions......Page 75 References......Page 76 1 Introduction......Page 78 2.1 Model and Assumptions......Page 80 2.3 Numerical Examples......Page 83 3 Periodic Policy for a System with Two Types ofInspection......Page 84 3.1 Model and Assumptions......Page 85 3.2 Optimal Policy......Page 87 4 Periodic Policy for a System with Self-Testing......Page 88 4.1 Model and Assumptions......Page 89 4.2 Optimal Policy......Page 91 4.3 Numerical Examples......Page 93 5 Optimal Policies for a Finite Interval......Page 94 5.1 Periodic Inspection Policy......Page 95 5.2 Sequential Inspection Policy......Page 96 5.3 Numerical Examples......Page 97 6 Conclusions......Page 98 References......Page 99 1 Introduction......Page 102 2 Time Warp Simulation and Hybrid State Saving......Page 104 3 Analytical Model......Page 110 4 Implementation of A Concrete Application: A Parallel Distributed Logic Circuit Simulator......Page 119 5 Numerical Examples......Page 122 6 Concluding Remarks......Page 128 References......Page 129 1 Introduction......Page 130 2 Optimal Reset Number of a Microprocessor System with Network Processing......Page 132 2.1 Model and Analysis......Page 133 (1) Policy 1......Page 137 (2) Policy 2......Page 138 2.3 Numerical Example......Page 139 3 Reliability Analysis for an Applet Execution Process......Page 140 3.1 Model and Analysis......Page 141 3.2 Optimal Policy......Page 146 3.3 Numerical Example......Page 147 4.1 Model and Analysis......Page 148 4.2 Optimal Policy......Page 154 4.3 Numerical Example......Page 155 5 Conclusions......Page 156 References......Page 157 1 Introduction......Page 160 2 Communication System with Rollback Recovery......Page 162 2.1 Reliability Quantities......Page 163 2.2 Optimal Policy......Page 166 3 Mobile Communication System with Error Recovery Schemes......Page 170 3.1 Reliability Quantities......Page 171 3.2 Optimal Policy......Page 175 4 Communication System with Window Flow Control Scheme......Page 176 4.1 Reliability Quantities......Page 177 4.2 Optimal Policy......Page 183 5 Conclusions......Page 185 References......Page 186 1 Introduction......Page 189 2 Cumulative Damage Model......Page 192 2.1 Standard Cumulative Damage Model......Page 193 2.2 Modified Cumulative Damage Model......Page 195 3.1 Incremental and Cumulative Backups......Page 196 3.2 Incremental Backup Policy......Page 198 3.3 Total and Cumulative Backups......Page 199 3.4 Cumulative Backup Policy......Page 202 4 Periodic Backup Policies......Page 207 4.1 Periodic Incremental Backup Policy......Page 208 4.2 Periodic Cumulative Backup Policies......Page 210 5 Conclusions......Page 214 References......Page 215 1 Introduction......Page 217 2 Two-level Recovery Schemes......Page 219 2.1 Performance Analysis......Page 220 2.2 Expected Overhead......Page 224 3 Error Detection by Multiple Modular Redundancies......Page 225 3.2 Performance Analysis......Page 226 4 Sequential Checkpoint Intervals for Error Detection......Page 229 4.1 Performance Analysis......Page 230 4.2 Modified Model......Page 234 5 Random Checkpoint Models......Page 238 (2) Scheme 2......Page 239 5.2 Majority Decision System......Page 247 References......Page 249 1 Introduction......Page 252 2 Missile Maintenance......Page 254 2.1 Expected Cost......Page 256 (1) Exponential Case......Page 257 (2) Weibull Case......Page 258 2.3 Concluding Remarks......Page 259 3 Phased Array Radar Maintenance......Page 260 3.1 Cyclic Maintenance......Page 261 3.2 Delayed Maintenance......Page 264 3.3 Concluding Remarks......Page 265 4 Self-diagnosis for FADEC......Page 266 4.1 Double Module System......Page 268 4.2 Triple Module System......Page 270 4.3 N Module System......Page 272 5 Co-generation System Maintenance......Page 273 5.1 Model and Assumptions......Page 274 5.2 Expected Cost......Page 275 5.3 Optimal Policy......Page 276 6 Aged Fossil-fired Power Plant Maintenance......Page 278 6.1 Model 1......Page 280 6.2 Model 2......Page 283 References......Page 285 1 Introduction......Page 288 2 Liquidation Profit Policy......Page 289 2.1 Model 1......Page 291 2.2 Model 2......Page 292 3 Prepayment Risk......Page 295 3.1 Model 1: Interval Estimation......Page 297 3.3 Optimal Policies......Page 298 3.4 Numerical Example......Page 299 4 Loan Interest Rate......Page 301 4.1 Expected Earning without Bankruptcy......Page 302 4.2 Expected Earning with Bankruptcy......Page 303 4.3 Numerical Examples......Page 306 References......Page 308 Cover 1 S-Title 2 Title 4 Copyright 5 © 2010 World Scientific Publishing Co. Pte. Ltd. 5 ISBN-13 978-981-4277-43-3 5 Preface 6 List of Contributors 10 Contents 12 Chapter 1: Multistate Coherent Systems 18 1 Introduction 18 Notations 20 2 Coherent Systems 21 3 k-out-of-n systems 28 4 Modules of Coherent Systems 32 5 Probabilistic Aspect of Coherent Systems 36 6 Hazard Transform of Multistate Coherent Systems 40 7 Concluding Remarks 47 References 48 Chapter 2: Cumulative Damage Models 50 1 Introduction 50 2 Standard Cumulative Damage Model 53 2.1 Shock Arrival 53 2.2 Cumulative Damage 54 2.3 Cumulative Damage Model 55 3 Failure Interaction Models 56 3.1 Age and Damage Limit Model 57 3.2 Numerical Examples 59 3.3 Shock Number and Damage Limit (N; k) Model 60 3.4 Numerical Examples 62 3.5 Age and Shock Number Model 64 3.6 Numerical examples 65 3.7 Conclusions 66 4 Oppotunistic Replacement Model 67 4.1 Age Model 68 4.2 Numerical examples 70 4.3 Damage Limit Model 72 4.4 Numerical Examples 74 4.5 Conclusions 75 References 76 Chapter 3: Extended Inspection Models 78 1 Introduction 78 2 Periodic Policy for a Two-Unit System 80 2.1 Model and Assumptions 80 2.2 Optimal Policy 83 2.3 Numerical Examples 83 3 Periodic Policy for a System with Two Types ofInspection 84 3.1 Model and Assumptions 85 3.2 Optimal Policy 87 3.3 Numerical Example 88 4 Periodic Policy for a System with Self-Testing 88 4.1 Model and Assumptions 89 4.2 Optimal Policy 91 4.3 Numerical Examples 93 5 Optimal Policies for a Finite Interval 94 5.1 Periodic Inspection Policy 95 5.2 Sequential Inspection Policy 96 5.3 Numerical Examples 97 6 Conclusions 98 References 99 Chapter 4: Stochastic Analyses for Hybrid StateSaving and Its Experimental Validation 102 1 Introduction 102 2 Time Warp Simulation and Hybrid State Saving 104 3 Analytical Model 110 4 Implementation of A Concrete Application: A Parallel Distributed Logic Circuit Simulator 119 5 Numerical Examples 122 6 Concluding Remarks 128 References 129 Chapter 5: Reliability Analysis of a System Connected with Networks 130 1 Introduction 130 2 Optimal Reset Number of a Microprocessor System with Network Processing 132 2.1 Model and Analysis 133 2.2 Optimal Policies 137 (1) Policy 1 137 (2) Policy 2 138 2.3 Numerical Example 139 3 Reliability Analysis for an Applet Execution Process 140 3.1 Model and Analysis 141 3.2 Optimal Policy 146 3.3 Numerical Example 147 4 Reliability Analysis of a Network Server System with DoS Attacks 148 4.1 Model and Analysis 148 4.2 Optimal Policy 154 4.3 Numerical Example 155 5 Conclusions 156 References 157 Chapter 6: Reliability Analysis of Communication Systems 160 1 Introduction 160 2 Communication System with Rollback Recovery 162 2.1 Reliability Quantities 163 2.2 Optimal Policy 166 3 Mobile Communication System with Error Recovery Schemes 170 3.1 Reliability Quantities 171 3.2 Optimal Policy 175 4 Communication System with Window Flow Control Scheme 176 4.1 Reliability Quantities 177 4.2 Optimal Policy 183 5 Conclusions 185 References 186 Chapter 7: Backup Policies for a Database System 189 1 Introduction 189 2 Cumulative Damage Model 192 2.1 Standard Cumulative Damage Model 193 2.2 Modified Cumulative Damage Model 195 3 Comparison of Backup Schemes and Policies 196 3.1 Incremental and Cumulative Backups 196 3.2 Incremental Backup Policy 198 3.3 Total and Cumulative Backups 199 3.4 Cumulative Backup Policy 202 4 Periodic Backup Policies 207 4.1 Periodic Incremental Backup Policy 208 4.2 Periodic Cumulative Backup Policies 210 5 Conclusions 214 Acknowledgements 215 References 215 Chapter 8: Optimal Checkpoint Intervals for Computer Systems 217 1 Introduction 217 2 Two-level Recovery Schemes 219 2.1 Performance Analysis 220 2.2 Expected Overhead 224 3 Error Detection by Multiple Modular Redundancies 225 3.1 Multiple Modular System 226 3.2 Performance Analysis 226 4 Sequential Checkpoint Intervals for Error Detection 229 4.1 Performance Analysis 230 4.2 Modified Model 234 5 Random Checkpoint Models 238 5.1 Performance Analysis 239 (1) Scheme 1 239 (2) Scheme 2 239 5.2 Majority Decision System 247 6 Conclusion 249 References 249 Chapter 9: Maintenance Models of Miscellaneous Systems 252 1 Introduction 252 2 Missile Maintenance 254 2.1 Expected Cost 256 2.2 Optimal Policies 257 (1) Exponential Case 257 (2) Weibull Case 258 2.3 Concluding Remarks 259 3 Phased Array Radar Maintenance 260 3.1 Cyclic Maintenance 261 3.2 Delayed Maintenance 264 3.3 Concluding Remarks 265 4 Self-diagnosis for FADEC 266 4.1 Double Module System 268 4.2 Triple Module System 270 4.3 N Module System 272 4.4 Concluding Remarks 273 5 Co-generation System Maintenance 273 5.1 Model and Assumptions 274 5.2 Expected Cost 275 5.3 Optimal Policy 276 5.4 Concluding Remarks 278 6 Aged Fossil-fired Power Plant Maintenance 278 6.1 Model 1 280 6.2 Model 2 283 6.3 Concluding Remarks 285 References 285 Chapter 10: Management Policies for Stochastic Models with Monetary Facilities 288 1 Introduction 288 2 Liquidation Profit Policy 289 2.1 Model 1 291 2.2 Model 2 292 3 Prepayment Risk 295 3.1 Model 1: Interval Estimation 297 3.2 Model 2: Linear Estimation 298 3.3 Optimal Policies 298 3.4 Numerical Example 299 4 Loan Interest Rate 301 4.1 Expected Earning without Bankruptcy 302 4.2 Expected Earning with Bankruptcy 303 4.3 Numerical Examples 306 References 308 "Reliability theory and applications become major concerns of engineers and managers engaged in making high quality products and designing highly reliable systems. This book aims to survey new research topics in reliability theory and useful applied techniques in reliability engineering." "The reader will learn new topics and techniques, and how to apply reliability models to actual ones. The book will serve as an essential guide to a subject of study for graduate students and researchers and as a useful guide for reliability engineers engaged not only in maintenance work but also in management and computer works."--Jacket