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| موضوع: كتاب Handbook of Reliability Engineering - Hoang Pham الثلاثاء 12 ديسمبر 2017, 8:24 am | |
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أخوانى فى الله أحضرت لكم كتاب Handbook of Reliability Engineering Hoang Pham
ويتناول الموضوعات الأتية :
Contents PART I. System Reliability and Optimization 1 Multi-state k-out-of-n Systems Ming J. Zuo, Jinsheng Huang and Way Kuo . 3 1.1 Introduction 3 1.2 Relevant Concepts in Binary Reliability Theory . 3 1.3 Binary k-out-of-n Models . 4 1.3.1 The k-out-of-n:G System with Independently and Identically Distributed Components . 5 1.3.2 Reliability Evaluation Using Minimal Path or Cut Sets . 5 1.3.3 Recursive Algorithms 6 1.3.4 Equivalence Between a k-out-of-n:G System and an (n ? k + 1)-out-of-n:F system 6 1.3.5 The Dual Relationship Between the k-out-of-n G and F Systems 7 1.4 Relevant Concepts in Multi-state Reliability Theory 8 1.5 A Simple Multi-state k-out-of-n:G Model 10 1.6 A Generalized Multi-state k-out-of-n:G System Model . 11 1.7 Properties of Generalized Multi-state k-out-of-n:G Systems 13 1.8 Equivalence and Duality in Generalized Multi-state k-out-of-n Systems 15 2 Reliability of Systems with Multiple Failure Modes Hoang Pham . 19 2.1 Introduction 19 2.2 The Series System . 20 2.3 The Parallel System 21 2.3.1 Cost Optimization 21 2.4 The Parallel–Series System 22 2.4.1 The Profit Maximization Problem 23 2.4.2 Optimization Problem 24 2.5 The Series–Parallel System 25 2.5.1 Maximizing the Average System Profit . 26 2.5.2 Consideration of Type I Design Error 27 2.6 The k-out-of-n Systems 27 2.6.1 Minimizing the Average System Cost 29 2.7 Fault-tolerant Systems 32 2.7.1 Reliability Evaluation 33xii Contents 2.7.2 Redundancy Optimization 34 2.8 Weighted Systems with Three Failure Modes 34 3 Reliabilities of Consecutive-k Systems Jen-Chun Chang and Frank K. Hwang 37 3.1 Introduction 37 3.1.1 Background 37 3.1.2 Notation . 38 3.2 Computation of Reliability 39 3.2.1 The Recursive Equation Approach . 39 3.2.2 The Markov Chain Approach 40 3.2.3 Asymptotic Analysis . 41 3.3 Invariant Consecutive Systems 41 3.3.1 Invariant Consecutive-2 Systems 41 3.3.2 Invariant Consecutive-k Systems 42 3.3.3 Invariant Consecutive-k G System 43 3.4 Component Importance and the Component Replacement Problem . 43 3.4.1 The Birnbaum Importance 44 3.4.2 Partial Birnbaum Importance 45 3.4.3 The Optimal Component Replacement . 45 3.5 The Weighted-consecutive-k-out-of-n System 47 3.5.1 The Linear Weighted-consecutive-k-out-of-n System . 47 3.5.2 The Circular Weighted-consecutive-k-out-of-n System 47 3.6 Window Systems . 48 3.6.1 The f -within-consecutive-k-out-of-n System . 49 3.6.2 The 2-within-consecutive-k-out-of-n System 51 3.6.3 The b-fold-window System . 52 3.7 Network Systems . 53 3.7.1 The Linear Consecutive-2 Network System . 53 3.7.2 The Linear Consecutive-k Network System . 54 3.7.3 The Linear Consecutive-k Flow Network System 55 3.8 Conclusion 57 4 Multi-state System Reliability Analysis and Optimization G. Levitin and A. Lisnianski . 61 4.1 Introduction 61 4.1.1 Notation . 63 4.2 Multi-state System Reliability Measures . 63 4.3 Multi-state System Reliability Indices Evaluation Based on the Universal Generating Function 64 4.4 Determination of u-function of Complex Multi-state System Using Composition Operators 67 4.5 Importance and Sensitivity Analysis of Multi-state Systems 68 4.6 Multi-state System Structure Optimization Problems 72 4.6.1 Optimization Technique . 73 4.6.1.1 Genetic Algorithm 73Contents xiii 4.6.1.2 Solution Representation and Decoding Procedure . 75 4.6.2 Structure Optimization of Series–Parallel System with Capacity-based Performance Measure . 75 4.6.2.1 Problem Formulation . 75 4.6.2.2 Solution Quality Evaluation . 76 4.6.3 Structure Optimization of Multi-state System with Two Failure Modes . 77 4.6.3.1 Problem Formulation . 77 4.6.3.2 Solution Quality Evaluation . 80 4.6.4 Structure Optimization for Multi-state System with Fixed Resource Requirements and Unreliable Sources 83 4.6.4.1 Problem Formulation . 83 4.6.4.2 Solution Quality Evaluation . 84 4.6.4.3 The Output Performance Distribution of a System Containing Identical Elements in the Main Producing Subsystem . 85 4.6.4.4 The Output Performance Distribution of a System Containing Different Elements in the Main Producing Subsystem . 85 4.6.5 Other Problems of Multi-state System Optimization 87 5 Combinatorial Reliability Optimization C. S. Sung, Y. K. Cho and S. H. Song . 91 5.1 Introduction 91 5.2 Combinatorial Reliability Optimization Problems of Series Structure . 95 5.2.1 Optimal Solution Approaches 95 5.2.1.1 Partial Enumeration Method . 95 5.2.1.2 Branch-and-bound Method 96 5.2.1.3 Dynamic Programming 98 5.2.2 Heuristic Solution Approach 99 5.3 Combinatorial Reliability Optimization Problems of a Non-series Structure . 102 5.3.1 Mixed Series–Parallel System Optimization Problems . 102 5.3.2 General System Optimization Problems 106 5.4 Combinatorial Reliability Optimization Problems with Multiple-choice Constraints . 107 5.4.1 One-dimensional Problems . 108 5.4.2 Multi-dimensional Problems 111 5.5 Summary . 113 PART II. Statistical Reliability Theory 6 Modeling the Observed Failure Rate M. S. Finkelstein . 117 6.1 Introduction 117 6.2 Survival in the Plane . 118xiv Contents 6.2.1 One-dimensional Case 118 6.2.2 Fixed Obstacles 119 6.2.3 Failure Rate Process . 121 6.2.4 Moving Obstacles . 122 6.3 Multiple Availability . 124 6.3.1 Statement of the Problem 124 6.3.2 Ordinary Multiple Availability 125 6.3.3 Accuracy of a Fast Repair Approximation 126 6.3.4 Two Non-serviced Demands in a Row 127 6.3.5 Not More than N Non-serviced Demands . 129 6.3.6 Time Redundancy 130 6.4 Modeling the Mixture Failure Rate 132 6.4.1 Definitions and Conditional Characteristics 132 6.4.2 Additive Model 133 6.4.3 Multiplicative Model . 133 6.4.4 Some Examples 135 6.4.5 Inverse Problem . 136 7 Concepts of Stochastic Dependence in Reliability Analysis C. D. Lai and M. Xie . 141 7.1 Introduction 141 7.2 Important Conditions Describing Positive Dependence 142 7.2.1 Six Basic Conditions . 143 7.2.2 The Relative Stringency of the Conditions . 143 7.2.3 Positive Quadrant Dependent in Expectation 144 7.2.4 Associated Random Variables 144 7.2.5 Positively Correlated Distributions . 145 7.2.6 Summary of Interrelationships . 145 7.3 Positive Quadrant Dependent Concept . 145 7.3.1 Constructions of Positive Quadrant Dependent Bivariate Distributions . 146 7.3.2 Applications of Positive Quadrant Dependence Concept to Reliability . 146 7.3.3 Effect of Positive Dependence on the Mean Lifetime of a Parallel System 146 7.3.4 Inequality Without Any Aging Assumption . 147 7.4 Families of Bivariate Distributions that are Positive Quadrant Dependent . 147 7.4.1 Positive Quadrant Dependent Bivariate Distributions with Simple Structures 148 7.4.2 Positive Quadrant Dependent Bivariate Distributions with More Complicated Structures 149 7.4.3 Positive Quadrant Dependent Bivariate Uniform Distributions 150 7.4.3.1 Generalized Farlie–Gumbel–Morgenstern Family of Copulas 151 7.5 Some Related Issues on Positive Dependence 152Contents xv 7.5.1 Examples of Bivariate Positive Dependence Stronger than Positive Quadrant Dependent Condition 152 7.5.2 Examples of Negative Quadrant Dependence 153 7.6 Positive Dependence Orderings . 153 7.7 Concluding Remarks . 154 8 Statistical Reliability Change-point Estimation Models Ming Zhao 157 8.1 Introduction 157 8.2 Assumptions in Reliability Change-point Models 158 8.3 Some Specific Change-point Models . 159 8.3.1 Jelinski–Moranda De-eutrophication Model with a Change Point . 159 8.3.1.1 Model Review . 159 8.3.1.2 Model with One Change Point 159 8.3.2 Weibull Change-point Model 160 8.3.3 Littlewood Model with One Change Point . 160 8.4 Maximum Likelihood Estimation 160 8.5 Application 161 8.6 Summary . 162 9 Concepts and Applications of Stochastic Aging in Reliability C. D. Lai and M. Xie . 165 9.1 Introduction 165 9.2 Basic Concepts for Univariate Reliability Classes 167 9.2.1 Some Acronyms and the Notions of Aging . 167 9.2.2 Definitions of Reliability Classes 167 9.2.3 Interrelationships 169 9.3 Properties of the Basic Concepts . 169 9.3.1 Properties of Increasing and Decreasing Failure Rates . 169 9.3.2 Property of Increasing Failure Rate on Average . 169 9.3.3 Properties of NBU, NBUC, and NBUE 169 9.4 Distributions with Bathtub-shaped Failure Rates 169 9.5 Life Classes Characterized by the Mean Residual Lifetime . 170 9.6 Some Further Classes of Aging 171 9.7 Partial Ordering of Life Distributions 171 9.7.1 Relative Aging 172 9.7.2 Applications of Partial Orderings 172 9.8 Bivariate Reliability Classes . 173 9.9 Tests of Stochastic Aging . 173 9.9.1 A General Sketch of Tests 174 9.9.2 Summary of Tests of Aging in Univariate Case . 177 9.9.3 Summary of Tests of Bivariate Aging 177 9.10 Concluding Remarks on Aging 177xvi Contents 10 Class of NBU-t0 Life Distribution Dong Ho Park . 181 10.1 Introduction 181 10.2 Characterization of NBU-t0 Class 182 10.2.1 Boundary Members of NBU-t0 and NWU-t0 182 10.2.2 Preservation of NBU-t0 and NWU-t0 Properties under Reliability Operations 184 10.3 Estimation of NBU-t0 Life Distribution . 186 10.3.1 Reneau–Samaniego Estimator 186 10.3.2 Chang–Rao Estimator 188 10.3.2.1 Positively Biased Estimator 188 10.3.2.2 Geometric Mean Estimator 188 10.4 Tests for NBU-t0 Life Distribution 189 10.4.1 Tests for NBU-t0 Alternatives Using Complete Data 189 10.4.1.1 Hollander–Park–Proschan Test 190 10.4.1.2 Ebrahimi–Habibullah Test 192 10.4.1.3 Ahmad Test 193 10.4.2 Tests for NBU-t0 Alternatives Using Incomplete Data . 195 PART III. Software Reliability 11 Software Reliability Models: A Selective Survey and New Directions Siddhartha R. Dalal . 201 11.1 Introduction 201 11.2 Static Models . 203 11.2.1 Phase-based Model: Gaffney and Davis . 203 11.2.2 Predictive Development Life Cycle Model: Dalal and Ho 203 11.3 Dynamic Models: Reliability Growth Models for Testing and Operational Use 205 11.3.1 A General Class of Models 205 11.3.2 Assumptions Underlying the Reliability Growth Models 206 11.3.3 Caution in Using Reliability Growth Models 207 11.4 Reliability Growth Modeling with Covariates 207 11.5 When to Stop Testing Software 208 11.6 Challenges and Conclusions . 209 12 Software Reliability Modeling James Ledoux . 213 12.1 Introduction 213 12.2 Basic Concepts of Stochastic Modeling . 214 12.2.1 Metrics with Regard to the First Failure . 214 12.2.2 Stochastic Process of Times of Failure 215 12.3 Black-box Software Reliability Models 215 12.3.1 Self-exciting Point Processes . 216 12.3.1.1 Counting Statistics for a Self-exciting Point Process . 218Contents xvii 12.3.1.2 Likelihood Function for a Self-exciting Point Process 218 12.3.1.3 Reliability and Mean Time to Failure Functions . 218 12.3.2 Classification of Software Reliability Models 219 12.3.2.1 0-Memory Self-exciting Point Process 219 12.3.2.2 Non-homogeneous Poisson Process Model: ?(t; Ht, F0) = f (t; F0) and is Deterministic 220 12.3.2.3 1-Memory Self-exciting Point Process with ?(t; Ht, F0) = f (N(t), t ? TN(t), F0) 221 12.3.2.4 m ? 2-Memory 221 12.4 White-box Modeling . 222 12.5 Calibration of Model . 223 12.5.1 Frequentist Procedures 223 12.5.2 Bayesian Procedure . 225 12.6 Current Issues . 225 12.6.1 Black-box Modeling . 225 12.6.1.1 Imperfect Debugging . 225 12.6.1.2 Early Prediction of Software Reliability . 226 12.6.1.3 Environmental Factors 227 12.6.1.4 Conclusion . 228 12.6.2 White-box Modeling . 229 12.6.3 Statistical Issues . 230 13 Software Availability Theory and Its Applications Koichi Tokuno and Shigeru Yamada . 235 13.1 Introduction 235 13.2 Basic Model and Software Availability Measures 236 13.3 Modified Models . 239 13.3.1 Model with Two Types of Failure 239 13.3.2 Model with Two Types of Restoration 240 13.4 Applied Models 241 13.4.1 Model with Computation Performance . 241 13.4.2 Model for Hardware–Software System . 242 13.5 Concluding Remarks . 243 14 Software Rejuvenation: Modeling and Applications Tadashi Dohi, Katerina Go?eva-Popstojanova, Kalyanaraman Vaidyanathan, Kishor S. Trivedi and Shunji Osaki 245 14.1 Introduction 245 14.2 Modeling-based Estimation . 246 14.2.1 Examples in Telecommunication Billing Applications . 247 14.2.2 Examples in a Transaction-based Software System . 251 14.2.3 Examples in a Cluster System 255 14.3 Measurement-based Estimation . 257 14.3.1 Time-based Estimation . 258 14.3.2 Time and Workload-based Estimation . 260 14.4 Conclusion and Future Work . 262xviii Contents 15 Software Reliability Management: Techniques and Applications Mitsuhiro Kimura and Shigeru Yamada . 265 15.1 Introduction 265 15.2 Death Process Model for Software Testing Management 266 15.2.1 Model Description 267 15.2.1.1 Mean Number of Remaining Software Faults/Testing Cases 268 15.2.1.2 Mean Time to Extinction . 268 15.2.2 Estimation Method of Unknown Parameters 268 15.2.2.1 Case of 0 < ? ? 1 . 268 15.2.2.2 Case of ? = 0 . 269 15.2.3 Software Testing Progress Evaluation 269 15.2.4 Numerical Illustrations . 270 15.2.5 Concluding Remarks . 271 15.3 Estimation Method of Imperfect Debugging Probability 271 15.3.1 Hidden-Markov modeling for software reliability growth phenomenon . 271 15.3.2 Estimation Method of Unknown Parameters 272 15.3.3 Numerical Illustrations . 273 15.3.4 Concluding Remarks . 274 15.4 Continuous State Space Model for Large-scale Software 274 15.4.1 Model Description 275 15.4.2 Nonlinear Characteristics of Software Debugging Speed 277 15.4.3 Estimation Method of Unknown Parameters 277 15.4.4 Software Reliability Assessment Measures . 279 15.4.4.1 Expected Number of Remaining Faults and Its Variance 279 15.4.4.2 Cumulative and Instantaneous Mean Time Between Failures 279 15.4.5 Concluding Remarks . 280 15.5 Development of a Software Reliability Management Tool 280 15.5.1 Definition of the Specification Requirement 280 15.5.2 Object-oriented Design . 281 15.5.3 Examples of Reliability Estimation and Discussion 282 16 Recent Studies in Software Reliability Engineering Hoang Pham . 285 16.1 Introduction 285 16.1.1 Software Reliability Concepts 285 16.1.2 Software Life Cycle 288 16.2 Software Reliability Modeling 288 16.2.1 A Generalized Non-homogeneous Poisson Process Model . 289 16.2.2 Application 1: The Real-time Control System 289 16.3 Generalized Models with Environmental Factors 289 16.3.1 Parameters Estimation 292 16.3.2 Application 2: The Real-time Monitor Systems . 292Contents xix 16.4 Cost Modeling . 295 16.4.1 Generalized Risk–Cost Models . 295 16.5 Recent Studies with Considerations of Random Field Environments . 296 16.5.1 A Reliability Model 297 16.5.2 A Cost Model . 297 16.6 Further Reading 300 PART IV. Maintenance Theory and Testing 17 Warranty and Maintenance D. N. P. Murthy and N. Jack 305 17.1 Introduction 305 17.2 Product Warranties: An Overview 306 17.2.1 Role and Concept . 306 17.2.2 Product Categories 306 17.2.3 Warranty Policies . 306 17.2.3.1 Warranties Policies for Standard Products Sold Individually 306 17.2.3.2 Warranty Policies for Standard Products Sold in Lots 307 17.2.3.3 Warranty Policies for Specialized Products . 307 17.2.3.4 Extended Warranties . 307 17.2.3.5 Warranties for Used Products 308 17.2.4 Issues in Product Warranty . 308 17.2.4.1 Warranty Cost Analysis 308 17.2.4.2 Warranty Servicing 309 17.2.5 Review of Warranty Literature 309 17.3 Maintenance: An Overview 309 17.3.1 Corrective Maintenance . 309 17.3.2 Preventive Maintenance . 310 17.3.3 Review of Maintenance Literature 310 17.4 Warranty and Corrective Maintenance . 311 17.5 Warranty and Preventive Maintenance . 312 17.6 Extended Warranties and Service Contracts . 313 17.7 Conclusions and Topics for Future Research 314 18 Mechanical Reliability and Maintenance Models Gianpaolo Pulcini . 317 18.1 Introduction 317 18.2 Stochastic Point Processes 318 18.3 Perfect Maintenance . 320 18.4 Minimal Repair 321 18.4.1 No Trend with Operating Time . 323 18.4.2 Monotonic Trend with Operating Time . 323 18.4.2.1 The Power Law Process 324 18.4.2.2 The Log–Linear Process 325 18.4.2.3 Bounded Intensity Processes . 326xx Contents 18.4.3 Bathtub-type Intensity 327 18.4.3.1 Numerical Example 328 18.4.4 Non-homogeneous Poisson Process Incorporating Covariate Information 329 18.5 Imperfect or Worse Repair 330 18.5.1 Proportional Age Reduction Models 330 18.5.2 Inhomogeneous Gamma Processes . 331 18.5.3 Lawless–Thiagarajah Models 333 18.5.4 Proportional Intensity Variation Model . 334 18.6 Complex Maintenance Policy . 335 18.6.1 Sequence of Perfect and Minimal Repairs Without Preventive Maintenance . 336 18.6.2 Minimal Repairs Interspersed with Perfect Preventive Maintenance . 338 18.6.3 Imperfect Repairs Interspersed with Perfect Preventive Maintenance . 339 18.6.4 Minimal Repairs Interspersed with Imperfect Preventive Maintenance . 340 18.6.4.1 Numerical Example 341 18.6.5 Corrective Repairs Interspersed with Preventive Maintenance Without Restrictive Assumptions 342 18.7 Reliability Growth . 343 18.7.1 Continuous Models 344 18.7.2 Discrete Models . 345 19 Preventive Maintenance Models: Replacement, Repair, Ordering, and Inspection Tadashi Dohi, Naoto Kaio and Shunji Osaki . 349 19.1 Introduction 349 19.2 Block Replacement Models 350 19.2.1 Model I 350 19.2.2 Model II 352 19.2.3 Model III . 352 19.3 Age Replacement Models . 354 19.3.1 Basic Age Replacement Model 354 19.4 Ordering Models . 356 19.4.1 Continuous-time Model . 357 19.4.2 Discrete-time Model . 358 19.4.3 Combined Model with Minimal Repairs 359 19.5 Inspection Models 361 19.5.1 Nearly Optimal Inspection Policy by Kaio and Osaki (K&O Policy) 362 19.5.2 Nearly Optimal Inspection Policy by Munford and Shahani (M&S Policy) . 363 19.5.3 Nearly Optimal Inspection Policy by Nakagawa and Yasui (N&Y Policy) . 363 19.6 Concluding Remarks . 363Contents xxi 20 Maintenance and Optimum Policy Toshio Nakagawa . 367 20.1 Introduction 367 20.2 Replacement Policies . 368 20.2.1 Age Replacement . 368 20.2.2 Block Replacement 370 20.2.2.1 No Replacement at Failure 370 20.2.2.2 Replacement with Two Variables . 371 20.2.3 Periodic Replacement 371 20.2.3.1 Modified Models with Two Variables . 372 20.2.3.2 Replacement at N Variables . 373 20.2.4 Other Replacement Models . 373 20.2.4.1 Replacements with Discounting . 373 20.2.4.2 Discrete Replacement Models 374 20.2.4.3 Replacements with Two Types of Unit 375 20.2.4.4 Replacement of a Shock Model 376 20.2.5 Remarks . 377 20.3 Preventive Maintenance Policies . 378 20.3.1 One-unit System . 378 20.3.1.1 Interval Reliability 379 20.3.2 Two-unit System . 380 20.3.3 Imperfect Preventive Maintenance . 381 20.3.3.1 Imperfect with Probability 383 20.3.3.2 Reduced Age 383 20.3.4 Modified Preventive Maintenance 384 20.4 Inspection Policies 385 20.4.1 Standard Inspection . 386 20.4.2 Inspection with Preventive Maintenance 387 20.4.3 Inspection of a Storage System . 388 21 Optimal Imperfect Maintenance Models Hongzhou Wang and Hoang Pham 397 21.1 Introduction 397 21.2 Treatment Methods for Imperfect Maintenance . 399 21.2.1 Treatment Method 1 . 399 21.2.2 Treatment Method 2 . 400 21.2.3 Treatment Method 3 . 401 21.2.4 Treatment Method 4 . 402 21.2.5 Treatment Method 5 . 403 21.2.6 Treatment Method 6 . 403 21.2.7 Treatment Method 7 . 403 21.2.8 Other Methods 404 21.3 Some Results on Imperfect Maintenance 404 21.3.1 A Quasi-renewal Process and Imperfect Maintenance . 404 21.3.1.1 Imperfect Maintenance Model A . 405 21.3.1.2 Imperfect Maintenance Model B . 405xxii Contents 21.3.1.3 Imperfect Maintenance Model C . 405 21.3.1.4 Imperfect Maintenance Model D . 407 21.3.1.5 Imperfect Maintenance Model E . 408 21.3.2 Optimal Imperfect Maintenance of k-out-of-n Systems 409 21.4 Future Research on Imperfect Maintenance . 411 21.A Appendix . 412 21.A.1 Acronyms and Definitions 412 21.A.2 Exercises . 412 22 Accelerated Life Testing Elsayed A. Elsayed 415 22.1 Introduction 415 22.2 Design of Accelerated Life Testing Plans . 416 22.2.1 Stress Loadings 416 22.2.2 Types of Stress 416 22.3 Accelerated Life Testing Models . 417 22.3.1 Parametric Statistics-based Models . 418 22.3.2 Acceleration Model for the Exponential Model . 419 22.3.3 Acceleration Model for the Weibull Model . 420 22.3.4 The Arrhenius Model 422 22.3.5 Non-parametric Accelerated Life Testing Models: Cox’s Model 424 22.4 Extensions of the Proportional Hazards Model . 426 23 Accelerated Test Models with the Birnbaum–Saunders Distribution W. Jason Owen and William J. Padgett 429 23.1 Introduction 429 23.1.1 Accelerated Testing 430 23.1.2 The Birnbaum–Saunders Distribution . 431 23.2 Accelerated Birnbaum–Saunders Models 431 23.2.1 The Power-law Accelerated Birnbaum–Saunders Model 432 23.2.2 Cumulative Damage Models . 432 23.2.2.1 Additive Damage Models . 433 23.2.2.2 Multiplicative Damage Models 434 23.3 Inference Procedures with Accelerated Life Models . 435 23.4 Estimation from Experimental Data . 437 23.4.1 Fatigue Failure Data . 437 23.4.2 Micro-Composite Strength Data . 437 24 Multiple-steps Step-stress Accelerated Life Test Loon-Ching Tang . 441 24.1 Introduction 441 24.2 Cumulative Exposure Models 443 24.3 Planning a Step-stress Accelerated Life Test . 445 24.3.1 Planning a Simple Step-stress Accelerated Life Test 446 24.3.1.1 The Likelihood Function . 446 24.3.1.2 Setting a Target Accelerating Factor . 447Contents xxiii 24.3.1.3 Maximum Likelihood Estimator and Asymptotic Variance 447 24.3.1.4 Nonlinear Programming for Joint Optimality in Hold Time and Low Stress 447 24.3.2 Multiple-steps Step-stress Accelerated Life Test Plans . 448 24.4 Data Analysis in the Step-stress Accelerated Life Test 450 24.4.1 Multiply Censored, Continuously Monitored Step-stress Accelerated Life Test . 450 24.4.1.1 Parameter Estimation for Weibull Distribution . 451 24.4.2 Read-out Data 451 24.5 Implementation in Microsoft ExcelTM 453 24.6 Conclusion 454 25 Step-stress Accelerated Life Testing Chengjie Xiong 457 25.1 Introduction 457 25.2 Step-stress Life Testing with Constant Stress-change Times 457 25.2.1 Cumulative Exposure Model . 457 25.2.2 Estimation with Exponential Data 459 25.2.3 Estimation with Other Distributions 462 25.2.4 Optimum Test Plan 463 25.3 Step-stress Life Testing with Random Stress-change Times 463 25.3.1 Marginal Distribution of Lifetime 463 25.3.2 Estimation 467 25.3.3 Optimum Test Plan 467 25.4 Bibliographical Notes . 468 PART V. Practices and Emerging Applications 26 Statistical Methods for Reliability Data Analysis Michael J. Phillips . 475 26.1 Introduction 475 26.2 Nature of Reliability Data . 475 26.3 Probability and Random Variables 478 26.4 Principles of Statistical Methods . 479 26.5 Censored Data . 480 26.6 Weibull Regression Model 483 26.7 Accelerated Failure-time Model . 485 26.8 Proportional Hazards Model . 486 26.9 Residual Plots for the Proportional Hazards Model . 489 26.10 Non-proportional Hazards Models . 490 26.11 Selecting the Model and the Variables 491 26.12 Discussion . 491xxiv Contents 27 The Application of Capture–Recapture Methods in Reliability Studies Paul S. F. Yip, Yan Wang and Anne Chao 493 27.1 Introduction 493 27.2 Formulation of the Problem . 495 27.2.1 Homogeneous Model with Recapture 496 27.2.2 A Seeded Fault Approach Without Recapture 498 27.2.3 Heterogeneous Model 499 27.2.3.1 Non-parametric Case: ?i(t) = ?i?t 499 27.2.3.2 Parametric Case: ?i(t) = ?i 501 27.3 A Sequential Procedure 504 27.4 Real Examples . 504 27.5 Simulation Studies 505 27.6 Discussion . 508 28 Reliability of Electric Power Systems: An Overview Roy Billinton and Ronald N. Allan 511 28.1 Introduction 511 28.2 System Reliability Performance . 512 28.3 System Reliability Prediction . 515 28.3.1 System Analysis . 515 28.3.2 Predictive Assessment at HLI 516 28.3.3 Predictive Assessment at HLII 518 28.3.4 Distribution System Reliability Assessment . 519 28.3.5 Predictive Assessment at HLIII . 520 28.4 System Reliability Data 521 28.4.1 Canadian Electricity Association Database . 522 28.4.2 Canadian Electricity Association Equipment Reliability Information System Database for HLI Evaluation . 523 28.4.3 Canadian Electricity Association Equipment Reliability Information System Database for HLII Evaluation . 523 28.4.4 Canadian Electricity Association Equipment Reliability Information System Database for HLIII Evaluation 524 28.5 System Reliability Worth . 525 28.6 Guide to Further Study 527 29 Human and Medical Device Reliability B. S. Dhillon 529 29.1 Introduction 529 29.2 Human and Medical Device Reliability Terms and Definitions . 529 29.3 Human Stress—Performance Effectiveness, Human Error Types, and Causes of Human Error 530 29.4 Human Reliability Analysis Methods 531 29.4.1 Probability Tree Method . 531 29.4.2 Fault Tree Method 532 29.4.3 Markov Method . 534Contents xxv 29.5 Human Unreliability Data Sources 535 29.6 Medical Device Reliability Related Facts and Figures 535 29.7 Medical Device Recalls and Equipment Classification . 536 29.8 Human Error in Medical Devices 537 29.9 Tools for Medical Device Reliability Assurance . 537 29.9.1 General Method . 538 29.9.2 Failure Modes and Effect Analysis 538 29.9.3 Fault Tree Method 538 29.9.4 Markov Method . 538 29.10 Data Sources for Performing Medical Device Reliability Studies 539 29.11 Guidelines for Reliability Engineers with Respect to Medical Devices . 539 30 Probabilistic Risk Assessment Robert A. Bari . 543 30.1 Introduction 543 30.2 Historical Comments . 544 30.3 Probabilistic Risk Assessment Methodology 546 30.4 Engineering Risk Versus Environmental Risk 549 30.5 Risk Measures and Public Impact 550 30.6 Transition to Risk-informed Regulation . 553 30.7 Some Successful Probabilistic Risk Assessment Applications 553 30.8 Comments on Uncertainty 554 30.9 Deterministic, Probabilistic, Prescriptive, Performance-based . 554 30.10 Outlook 555 31 Total Dependability Management Per Anders Akersten and Bengt Klefsj? . 559 31.1 Introduction 559 31.2 Background 559 31.3 Total Dependability Management 560 31.4 Management System Components 561 31.5 Conclusions 564 32 Total Quality for Software Engineering Management G. Albeanu and Fl. Popentiu Vladicescu . 567 32.1 Introduction 567 32.1.1 The Meaning of Software Quality 567 32.1.2 Approaches in Software Quality Assurance . 569 32.2 The Practice of Software Engineering 571 32.2.1 Software Lifecycle 571 32.2.2 Software Development Process . 574 32.2.3 Software Measurements . 575 32.3 Software Quality Models . 577 32.3.1 Measuring Aspects of Quality 577 32.3.2 Software Reliability Engineering 577 32.3.3 Effort and Cost Models 579xxvi Contents 32.4 Total Quality Management for Software Engineering 580 32.4.1 Deming’s Theory . 580 32.4.2 Continuous Improvement 581 32.5 Conclusions 582 33 Software Fault Tolerance Xiaolin Teng and Hoang Pham 585 33.1 Introduction 585 33.2 Software Fault-tolerant Methodologies . 586 33.2.1 N-version Programming . 586 33.2.2 Recovery Block 586 33.2.3 Other Fault-tolerance Techniques 587 33.3 N-version Programming Modeling . 588 33.3.1 Basic Analysis 588 33.3.1.1 Data-domain Modeling 588 33.3.1.2 Time-domain Modeling 589 33.3.2 Reliability in the Presence of Failure Correlation 590 33.3.3 Reliability Analysis and Modeling 591 33.4 Generalized Non-homogeneous Poisson Process Model Formulation . 594 33.5 Non-homogeneous Poisson Process Reliability Model for N-version Programming Systems 595 33.5.1 Model Assumptions . 597 33.5.2 Model Formulations . 599 33.5.2.1 Mean Value Functions . 599 33.5.2.2 Common Failures . 600 33.5.2.3 Concurrent Independent Failures 601 33.5.3 N-version Programming System Reliability 601 33.5.4 Parameter Estimation 602 33.6 N-version programming–Software Reliability Growth . 602 33.6.1 Applications of N-version Programming–Software Reliability Growth Models 602 33.6.1.1 Testing Data 602 33.7 Conclusion 610 34 Markovian Dependability/Performability Modeling of Fault-tolerant Systems Juan A. Carrasco . 613 34.1 Introduction 613 34.2 Measures . 615 34.2.1 Expected Steady-state Reward Rate . 617 34.2.2 Expected Cumulative Reward Till Exit of a Subset of States 618 34.2.3 Expected Cumulative Reward During Stay in a Subset of States 618 34.2.4 Expected Transient Reward Rate 619 34.2.5 Expected Averaged Reward Rate . 619 34.2.6 Cumulative Reward Distribution Till Exit of a Subset of States 619 34.2.7 Cumulative Reward Distribution During Stay in a Subset of States 620Contents xxvii 34.2.8 Cumulative Reward Distribution 621 34.2.9 Extended Reward Structures . 621 34.3 Model Specification 622 34.4 Model Solution 625 34.5 The Largeness Problem 630 34.6 A Case Study . 632 34.7 Conclusions 640 35 Random-request Availability Kang W. Lee 643 35.1 Introduction 643 35.2 System Description and Definition 644 35.3 Mathematical Expression for the Random-request Availability 645 35.3.1 Notation . 645 35.3.2 Mathematical Assumptions . 645 35.3.3 Mathematical Expressions 645 35.4 Numerical Examples . 647 35.5 Simulation Results 647 35.6 Approximation 651 35.7 Concluding Remarks . 652 Index .
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