12.1.1.0......Page 2
B.1 Preliminary Concepts of Fuzzy Set Theory......Page 4
12.2.1 N-version Programming Scheme......Page 8
Acknowledgments......Page 9
12.3.2.2 System Reliability......Page 19
Cover......Page 1
1 Introduction......Page 23
12.3.1 Faults in NVP Systems......Page 14
12.3.2 Testing Efficiency Based Continuous Time SRGM for NVP System......Page 15
9.5.3 Discrete SRGM Modeling Severity of Faults with Respect to Test Case Execution Number......Page 16
12.3.2.1 Model Development......Page 17
10.2.3 Release Policy Based on Testing Effort Dependent SRGM......Page 18
Acronym......Page 20
12.3.3 A Testing Efficiency Based Discrete SRGM for a NVP System......Page 21
11.3.2.1......Page 24
12.3.3.2 System Reliability......Page 25
12.3.4 Parameter Estimation and Model Validation......Page 26
Index......Page 27
6.5.1 Equivalence of Unification Schemes Based on Infinite Server Queues for the Hard Faults and Fault Detection Correction Process with a Delay Function......Page 28
Data Analysis of a 3VP System......Page 29
10.2.7 Release Policy Based on SRGM Incorporating Imperfect Fault Debugging......Page 30
11.3.2 Minimizing Testing Cost Under Resource and Reliability Constraint......Page 31
Exercises......Page 32
5.11.3 Change-Point SRGM Based on Multiple Change-Point Weibull Type TEF......Page 35
1.5.1 Let Us Compare: Software Versus Hardware Reliability......Page 36
1.5.2 Reliability Measures......Page 37
1.5.2.3 System Mean Time to Failure......Page 39
1.5.2.4 Hazard Function......Page 40
1.5.3.1 Binomial Distribution......Page 41
1.5.3.2 Poisson Distribution......Page 42
1.5.3.4 Normal Distribution......Page 43
Model 1 Without Redundancy......Page 44
1.5.3.5 Weibull Distribution......Page 45
Preface......Page 5
11.2.3 Dynamic Allocation of Resources for Modular Software......Page 7
Contents......Page 10
12.2.3.3 Distributed Execution of Recovery Blocks......Page 11
Answers to the Selected Exercises......Page 12
12.3…Reliability Growth Analysis of NVP Systems......Page 13
Data Analysis of a 2VP System......Page 33
10.2.8 Release Policy on Pure Error Generation Fault Complexity Based SRGM......Page 34
2.1…Introduction......Page 70
11.2.2 Minimizing Testing Resource Expenditures......Page 6
Software Reliability Assessment with OR Applications......Page 3
12.3.3.1 Model Development......Page 22
1.5.2.2 Failure Time Distribution and Reliability Measure......Page 38
1.5.3.6 Gamma Distribution......Page 46
1.5.3.8 Logistic Distribution......Page 47
Model 2......Page 55
1.5.4.1 Model Classification......Page 48
1.5.4.1......Page 50
1.5.5 Counting Process......Page 52
12.4.4 Optimization Models for Recovery Blocks with Multiple Alternatives for Each Version Having Different Reliability......Page 56
References......Page 60
1.5.4.1......Page 49
1.5.4.2 Model Selection......Page 51
1.5.5.1 NHPP in Continuous Time Space......Page 53
1.5.6 NHPP Based Software Reliability Growth Modeling......Page 54
1.6.1.1 Some Definitions......Page 57
1.6.1.2 Non-Linear Least Square Method......Page 58
1.6.1.3 Maximum Likelihood Estimation Method......Page 59
1.6.2 Interval Estimation......Page 61
1.6.2.3 Confidence Limits for the Mean mu When sigma 2 is Unknown......Page 62
1.6.2.4 Confidence Limits on sigma 2......Page 63
1.7.2 Goodness of Fit Test......Page 64
1.7.2.1 Chi-Square ( chi 2) Test......Page 65
1.7.3 Predictive Validity Criterion......Page 66
References......Page 67
2.2.1 The Basic Execution Time Model......Page 73
2.2.2 The Logarithmic Poisson Model......Page 74
2.3.1 Goel--Okumoto Model......Page 76
2.3.2 Hyper-Exponential Model......Page 77
2.3.3 Exponential Fault Categorization (Modified Exponential) Model......Page 78
2.3.5 Inflection S-Shaped Model......Page 79
2.3.7 SRGM for Error Removal Phenomenon......Page 80
2.4…SRGM Defining Complexity of Faults......Page 81
2.4.1 Generalized SRGM (Erlang Model)......Page 82
2.4.2 Incorporating Fault Complexity Considering Learning Phenomenon......Page 83
2.5…Managing Reliability in Operational Phase......Page 85
2.5.1 Operational Usage Models---Initial Studies......Page 86
2.6…Modeling Fault Dependency and Debugging Time Lag......Page 87
2.6.1 Model for Fault-Correction---The Initial Study......Page 88
2.6.2 Fault Dependency and Debugging Time Lag Model......Page 90
2.6.3 Modeling Fault Complexity with Debugging Time Lag......Page 92
2.7.1 Rayleigh Test Effort Model......Page 93
2.7.2 Weibull Test Effort Model......Page 94
2.7.3 Logistic and Generalized Testing Effort Functions......Page 96
2.7.4 Log Logistic Testing Effort Functions......Page 97
2.7.5 Modeling the Effect of Fault Complexity with Respect to Testing Efforts Considering Debugging Time Lag......Page 98
2.8…Software Reliability Growth Modeling Under Distributed Development Environment......Page 99
2.8.1 Flexible Software Reliability Growth Models for Distributed Systems......Page 100
Components Containing Hard Faults......Page 101
Components Containing Complex Faults......Page 102
2.8.2.1 Model for Reused Components......Page 103
Components Containing Hard Faults......Page 104
2.8.2.3 Modeling Total Fault Removal Phenomenon......Page 105
Failure data set......Page 106
2.9.2 Application of Test Effort Based Models......Page 110
References......Page 114
3.1…Introduction......Page 117
3.3.1 Pure Imperfect Fault Debugging Model......Page 120
3.3.3 Using Different Fault Content Functions......Page 121
3.3.4.1 Pure Imperfect Fault Debugging Model......Page 122
3.3.4.2 Pure Error Generation Model......Page 123
3.3.5 Modeling Error Generation Considering Fault Removal Time Delay......Page 124
3.4.1 An S-Shaped Imperfect Debugging SRGM......Page 125
3.4.2 General Imperfect Software Debugging Model with S-Shaped FDR......Page 126
3.4.3 Delayed Removal Process Modeling Under Imperfect Debugging Environment......Page 127
3.5…Integrated Imperfect Debugging SRGM......Page 128
3.5.1 Testing Efficiency Model......Page 129
3.5.2 Integrated Exponential and Flexible Testing Efficiency Models......Page 130
3.6.1 Pure Imperfect Fault Debugging Model......Page 132
3.6.3 Integrated Imperfect Debugging Models......Page 133
3.7…Reliability Analysis Under Imperfect Debugging Environment During Field Use......Page 134
3.7.1 A Pure Imperfect Fault Repair Model for Operational Phase......Page 135
3.7.2 An Integrated Imperfect Debugging SRGM for Operational Phase......Page 136
3.7.2.2 Usage Function for Product Type Software......Page 137
3.8.1 Application of Time Dependent SRGM......Page 139
3.8.2 An Application for Integrated Test Effort Based Testing Efficiency SRGM......Page 143
3.8.3 An Application for Integrated Operational Phase Testing Efficiency SRGM......Page 144
Failure Data Set......Page 145
3.8.3.2 Data Analysis of SRGM for Product Type Software......Page 146
Exercises......Page 148
References......Page 149
4.1.1 An Introduction to Testing-Coverage......Page 151
4.1.1.1 Statement Coverage......Page 153
4.1.1.4 Path Coverage......Page 154
4.1.1.5 Data Flow Coverage......Page 155
4.2.1 Relating Testing Coverage to Software Reliability: An Initial Study......Page 157
4.2.1.1 One Parameter Model for Testing Coverage......Page 159
4.2.1.2 Logarithmic Coverage Model......Page 160
4.2.1.3 Defect Density and Reliability......Page 161
4.2.3 Incorporating Testing Efficiency in ENHPP......Page 163
4.2.4 Two Dimensional Software Reliability Assessment with Testing Coverage......Page 165
4.2.4.1 The Coverage Function......Page 166
4.2.4.2 The One Dimensional SRGM......Page 167
4.2.5 Considering Testing Coverage in a Testing Effort Dependent SRGM......Page 168
4.2.6 A Coverage-Based SRGM for Operational Phase......Page 169
4.3.1.1 Description of Testing Domains......Page 171
4.3.1.2 Software Reliability Modeling......Page 173
4.3.2 Application of Testing Domain Dependent SRGM in Distributed Development Environment......Page 175
4.3.2.2 Model for New Components: the Case of Hard and Complex Faults......Page 176
4.3.2.3 Modeling Total Fault Removal Phenomenon......Page 178
4.3.3.1 Testing Domain with Skill Factor......Page 179
4.3.3.2 Software Reliability Modeling......Page 180
4.4.1 Application of Coverage Models......Page 181
4.4.2 Application of Testing Domain Based Models......Page 184
References......Page 189
5.1…Introduction......Page 191
5.2…Change-Point Models: An Initial Study......Page 195
5.2.2 Change-Point Weibull Model......Page 196
5.3…Exponential Single Change-Point Model......Page 197
5.4…A Generalized Framework for Single Change-Point SRGM......Page 198
5.4.2 Obtaining S-Shaped\Flexible SRGM from the Generalized Approach......Page 199
5.4.3 More SRGM Obtained from the Generalized Approach......Page 201
5.5.1 Exponential Imperfect Debugging Model......Page 202
5.5.2 Integrated Flexible Imperfect Debugging Model......Page 203
5.6.1 Exponential Test Effort Models......Page 205
5.6.2 Flexible/S-Shaped Test Efforts Based SRGM......Page 206
5.7…SRGM with Multiple Change-Points......Page 207
5.7.1 Development of Exponential Multiple Change-Point Model......Page 208
5.7.2 Development of Flexible/S-Shaped Multiple Change-Point Model......Page 209
5.8.1 Weibull Type Test Effort Function with Multiple Change Points......Page 210
5.8.2.1 Assumptions......Page 211
5.9…A Change-Point SRGM with Environmental Factor......Page 213
5.10…Testing Effort Control Problem......Page 218
5.11.1 Models with Single Change-Point......Page 220
5.11.2 Models with Multiple Change Points......Page 223
5.11.3 Change-Point SRGM Based on Multiple Change-Point Weibull Type TEF......Page 225
5.11.4 Application of Testing Effort Control Problem......Page 229
References......Page 232
6.1‡Introduction......Page 234
6.2…Unification Scheme for Fault Detection and Correction Process......Page 236
6.2.1 Fault Detection NHPP Models......Page 237
6.2.2.1 Exponentially Distributed Correction Time......Page 238
6.3…Unified Scheme Based on the Concept of Infinite Server Queue......Page 240
6.3.1.1 Conditional Distribution of Arrival Times......Page 241
6.3.2 Infinite Server Queuing Model......Page 242
6.3.2.1 Model for Complex Faults......Page 243
6.3.2.2 Model for Hard Faults......Page 245
6.3.2.3 Model for Simple Faults......Page 246
6.3.2.4 Model for Total FRP......Page 247
6.3.4.1 Exponential Distribution for Removal Times......Page 248
6.3.4.2 Weibull Distribution for Removal Times......Page 254
6.3.4.4 Normal Distribution for Removal Times......Page 255
6.4.1 Generalized SRGM Considering Immediate Removal of Faults on Failure Observation Under Imperfect Debugging Environment......Page 256
6.4.2 Generalized SRGM Considering Time Delay Between Failure Observation and Correction Procedures Under Imperfect Debugging Environment......Page 258
6.5.1 Equivalence of Unification Schemes Based on Infinite Server Queues for the Hard Faults and Fault Detection Correction Process with a Delay Function......Page 261
6.5.2 Equivalence of Unification Schemes Based on Infinite Server Queues for the Hard Faults and One Based on Hazard Rate Concept......Page 262
6.6.1 Application of SRGM for Fault Detection and Correction Process......Page 263
6.6.2 Application of SRGM Based on the Concept of Infinite Server Queues......Page 267
6.6.3 Application of SRGM Based on Unification Schemes for Testing Efficiency Models......Page 269
References......Page 271
7.1…Artificial Neural Networks: An Introduction......Page 273
7.4.4......Page 275
7.2.2 Network Architecture......Page 276
7.2.3 Learning Algorithm......Page 278
7.3…Neural Network Approaches in Software Reliability......Page 281
7.3.1 Building ANN for Existing Analytical SRGM......Page 283
7.3.2.1 Normalization......Page 284
7.4.1 Dynamic Weighted Combinational Model......Page 285
7.4.5......Page 294
7.5…Data Analysis and Parameter Estimation......Page 295
References......Page 298
8.2.1 Stochastic Process......Page 301
8.2.3.1 sigma -Algebra......Page 302
8.2.3.2 Probability Measure......Page 303
8.2.3.5 ItÔ Integrals [1, 2]......Page 304
8.3…Stochastic Differential Equation Based Software Reliability Models......Page 305
8.3.1.1 Exponential SDE Model......Page 308
Flexible SDE Model......Page 309
8.3.2.1 Instantaneous MTBF......Page 310
Flexible SDE Model......Page 311
Delayed S-Shaped SDE Model......Page 312
Three-Stage SDE Model......Page 313
8.4.2 The Fault Complexity Model Considering Learning Effect......Page 314
8.4.2.1 Simple Faults......Page 315
8.5…Change Point SDE Model......Page 316
8.5.2 Delayed S-Shaped Change Point SDE Model......Page 317
8.5.3 Flexible Change Point SDE Model......Page 318
8.6.1 SRGM Development: Basic Testing Domain......Page 320
8.6.2 SRGM for Testing Domain with Skill Factor......Page 321
8.6.3 Imperfect Testing Domain Dependent SDE Based SRGM......Page 322
8.6.4.1 Instantaneous MTBF for Basic Testing Domain Dependent SRGM......Page 323
8.6.4.5 Cumulative MTBF for Testing Domain with Skill Factor Dependent SRGM......Page 324
8.7…Data Analysis and Parameter Estimation......Page 325
References......Page 329
9.1…Introduction......Page 331
9.1.1 General Assumption......Page 332
9.2.1 Discrete Exponential Model......Page 333
9.2.2 Modified Discrete Exponential Model......Page 334
9.2.3 Discrete Delayed S-Shaped Model......Page 335
9.2.5.1 Discrete SRGM for Error Removal Phenomenon......Page 336
9.2.5.2 Discrete Time Fault Dependency with Lag Function......Page 337
9.3…Discrete SRGM under Imperfect Debugging Environment......Page 338
9.4…Discrete SRGM with Testing Effort......Page 339
9.5.1 Generalized Discrete Erlang SRGM......Page 340
9.5.1.2 Modeling the Hard Faults (Fault-Type II)......Page 341
9.5.2 Discrete SRGM with Errors of Different Severity Incorporating Logistic Learning Function......Page 342
9.5.2.3 Modeling the Complex Faults (i.e. Fault-Type III)......Page 343
9.5.2.4 Modeling the Fault-Type k......Page 344
9.5.3 Discrete SRGM Modeling Severity of Faults with Respect to Test Case Execution Number......Page 346
9.6…Discrete Software Reliability Growth Models for Distributed Systems......Page 348
9.6.1.1 Modeling Simple Faults......Page 349
9.6.2.1 Components Containing Hard Faults......Page 350
9.6.3 Modeling Total Fault Removal Phenomenon......Page 351
9.7.1 Discrete S-Shaped Single Change Point SRGM......Page 352
9.7.2 Discrete Flexible Single Change Point SRGM......Page 353
9.7.3 An Integrated Multiple Change Point Discrete SRGM Considering Fault Complexity......Page 354
9.7.3.1 Model for Simple Faults......Page 356
9.7.3.2 Model for Hard and Complex Faults......Page 357
9.8.1 Application of Fault Complexity Based Discrete Models......Page 360
Exercises......Page 362
References......Page 363
10 Software Release Time Decision Problems......Page 365
10.1…Introduction......Page 366
10.2.1 First Round Studies in SRTD Problem......Page 370
10.2.2 A Cost Model with Penalty Cost......Page 377
10.2.3 Release Policy Based on Testing Effort Dependent SRGM......Page 382
10.2.4 Release Policy for Random Software Life Cycle......Page 385
10.2.5 A Software Cost Model Incorporating the Cost of Dependent Faults Along with Independent Faults......Page 387
10.2.6 Release Policies Under Warranty and Risk Cost......Page 390
10.2.7 Release Policy Based on SRGM Incorporating Imperfect Fault Debugging......Page 394
10.2.8 Release Policy on Pure Error Generation Fault Complexity Based SRGM......Page 398
10.2.9 Release Policy for Integrated Testing Efficiency SRGM......Page 400
10.2.9.1 Effect of Variations in Minimum Reliability Requirement by the Release Time......Page 403
10.2.9.2 Effect of Variations in Level of Perfect Fault Debugging......Page 404
10.2.11 Release Problem with Change Point SRGM......Page 407
10.3.1 Problem Formulation......Page 409
10.3.1.1 The Cost Model......Page 410
10.3.2 Problem Solution......Page 411
References......Page 419
11 Allocation Problems at Unit Level Testing......Page 422
11.1…Introduction......Page 423
11.2.1 Minimizing Remaining Faults......Page 425
11.2.2 Minimizing Testing Resource Expenditures......Page 427
11.2.3 Dynamic Allocation of Resources for Modular Software......Page 428
11.2.4 Minimize the Mean Fault Content......Page 430
11.2.5 Minimizing Remaining Faults with a Reliability Objective......Page 432
11.2.6 Minimizing Testing Resources Utilization with a Reliability Objective......Page 435
11.2.7 Minimize the Cost of Testing Resources......Page 438
11.2.8 A Resource Allocation Problem to Maximize Operational Reliability......Page 442
11.3…Allocation of Resources for Flexible SRGM......Page 444
11.3.2.1......Page 445
11.3.2 Minimizing Testing Cost Under Resource and Reliability Constraint......Page 452
11.4…Optimal Testing Resource Allocation for Test Coverage Based Imperfect Debugging SRGM......Page 458
11.4.1 Problem Formulation......Page 460
11.4.2 Finding Properly Efficient Solution......Page 461
11.4.3 Solution Based on Goal Programming Approach......Page 462
References......Page 466
12.1…Introduction......Page 467
12.1.1.0......Page 468
12.1.1.0......Page 469
12.1.1.0......Page 470
12.2…Software Fault Tolerance Techniques......Page 471
12.2.1 N-version Programming Scheme......Page 474
12.2.2 Recovery Block Scheme......Page 475
12.2.3.3 Distributed Execution of Recovery Blocks......Page 477
12.2.3.4 Consensus Recovery Blocks......Page 478
12.3…Reliability Growth Analysis of NVP Systems......Page 479
12.3.1 Faults in NVP Systems......Page 480
12.3.2 Testing Efficiency Based Continuous Time SRGM for NVP System......Page 481
12.3.2.1 Model Development......Page 483
12.3.2.2 System Reliability......Page 485
12.3.3 A Testing Efficiency Based Discrete SRGM for a NVP System......Page 487
12.3.3.1 Model Development......Page 488
12.3.3.2 System Reliability......Page 491
12.3.4 Parameter Estimation and Model Validation......Page 492
Data Analysis of a 2VP System......Page 493
Data Analysis of a 3VP System......Page 495
Data Analysis of a 2VP System......Page 499
Data Analysis of a 3VP System......Page 502
12.4…COTS Based Reliability Allocation Problem......Page 503
12.4.1.1 Model Without Redundancy......Page 506
12.4.1.2 Model with Redundancy......Page 508
12.4.2 Optimization Models for Selection of Programs for Software Performing Each Function with a Set of Modules......Page 509
Model 1 Without Redundancy......Page 510
Model 2 With Redundancy......Page 511
Model 3 Without Redundancy......Page 512
Model 4 With Redundancy......Page 513
12.4.3.1 Independent Recovery Block......Page 514
12.4.3.2 Consensus Recovery Block......Page 516
12.4.3.3 Independent Recovery Block with Exponential Execution Time......Page 518
Model 2......Page 521
12.4.4 Optimization Models for Recovery Blocks with Multiple Alternatives for Each Version Having Different Reliability......Page 522
References......Page 526
A.1 Standard Normal (Z) Table......Page 529
A.2 Kolmogorov–Smirnov Test Table......Page 531
B.1 Preliminary Concepts of Fuzzy Set Theory......Page 532
C.1 Mean Value Functions of Failure and Removal Phenomenonfor Faults of Type AC, BC, B and C......Page 537
Answers to the Selected Exercises......Page 540
Index......Page 555