《Reliability and Optimal Maintenance》
《Reliability and Optimal Maintenance》可靠性与最佳维修
作者：
HongzhouWang
Hoang Pham
出版社：Springer
出版时间：2006年
目录
Contents
1 Introduction....................................................................................................... 1
1.1 Imperfect Maintenance ................................................................................. 2
1.2 Dependence...................................................................................................4
1.3 Warranty, Dependence, Imperfect Maintenance........................................... 6
1.4 Criteria on Maintenance Optimization.......................................................... 7
1.5 Scope of this Book........................................................................................ 7
1.5.1 General Methodologies........................................................................ 7
1.5.2 Directions............................................................................................. 8
1.5.3 Framework......................................................................................... 11
2 Imperfect Maintenance and Dependence ..................................................... 13
2.1 Imperfect Maintenance ............................................................................... 13
2.1.1 Modeling Methods for Imperfect Maintenance................................. 14
2.1.2 Typical Imperfect Maintenance Models by Maintenance Policies ... 23
2.2 Dependence................................................................................................29
3 Maintenance Policies and Analysis................................................................ 31
3.1 Introduction.................................................................................................31
3.2 Maintenance Policies for One-unit Systems ............................................... 32
3.2.1 Age-dependent PM Policy ................................................................ 32
3.2.2 Periodic PM Policy ........................................................................... 35
3.2.3 Failure Limit Policy .......................................................................... 38
3.2.4 Sequential PM Policy........................................................................ 39
3.2.5 Repair Limit Policy........................................................................... 40
3.2.6 Repair Number Counting and Reference Time Policy...................... 42
3.2.7 On the Maintenance Policies for Single-unit Systems ...................... 43
3.3 Maintenance Policies of Multi-unit Systems .............................................. 45
3.3.1 Group Maintenance Policy ............................................................... 46
3.3.2 Opportunistic Maintenance Policies ................................................. 47
4 A Quasi-renewal Process and Its Applications............................................. 51
4.1 A Quasi-renewal Process ............................................................................ 52
4.1.1 Definition.......................................................................................... 52
4.1.2 Quasi-renewal Function.................................................................... 55
4.1.3 Associated Statistical Testing Problems ........................................... 56
4.1.4 Truncated Quasi-renewal Processes ................................................. 59
4.2 Periodic PM with Imperfect Maintenance .................................................. 62
4.2.1 Model 1: Imperfect Repair and Perfect PM...................................... 62
4.2.2 Model 2: Imperfect Repair and Imperfect PM.................................. 63
4.2.3 Model 3: Imperfect Repair and Imperfect PM.................................. 64
4.2.4 Model 4: Imperfect Repair and Imperfect PM.................................. 68
4.2.5 Model 5: Imperfect Repair and Imperfect PM.................................. 70
4.2.6 Model 6: Imperfect Repair and Imperfect PM.................................. 72
4.3 Cost Limit Replacement Policy – Model 7................................................. 73
4.4 Age-dependent PM Policies with Imperfect Maintenance.......................... 76
4.4.1 Model 8: Imperfect Repair................................................................ 76
4.4.2 Model 9: Imperfect CM and Imperfect PM ...................................... 80
4.4.3 Model 10: Two Imperfect Repairs .................................................... 82
4.4.4 Model 10a: Two Imperfect Repairs Considering Repair Time ......... 85
4.4.5 Model 11: Imperfect Repair and Perfect PM .................................... 87
4.5 Concluding Discussions..............................................................................88
5 Reliability and Optimal Maintenance of Series Systems
with Imperfect Repair and Dependence ....................................................... 91
5.1 Introduction.................................................................................................91
5.2 System Availability Indices Modeling........................................................ 94
5.3 Modeling of Maintenance Costs ............................................................... 101
5.3.1 Cost Model 1................................................................................... 101
5.3.2 Cost Model 2................................................................................... 102
5.4 Optimal System Maintenance Policies ..................................................... 103
5.4.1 Optimality of Availability and Maintenance Cost Rates................. 103
5.4.2 Optimal Repair Policy..................................................................... 108
5.5 Concluding Discussions............................................................................110
6 Opportunistic Maintenance of Multi-unit Systems.................................... 111
6.1 Optimal Maintenance Policies by the (p, q) Rule ..................................... 114
6.1.1 Modeling of Availability and Cost Rate ......................................... 115
6.1.2 Other Operating Characteristics...................................................... 120
6.1.3 Optimization Models....................................................................... 123
6.2 Optimal Maintenance Policies by the (p(t), q(t)) Rule.............................. 124
6.2.1 Modeling of Availability and Cost Rate ......................................... 124
6.2.2 Other Performance Measures.......................................................... 130
6.2.3 Optimal Maintenance Policy........................................................... 131
6.3 Concluding Remarks................................................................................. 132
7 Optimal Preparedness Maintenance of Multi-unit Systems
with Imperfect Maintenance and Economic Dependence ......................... 135
7.1 Introduction...............................................................................................135
7.2 System Maintenance Cost Rate and ‘Availability’ ................................... 140
7.3 Other Operating Characteristics................................................................ 146
7.4 Optimization Models ................................................................................149
7.5 Concluding Discussions............................................................................150
8 Optimal Opportunistic Maintenance Policies of k-out-of-n Systems ........ 151
8.1 Introduction...............................................................................................151
8.2 Perfect PM................................................................................................155
8.3 Imperfect PM: Case 1 ............................................................................... 159
8.4 Imperfect PM: Case 2 ............................................................................... 161
8.5 Special Cases ............................................................................................ 163
8.6 Optimization Problems .............................................................................166
8.7 Numerical Example ..................................................................................167
8.8 Concluding Discussions............................................................................169
9 Reliability and Optimal Inspection-maintenance Models
of Multi-degraded Systems........................................................................... 171
9.1 Reliability Modeling .................................................................................174
9.1.1 System Description and Modeling Methodologies ......................... 174
9.1.2 Reliability Modeling ....................................................................... 179
9.1.3 Numerical Examples .......................................................................180
9.2 Optimal Inspection-maintenance ..............................................................185
9.2.1 A General Inspection-maintenance Policy...................................... 187
9.2.2 Average Long-run Maintenance Cost Analysis .............................. 189
9.2.3 Algorithms for Optimal Inspection-maintenance Policy................. 196
9.2.4 Numerical Example.........................................................................199
10 Warranty Cost Models with Dependence and Imperfect Repair ............. 203
10.1 RFSW Policies for Multi-component Systems ....................................... 207
10.1.1 Background.................................................................................. 207
10.1.2 Model Details............................................................................... 208
10.1.3 RFSW for Series Systems ............................................................ 210
10.1.4 RFSW for Parallel Systems.......................................................... 215
10.1.5 RFSW for Series-parallel Systems............................................... 216
10.1.6 RFSW for Parallel-series Systems ............................................... 218
10.1.7 A Numerical Example and Sensitivity Study............................... 222
10.2 DWC for Minimally Repaired Series Systems ....................................... 225
10.2.1 Preliminary Results...................................................................... 227
10.2.2 DWC Under an FRW Policy........................................................ 228
10.2.3 DWC Under an PRW Policy........................................................ 231
10.2.4 Numerical Examples .................................................................... 231
10.2.5 Future Research ........................................................................... 235
10.3 RLRFW Policies with Imperfect Repair................................................. 236
10.3.1 Introduction..................................................................................236
10.3.2 Analysis of Repair-limit Risk-free Warranties............................. 237
10.3.3 Special Cases ............................................................................... 240
10.3.4 Numerical Examples and Sensitivity Analysis ............................ 242
10.3.5 Concluding Remarks.................................................................... 244
10.4 Optimal RRLRFW Policies with Minimal Repair .................................. 245
10.4.1 A General Optimization Model.................................................... 247
10.4.2 Cost Analysis of RRLRFW Policy .............................................. 249
10.4.3 Optimal RRLRFW Policy............................................................ 252
10.4.4 Remarks ....................................................................................... 253
10.5 On Warranty Policies and their Comparison .......................................... 254
11 Software Reliability, Cost, and Optimization Models ............................... 259
11.1 Introduction.............................................................................................259
11.2 Use of Quasi-renewal Process in Software Reliability ........................... 261
11.3 Software Reliability and Cost Modeling................................................. 261
11.3.1 Model 1 ........................................................................................ 262
11.3.2 Model 2 ........................................................................................ 265
11.4 Optimization Models .............................................................................. 269
11.5 Concluding Discussions..........................................................................274
12 Monte Carlo Reliability Simulation of Complex Systems......................... 275
12.1 Introduction.............................................................................................275
12.2 Typical Monte Carlo Algorithms for Reliability .................................... 277
12.2.1 K-R Method ................................................................................. 277
12.2.2 R-M Method................................................................................. 280
12.2.3 C-H Method ................................................................................. 282
12.2.4 L-D-L Method.............................................................................. 283
12.2.5 L-D Method ................................................................................. 284
12.2.6 Other Methods for Non-repairable Systems................................. 284
12.2.7 Monte Carlo Methods for Repairable Systems ............................ 286
12.3 Variance Reduction and Random Number Generation........................... 288
12.4 On Monte Carlo Reliability Simulation .................................................. 290
12.5 Commercial Monte Carlo Reliability Simulation Tools ......................... 292
12.6 A General Monte Carlo Reliability Procedure........................................ 293
Appendix Elements of Reliability and Probability .......................................... 295
A.1 Reliability Measures ................................................................................295
A.2 Common Probability Distribution Functions ........................................... 296
A.2.1 Discrete Random Variable Distributions ....................................... 296
A.2.2 Continuous Random Variable Distributions .................................. 298
A.3 Stochastic Processes Concepts................................................................. 302
A.3.1 Markov Processes ..........................................................................302
A.3.2 Counting Processes ........................................................................303
A.3.3 Poisson Processes...........................................................................303
A.3.4 Renewal Processes ......................................................................... 304
A.3.5 Non-homogeneous Poisson Processes............................................305
References ....................................................................................................309
Index ....................................................................................................341
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