Multistate systems reliability : theory with applications

Multistate Systems Reliability Theory with Applications......Page 5
Contents......Page 9
Preface......Page 13
Acknowledgements......Page 17
List of abbreviations......Page 19
1 Introduction......Page 21
1.1 Basic notation and two simple examples......Page 22
1.2 An offshore electrical power generation system......Page 24
1.3 Basic definitions from binary theory......Page 26
1.4 Early attempts to define multistate coherent systems......Page 29
1.5 Exercises......Page 30
2.1 Multistate monotone and coherent systems......Page 31
2.2 Binary type multistate systems......Page 36
2.3 Multistate minimal path and cut vectors......Page 42
2.4 Stochastic performance of multistate monotone and coherent systems......Page 50
2.5 Stochastic performance of binary type multistate strongly coherent systems......Page 63
2.6 Exercises......Page 66
3 Bounds for system availabilities and unavailabilities......Page 69
3.1 Performance processes of the components and the system......Page 70
3.2 Basic bounds in a time interval......Page 73
3.3 Improved bounds in a time interval using modular decompositions......Page 81
3.4 Improved bounds at a fixed point of time using modular decompositions......Page 87
3.5 Strict and exactly correct bounds......Page 95
3.6 Availabilities and unavailabilities of the components......Page 100
3.7 The simple network system revisited......Page 104
3.8 The offshore electrical power generation system revisited......Page 111
4.1 Description of the system......Page 119
4.2 Bounds for system availabilities and unavailabilities......Page 127
5.1 Basic ideas......Page 133
5.2 Moments for posterior component availabilities and unavailabilities......Page 137
5.3 Bounds for moments for system availabilities and unavailabilities......Page 139
5.4 A simulation approach and an application to the simple network system......Page 147
6.1 Introduction......Page 153
6.2 Measures of component importance in nonrepairable systems......Page 154
6.2.1 The Birnbaum measure......Page 155
6.2.2 The Barlow–Proschan measure......Page 157
6.2.3 The Natvig measure......Page 158
6.3.1 The Birnbaum measure......Page 162
6.3.2 The Barlow–Proschan measure......Page 163
6.3.3 The dual extension of the Barlow–Proschan measure......Page 167
6.4.1 The Natvig measure......Page 169
6.4.2 The dual extension of the Natvig measure......Page 174
6.5 Concluding remarks......Page 180
7.1 Introduction......Page 181
7.2 Component importance in two three-component systems......Page 182
7.3 Component importance in the bridge system......Page 193
7.4 Application to an offshore oil and gas production system......Page 201
7.4.1 Exponentially distributed repair times and times spent in each of the non complete failure states......Page 205
7.4.2 Gamma distributed repair times and times spent in each of the non complete failure states......Page 207
7.5 Concluding remarks......Page 213
8.1 Introduction and basic marked point process......Page 215
8.2 Partial monitoring of components and the corresponding likelihood formula......Page 217
8.3 Incorporation of information from the observed system history process......Page 219
8.4 Cause control and transition rate control......Page 222
8.5 Maintenance, repair and aggregation of operational periods......Page 224
8.6 The offshore electrical power generation system......Page 226
8.7 The data augmentation approach......Page 228
A.1 Proof of the inequalities 14, 7 and 8 of Theorem 3.12......Page 231
A.2 Proof of inequality 14 of Theorem 3.13......Page 234
A.3 Proof of inequality 10 of Theorem 3.17......Page 235
Appendix B Remaining intensity matrices in Chapter 4......Page 239
References......Page 243
Index......Page 247