|
|
1 | (16) |
|
|
1 | (6) |
|
|
2 | (1) |
|
|
3 | (1) |
|
1.1.3 Different Information Levels |
|
|
4 | (1) |
|
|
4 | (1) |
|
1.1.5 Predictable Lifetime |
|
|
5 | (1) |
|
1.1.6 A General Failure Model |
|
|
6 | (1) |
|
|
7 | (2) |
|
1.2.1 Availability Analysis |
|
|
8 | (1) |
|
1.2.2 Optimization Models |
|
|
9 | (1) |
|
|
9 | (8) |
|
1.3.1 Nuclear Power Station |
|
|
11 | (2) |
|
1.3.2 Gas Compression System |
|
|
13 | (4) |
|
2 Basic Reliability Theory |
|
|
17 | (40) |
|
|
17 | (17) |
|
2.1.1 Binary Monotone Systems |
|
|
17 | (14) |
|
2.1.2 Multistate Monotone Systems |
|
|
31 | (3) |
|
2.2 Basic Notions of Aging |
|
|
34 | (8) |
|
2.2.1 Nonparametric Classes of Lifetime Distributions |
|
|
35 | (3) |
|
|
38 | (2) |
|
2.2.3 Stochastic Comparison |
|
|
40 | (2) |
|
2.3 Copula Models of Complex Systems in Reliability |
|
|
42 | (15) |
|
2.3.1 Introduction to Copula Models |
|
|
42 | (3) |
|
2.3.2 The Influence of the Copula on the Lifetime Distribution of the System |
|
|
45 | (4) |
|
2.3.3 Archimedean Copulas |
|
|
49 | (1) |
|
2.3.4 The Expectation of the Lifetime of a Two-Component-System with Exponential Marginals |
|
|
50 | (2) |
|
2.3.5 Marshall-Olkin Distribution |
|
|
52 | (5) |
|
3 Stochastic Failure Models |
|
|
57 | (48) |
|
3.1 Notation and Fundamentals |
|
|
57 | (13) |
|
3.1.1 The Semimartingale Representation |
|
|
59 | (9) |
|
3.1.2 Transformations of SSMs |
|
|
68 | (2) |
|
3.2 A General Lifetime Model |
|
|
70 | (11) |
|
3.2.1 Existence of Failure Rate Processes |
|
|
72 | (1) |
|
3.2.2 Failure Rate Processes in Complex Systems |
|
|
73 | (4) |
|
3.2.3 Monotone Failure Rate Processes |
|
|
77 | (1) |
|
3.2.4 Change of Information Level |
|
|
78 | (3) |
|
3.3 Point Processes in Reliability: Failure Time and Repair Models |
|
|
81 | (24) |
|
3.3.1 Alternating Renewal Processes: One-Component Systems with Repair |
|
|
84 | (1) |
|
3.3.2 Number of System Failures for Monotone Systems |
|
|
85 | (1) |
|
3.3.3 Compound Point Process: Shock Models |
|
|
86 | (2) |
|
3.3.4 Shock Models with State-Dependent Failure Probability |
|
|
88 | (1) |
|
3.3.5 Shock Models with Failures of Threshold Type |
|
|
89 | (1) |
|
3.3.6 Minimal Repair Models |
|
|
90 | (5) |
|
3.3.7 Comparison of Repair Processes for Different Information Levels |
|
|
95 | (2) |
|
3.3.8 Repair Processes with Varying Degrees of Repair |
|
|
97 | (1) |
|
3.3.9 Minimal Repairs and Probability of Ruin |
|
|
98 | (7) |
|
4 Availability Analysis of Complex Systems |
|
|
105 | (70) |
|
|
105 | (1) |
|
4.2 One-Component Systems |
|
|
106 | (14) |
|
|
108 | (1) |
|
4.2.2 The Distribution of the Number of System Failures |
|
|
109 | (7) |
|
4.2.3 The Distribution of the Downtime in a Time Interval |
|
|
116 | (3) |
|
4.2.4 Steady-State Distribution |
|
|
119 | (1) |
|
4.3 Point Availability and Mean Number of System Failures |
|
|
120 | (5) |
|
|
120 | (1) |
|
4.3.2 Mean Number of System Failures |
|
|
121 | (4) |
|
4.4 Distribution of the Number of System Failures |
|
|
125 | (20) |
|
4.4.1 Asymptotic Analysis for the Time to the First System Failure |
|
|
126 | (5) |
|
4.4.2 Some Sufficient Conditions |
|
|
131 | (4) |
|
4.4.3 Asymptotic Analysis of the Number of System Failures |
|
|
135 | (10) |
|
4.5 Downtime Distribution Given System Failure |
|
|
145 | (6) |
|
|
146 | (2) |
|
4.5.2 General Monotone System |
|
|
148 | (1) |
|
4.5.3 Downtime Distribution of the ith System Failure |
|
|
149 | (2) |
|
4.6 Distribution of the System Downtime in an Interval |
|
|
151 | (7) |
|
4.6.1 Compound Poisson Process Approximation |
|
|
152 | (1) |
|
4.6.2 Asymptotic Analysis |
|
|
153 | (5) |
|
4.7 Generalizations and Related Models |
|
|
158 | (17) |
|
4.7.1 Multistate Monotone Systems |
|
|
158 | (7) |
|
4.7.2 Parallel System with Repair Constraints |
|
|
165 | (1) |
|
|
166 | (9) |
|
5 Maintenance Optimization |
|
|
175 | (70) |
|
5.1 Basic Replacement Models |
|
|
175 | (5) |
|
5.1.1 Age Replacement Policy |
|
|
175 | (2) |
|
5.1.2 Block Replacement Policy |
|
|
177 | (1) |
|
5.1.3 Comparisons and Generalizations |
|
|
178 | (2) |
|
5.2 A General Replacement Model |
|
|
180 | (10) |
|
5.2.1 An Optimal Stopping Problem |
|
|
180 | (3) |
|
5.2.2 A Related Stopping Problem |
|
|
183 | (6) |
|
5.2.3 Different Information Levels |
|
|
189 | (1) |
|
|
190 | (17) |
|
5.3.1 The Generalized Age Replacement Model |
|
|
190 | (3) |
|
5.3.2 A Shock Model of Threshold Type |
|
|
193 | (1) |
|
5.3.3 Information-Based Replacement of Complex Systems |
|
|
194 | (3) |
|
5.3.4 A Parallel System with Two Dependent Components |
|
|
197 | (1) |
|
5.3.5 Complete Information About T1, T2 and T |
|
|
198 | (4) |
|
|
202 | (5) |
|
5.4 Repair Replacement Models |
|
|
207 | (8) |
|
5.4.1 Optimal Replacement Under a General Repair Strategy |
|
|
207 | (1) |
|
5.4.2 A Markov-Modulated Repair Process: Optimization with Partial Information |
|
|
208 | (6) |
|
5.4.3 The Case of m=2 States |
|
|
214 | (1) |
|
5.5 Maintenance Optimization Models Under Constraints |
|
|
215 | (30) |
|
5.5.1 A Delay Time Model with Safety Constraints |
|
|
215 | (14) |
|
5.5.2 Optimal Test Interval for a Monotone Safety System |
|
|
229 | (16) |
|
A Background in Probability and Stochastic Processes |
|
|
245 | (28) |
|
|
245 | (1) |
|
A.2 Random Variables, Conditional Expectations |
|
|
246 | (8) |
|
A.2.1 Random Variables and Expectations |
|
|
246 | (2) |
|
A.2.2 Lp-Spaces and Conditioning |
|
|
248 | (3) |
|
A.2.3 Properties of Conditional Expectations |
|
|
251 | (1) |
|
A.2.4 Regular Conditional Probabilities |
|
|
252 | (1) |
|
A.2.5 Computation of Conditional Expectations |
|
|
253 | (1) |
|
A.3 Stochastic Processes on a Filtered Probability Space |
|
|
254 | (3) |
|
|
257 | (2) |
|
|
259 | (7) |
|
|
266 | (7) |
|
|
267 | (1) |
|
|
268 | (5) |
|
|
273 | (10) |
|
B.1 Basic Theory of Renewal Processes |
|
|
273 | (7) |
|
B.2 Renewal Reward Processes |
|
|
280 | (1) |
|
B.3 Regenerative Processes |
|
|
281 | (1) |
|
B.4 Modified (Delayed) Processes |
|
|
281 | (2) |
References |
|
283 | (10) |
Index |
|
293 | |