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Preliminaries | p. 1 |
The Poisson process and distribution | p. 1 |
Waiting time distributions for a Poisson process | p. 6 |
Statistical estimation theory | p. 8 |
Basic ingredients | p. 8 |
Methods of estimation | p. 9 |
Consistency | p. 11 |
Sufficiency | p. 12 |
Rao-Blackwell improved estimator | p. 13 |
Complete statistic | p. 14 |
Confidence intervals | p. 14 |
Order statistics | p. 16 |
Generating a Poisson process | p. 18 |
Nonhomogeneous Poisson process | p. 19 |
Three important discrete distributions | p. 22 |
Problems and comments | p. 24 |
Statistical life length distributions | p. 39 |
Stochastic life length models | p. 39 |
Constant risk parameters | p. 39 |
Time-dependent risk parameters | p. 41 |
Generalizations | p. 42 |
Models based on the hazard rate | p. 45 |
IFR and DFR | p. 48 |
General remarks on large systems | p. 50 |
Problems and comments | p. 53 |
Reliability of various arrangements of units | p. 63 |
Series and parallel arrangements | p. 63 |
Series systems | p. 63 |
Parallel systems | p. 64 |
The k out of n system | p. 66 |
Series-parallel and parallel-series systems | p. 67 |
Various arrangements of switches | p. 70 |
Series arrangement | p. 71 |
Parallel arrangement | p. 72 |
Series-parallel arrangement | p. 72 |
Parallel-series arrangement | p. 72 |
Simplifications | p. 73 |
Example | p. 74 |
Standby redundancy | p. 76 |
Problems and comments | p. 77 |
Reliability of a one-unit repairable system | p. 91 |
Exponential times to failure and repair | p. 91 |
Generalizations | p. 97 |
Problems and comments | p. 98 |
Reliability of a two-unit repairable system | p. 101 |
Steady-state analysis | p. 101 |
Time-dependent analysis via Laplace transform | p. 105 |
Laplace transform method | p. 105 |
A numerical example | p. 111 |
On Model 2(c) | p. 113 |
Problems and Comments | p. 114 |
Continuous-time Markov chains | p. 117 |
The general case | p. 117 |
Definition and notation | p. 117 |
The transition probabilities | p. 119 |
Computation of the matrix P(t) | p. 120 |
A numerical example (continued) | p. 122 |
Multiplicity of roots | p. 126 |
Steady-state analysis | p. 127 |
Reliability of three-unit repairable systems | p. 128 |
Steady-state analysis | p. 128 |
Steady-state results for the n-unit repairable system | p. 130 |
Example 1 - Case 3(e) | p. 131 |
Example 2 | p. 131 |
Example 3 | p. 131 |
Example 4 | p. 132 |
Pure birth and death processes | p. 133 |
Example 1 | p. 133 |
Example 2 | p. 133 |
Example 3 | p. 134 |
Example 4 | p. 134 |
Some statistical considerations | p. 135 |
Estimating the rates | p. 136 |
Estimation in a parametric structure | p. 137 |
Problems and comments | p. 138 |
First passage time for systems reliability | p. 143 |
Two-unit repairable systems | p. 143 |
Case 2(a) of Section 5.1 | p. 143 |
Case 2(b) of Section 5.1 | p. 148 |
Repairable systems with three (or more) units | p. 150 |
Three units | p. 150 |
Mean first passage times | p. 152 |
Other initial states | p. 154 |
Examples | p. 157 |
Repair time follows a general distribution | p. 160 |
First passage time | p. 160 |
Examples | p. 164 |
Steady-state probabilities | p. 165 |
Problems and comments | p. 167 |
Embedded Markov chains and systems reliability | p. 173 |
Computations of steady-state probabilities | p. 173 |
Example 1: One-unit repairable system | p. 174 |
Example 2: Two-unit repairable system | p. 175 |
Example 3: n-unit repairable system | p. 177 |
Example 4: One out of n repairable systems | p. 183 |
Example 5: Periodic maintenance | p. 184 |
Example 6: Section 7.3 revisited | p. 189 |
Example 7: One-unit repairable system with prescribed on-off cycle | p. 192 |
Mean first passage times | p. 194 |
Example 1: A two-unit repairable system | p. 194 |
Example 2: General repair distribution | p. 195 |
Example 3: Three-unit repairable system | p. 195 |
Computations based on s[subscript jk] | p. 197 |
Problems and comments | p. 200 |
Integral equations in reliability theory | p. 207 |
Introduction | p. 207 |
Example 1: Renewal process | p. 208 |
Some basic facts | p. 208 |
Some asymptotic results | p. 210 |
More basic facts | p. 212 |
Example 2: One-unit repairable system | p. 213 |
Example 3: Preventive replacements or maintenance | p. 215 |
Example 4: Two-unit repairable system | p. 218 |
Example 5: One out of n repairable systems | p. 219 |
Example 6: Section 7.3 revisited | p. 220 |
Example 7: First passage time distribution | p. 223 |
Problems and comments | p. 224 |
References | p. 247 |
Index | p. 251 |
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