Introduction |
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ix | |
About the Author |
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xi | |
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1 Time-to-Failure Distributions and Reliability Measures |
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1 | (6) |
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1.1 Probability Density and Cumulative Distribution Functions |
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1 | (1) |
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1.2 Conditional Reliability, Failure Rate, Cumulative Failure Rate, and Average Failure Rate |
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2 | (1) |
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3 | (4) |
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2 Probabilistic Models for Nonrepairable Objects |
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7 | (72) |
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2.1 Shock Models and Component Life Distributions |
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7 | (26) |
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2.1.1 Poisson Distribution and Homogeneous Poisson Process |
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7 | (7) |
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2.1.2 Exponential Time-to-Failure Distribution |
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14 | (3) |
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2.1.3 Gamma Time-to-Failure Distribution |
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17 | (4) |
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2.1.4 Normal (Gaussian) Time-to-Failure Distribution |
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21 | (3) |
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2.1.5 Lognormal Time-to-Failure Distribution |
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24 | (4) |
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2.1.6 Weibull Time-to-Failure Distribution |
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28 | (4) |
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2.1.6.1 Weakest Link Model |
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32 | (1) |
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2.2 Classes of Aging/Rejuvenating Distributions and Their Properties |
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33 | (12) |
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2.2.1 Damage Accumulation Models Resulting in Aging TTF Distributions |
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36 | (1) |
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37 | (1) |
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38 | (1) |
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2.2.2 Some Useful Inequalities for Reliability Measures and Characteristics for Aging/Rejuvenating Distributions |
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39 | (1) |
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2.2.2.1 Bounds Based on a Known Quantile |
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39 | (1) |
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2.2.2.2 Bounds Based on a Known Mean |
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40 | (1) |
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2.2.2.3 Inequality for Coefficient of Variation |
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40 | (1) |
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2.2.3 Gini-Type Index for Aging/Rejuvenating Distributions |
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41 | (2) |
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2.2.3.1 GT Index for the Weibull Distribution |
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43 | (1) |
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2.2.3.2 GT Index for the Gamma Distribution |
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43 | (2) |
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2.3 Models with Explanatory Variables |
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45 | (34) |
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45 | (1) |
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46 | (1) |
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2.3.3 Models with Constant Explanatory Variables (Stress Factors) |
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46 | (1) |
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2.3.3.1 Accelerated Life Model |
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47 | (4) |
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2.3.3.2 Proportional Hazards Model |
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51 | (2) |
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2.3.3.3 Popular Accelerated Life Reliability Models |
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53 | (3) |
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2.3.3.4 Popular Proportional Hazards Models |
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56 | (2) |
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2.3.4 Models with Time-Dependent Explanatory Variables (Stress Factors) |
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58 | (1) |
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2.3.4.1 Accelerated Life Model with Time-Dependent Explanatory Variables |
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58 | (7) |
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2.3.4.2 Accelerated Life Reliability Model for Time-Dependent Stress and Palmgren-Miner's Rule |
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65 | (2) |
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2.3.4.3 Proportional Hazards Model with Time-Dependent Explanatory Variables |
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67 | (1) |
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2.3.5 Competing Failure Modes and Series System Model |
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68 | (2) |
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2.3.6 Competing Risks Model vs. Mixture Distribution Model |
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70 | (9) |
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3 Probabilistic Models for Repairable Objects |
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79 | (42) |
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3.1 Point Processes as Model for Repairable Systems Failure Processes |
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79 | (7) |
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3.2 Homogeneous Poisson Process as a Simplest Failure-Repair Model |
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86 | (1) |
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3.3 Renewal Process: As-Good-as-New Repair Model |
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87 | (5) |
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3.4 Nonhomogeneous Poisson Process: As-Good-as-Old Repair Model |
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92 | (6) |
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3.4.1 Power Law ROCOF and Weibull Distribution |
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94 | (1) |
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3.4.2 Log-Linear ROCOF and Truncated Gumbel Distribution |
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94 | (2) |
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3.4.3 Linear ROCOF and Competing Risks |
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96 | (1) |
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3.4.4 NHPP with Nonmonotonic ROCOF |
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97 | (1) |
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3.5 Generalized Renewal Process |
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98 | (9) |
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3.6 Inequalities for Reliability Measures and Characteristics for Renewal and Generalized Renewal Processes |
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107 | (6) |
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3.7 Geometric Process: Adding the Better than New Repair |
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113 | (5) |
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3.7.1 Geometric Process with Exponential Underlying Distribution |
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114 | (1) |
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3.7.2 Geometric Process with Weibull Underlying Distribution |
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115 | (3) |
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3.8 Gini-Type Index for Aging/Rejuvenating Processes |
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118 | (3) |
Appendix A Transformations of Random Variables |
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121 | (2) |
Appendix B Coherent Systems |
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123 | (2) |
Appendix C Uniform Distribution |
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125 | (2) |
References and Bibliography |
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127 | (6) |
Index |
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133 | |