Preface |
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xv | |
About the Author |
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xix | |
About the Companion Website |
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xxi | |
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1 | (8) |
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1 | (1) |
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1.2 Performance, Cost, and Reliability |
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2 | (2) |
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1.3 Quality, Reliability, and Safety Linkage |
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4 | (2) |
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1.4 Quality, Reliability, and Safety Engineering Tasks |
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6 | (1) |
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7 | (2) |
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7 | (2) |
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2 Probability and Discrete Distributions |
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9 | (38) |
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9 | (1) |
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9 | (14) |
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9 | (1) |
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10 | (1) |
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10 | (1) |
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Sample space (S) = set of all possible outcomes |
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10 | (1) |
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Outcome (e) = an element of the sample space |
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10 | (1) |
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Event = A subset of outcomes |
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11 | (1) |
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11 | (6) |
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17 | (4) |
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Combinations and Permutations |
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21 | (2) |
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2.3 Discrete Random Variables |
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23 | (24) |
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Properties of Discrete Variables |
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23 | (3) |
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The Binomial Distribution |
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26 | (4) |
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30 | (3) |
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33 | (1) |
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Motivation for Confidence Intervals |
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33 | (2) |
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Introduction to Confidence Intervals |
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35 | (2) |
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Binomial Confidence Intervals |
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37 | (2) |
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Cumulative Sums of the Poisson Distribution (Thorndike Chart) |
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39 | (2) |
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41 | (1) |
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Advanced texts in Probability |
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41 | (1) |
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42 | (5) |
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3 The Exponential Distribution and Reliability Basics |
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47 | (62) |
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47 | (1) |
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3.2 Reliability Characterization |
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47 | (6) |
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48 | (2) |
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50 | (3) |
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3.3 Constant Failure Rate Model |
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53 | (8) |
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The Exponential Distribution |
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54 | (1) |
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55 | (2) |
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57 | (4) |
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3.4 Time-Dependent Failure Rates |
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61 | (2) |
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3.5 Component Failures and Failure Modes |
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63 | (4) |
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63 | (1) |
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64 | (3) |
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67 | (4) |
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71 | (4) |
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Active and Standby Redundancy |
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72 | (1) |
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72 | (1) |
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73 | (1) |
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Constant Failure Rate Models |
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73 | (2) |
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3.8 Redundancy Limitations |
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75 | (6) |
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76 | (1) |
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77 | (2) |
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Switching and Standby Failures |
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79 | (1) |
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Cold, Warm, and Hot Standby |
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80 | (1) |
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3.9 Multiply Redundant Systems |
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81 | (5) |
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81 | (2) |
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83 | (1) |
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84 | (2) |
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3.10 Redundancy Allocation |
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86 | (8) |
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High- and Low-level Redundancy |
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88 | (2) |
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Fail Safe and Fail to Danger |
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90 | (2) |
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92 | (2) |
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3.11 Redundancy in Complex Configurations |
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94 | (15) |
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Series--Parallel Configurations |
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94 | (2) |
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96 | (2) |
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98 | (1) |
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98 | (5) |
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103 | (6) |
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4 Continuous Distributions -- Part 1 Normal and Related Continuous Distributions |
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109 | (40) |
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109 | (1) |
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4.2 Properties of Continuous Random Variables |
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109 | (8) |
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Probability Distribution Functions |
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110 | (2) |
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Characteristics of a Probability Distribution |
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112 | (2) |
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114 | (1) |
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Transformations of Variables |
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115 | (2) |
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4.3 Empirical Cumulative Distribution Function (Empirical CDF) |
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117 | (3) |
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120 | (2) |
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4.5 Normal and Related Distributions |
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122 | (13) |
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123 | (3) |
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Normal Distribution Cautions and Warnings!! |
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126 | (1) |
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127 | (1) |
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Central Limit Theorem in Practice |
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128 | (1) |
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The Lognormal Distribution |
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128 | (6) |
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Log Normal Distribution from a Physics of Failure Perspective |
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134 | (1) |
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135 | (5) |
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Point and Interval Estimates |
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135 | (4) |
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139 | (1) |
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4.7 Normal and Lognormal Parameters |
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140 | (9) |
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142 | (1) |
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143 | (6) |
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5 Continuous Distributions -- Part 2 Weibull and Extreme Value Distributions |
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149 | (72) |
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149 | (5) |
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The "Weakest Link" Theory from a Physics-of-Failure Point of View |
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149 | (1) |
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Uses of Weibull and Extreme Value Distributions |
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150 | (1) |
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151 | (1) |
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Age Parameters and Sample Sizes |
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151 | (1) |
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Engineering Changes, Maintenance Plan Evaluation, and Risk Prediction |
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152 | (1) |
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Weibulls with Cusps or Curves |
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152 | (1) |
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153 | (1) |
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154 | (1) |
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154 | (1) |
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154 | (1) |
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5.2 Statistics of the Weibull Distribution |
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154 | (35) |
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154 | (4) |
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The Weibull Probability Plot |
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158 | (2) |
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Probability Plotting Points -- Median Ranks |
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160 | (1) |
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How to Do a "Weibull Analysis" |
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161 | (2) |
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Weibull Plots and Their Estimates of β, η |
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163 | (4) |
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The Three-Parameter Weibull Did Not Work, What Are My Choices? |
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167 | (1) |
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The Data has a "Dogleg" Bend or Cusp When Plotted on Weibull Paper |
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167 | (4) |
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Steep Weibull Slopes (βs) May Hide Problems |
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171 | (1) |
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Low-Time Failures and Close Serial numbers -- Batch Problems |
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172 | (1) |
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Maximum-Likelihood Estimates of β and η |
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172 | (4) |
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176 | (1) |
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Weibayes Background (You Do Not Necessarily Have Any Failure Times) |
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177 | (3) |
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Weibull Analysis with Failures Only and Unknown Times on the Unfailed Population |
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180 | (1) |
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Shifting Weibull Procedure |
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180 | (1) |
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Confidence Bounds and the Weibull Distribution |
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181 | (3) |
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Arbitrary Censored Data -- Left-Censored, Right-Censored, and Interval Data |
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184 | (4) |
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The Weibull Distribution in a System of Independent Failure Modes |
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188 | (1) |
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5.3 Extreme Value Distributions |
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189 | (8) |
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5.4 Introduction to Risk Analysis |
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197 | (24) |
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Risk Analysis "Mathematics" |
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197 | (6) |
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203 | (2) |
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205 | (14) |
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Supplement 1 Weibull Derived from Weakest Link Theory |
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219 | (2) |
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221 | (106) |
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221 | (2) |
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6.2 Attribute Testing (Binomial Testing) |
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223 | (5) |
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The Classical Success Run |
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224 | (1) |
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Zero-Failure Attribute Tests |
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224 | (1) |
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Non-Zero-Failure Attribute Tests |
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225 | (3) |
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6.3 Constant Failure Rate Estimates |
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228 | (6) |
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228 | (2) |
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230 | (2) |
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232 | (2) |
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6.4 Weibull Substantiation and Reliability Testing |
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234 | (9) |
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Zero-Failure Test Plans for Substantiation Testing |
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235 | (2) |
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Weibull Zero-Failure Test Plans for Reliability Testing |
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237 | (2) |
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Reexpression of a Reliability Goal to Determine η |
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239 | (1) |
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239 | (2) |
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Test Units with Censored Times (due to Julius Wang, Fiat-Chrysler) |
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241 | (1) |
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242 | (1) |
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Why Not Simply Test to Failure? |
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243 | (1) |
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6.5 How to Reduce Test Time |
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243 | (12) |
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Run (Simultaneously) More Test Samples Than You Intend to Fail |
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243 | (2) |
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245 | (2) |
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247 | (8) |
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6.6 Normal and Lognormal Reliability Testing |
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255 | (7) |
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6.7 Accelerated Life Testing |
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262 | (20) |
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262 | (3) |
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Advanced-Stress Testing -- Linear and Acceleration Models |
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265 | (1) |
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Linear Model Stress Testing |
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266 | (4) |
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Advanced-Stress Testing -- Acceleration Models |
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270 | (1) |
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270 | (5) |
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The Inverse Power Law Model |
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275 | (5) |
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Other Acceleration Models |
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280 | (2) |
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6.8 Reliability-Enhancement Procedures |
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282 | (45) |
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Reliability Growth Modeling and Testing |
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282 | (5) |
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Calculation of Reliability Growth Parameters |
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287 | (1) |
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Goodness-of-Fit Tests for Reliability Growth Models |
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288 | (1) |
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For Time-Terminated Testing |
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288 | (1) |
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For Failure-Terminated Testing |
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289 | (1) |
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289 | (10) |
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Environmental Stress Screening |
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299 | (3) |
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What "Screens" are used for ESS? |
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302 | (1) |
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302 | (1) |
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303 | (1) |
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303 | (1) |
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Highly Accelerated Life Tests |
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304 | (1) |
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Highly Accelerated-Stress Screening |
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305 | (1) |
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305 | (1) |
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306 | (9) |
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Supplement 1 Tables for Weibull Zero-failure Substantiatioon testing |
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315 | (4) |
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Supplement 2 Tables For Weibull Zer-failure Substantiation testing using (t/Eta) |
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319 | (4) |
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Supplement 3 Critical Values for Cramer--Von Mises Goodness-of-Fit Test |
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323 | (1) |
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Supplement 4 Other Reliability Growth Models that have been Proposed and Studied (see AFWAL-TR-84-2024 for details) |
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323 | (1) |
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323 | (1) |
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(b) Poisson Process Models |
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324 | (1) |
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(c) Markov Processes/Time Series Models |
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325 | (1) |
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Supplement 5 Chi-Square Table |
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326 | (1) |
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7 Failure Modes and Effects Analysis -- Design and Process |
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327 | (34) |
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327 | (1) |
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328 | (4) |
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332 | (7) |
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332 | (7) |
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339 | (10) |
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349 | (12) |
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350 | (1) |
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350 | (9) |
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Supplement 1 Shortcut Tables for Stalled FMEA Teams |
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359 | (1) |
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Supplement 2 Future Changes in FMEA Approaches |
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360 | (1) |
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Supplement 3 DFMEA and PFMEA Forms |
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360 | (1) |
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8 Loads, Capacity, and Reliability |
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361 | (34) |
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361 | (1) |
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8.2 Reliability with a Single Loading |
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362 | (6) |
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363 | (1) |
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364 | (4) |
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8.3 Reliability and Safety Factors |
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368 | (8) |
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368 | (5) |
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373 | (1) |
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374 | (2) |
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376 | (6) |
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376 | (4) |
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380 | (2) |
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8.5 The Bathtub Curve -- Reconsidered |
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382 | (13) |
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383 | (2) |
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385 | (2) |
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387 | (1) |
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388 | (4) |
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Supplement 1 The Dirac Delta Distribution |
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392 | (3) |
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395 | (32) |
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395 | (1) |
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9.2 Preventive Maintenance |
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396 | (7) |
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396 | (5) |
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401 | (2) |
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403 | (1) |
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9.3 Corrective Maintenance |
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403 | (4) |
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404 | (1) |
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405 | (2) |
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9.4 Repair: Revealed Failures |
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407 | (4) |
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407 | (3) |
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410 | (1) |
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9.5 Testing and Repair: Unrevealed Failures |
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411 | (4) |
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411 | (2) |
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413 | (2) |
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415 | (12) |
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416 | (2) |
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418 | (1) |
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419 | (1) |
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420 | (2) |
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422 | (1) |
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422 | (5) |
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427 | (36) |
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427 | (1) |
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427 | (7) |
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Two Independent Components |
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429 | (3) |
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432 | (2) |
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10.3 Reliability With Standby Systems |
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434 | (10) |
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434 | (3) |
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Failures in the Standby State |
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437 | (2) |
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439 | (3) |
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442 | (2) |
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10.4 Multicomponent Systems |
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444 | (5) |
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Multicomponent Markov Formulations |
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444 | (4) |
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Combinations of Subsystems |
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448 | (1) |
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449 | (14) |
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449 | (4) |
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453 | (4) |
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Markov Availability -- Advantages and Disadvantages |
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457 | (1) |
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The Advantages of Markov Availability Analysis |
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457 | (1) |
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The Disadvantages of Markov Availability Analysis |
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457 | (1) |
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457 | (1) |
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457 | (6) |
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11 System Safety Analysis |
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463 | (58) |
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463 | (1) |
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11.2 Product and Equipment Hazards |
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464 | (2) |
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466 | (5) |
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468 | (2) |
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470 | (1) |
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471 | (9) |
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Failure Modes, Effects, and Criticality Analysis (FMECA) |
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472 | (1) |
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472 | (6) |
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478 | (2) |
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480 | (25) |
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482 | (1) |
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483 | (3) |
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486 | (1) |
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Primary, Secondary, and Command Faults |
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486 | (1) |
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Passive and Active Faults |
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486 | (1) |
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487 | (7) |
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Direct Evaluation of Fault Trees |
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494 | (1) |
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494 | (1) |
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495 | (1) |
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495 | (1) |
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496 | (1) |
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496 | (1) |
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Probability Relationships |
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497 | (1) |
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498 | (1) |
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Fault-Tree Evaluation by Cut Sets |
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499 | (1) |
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499 | (1) |
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Minimum Cut-Set Formulation |
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499 | (2) |
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501 | (1) |
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502 | (1) |
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503 | (1) |
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503 | (2) |
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505 | (1) |
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505 | (1) |
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11.6 Reliability/Safety Risk Analysis |
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505 | (16) |
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Conclusion: Assuming Worst Case can be Misleading |
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508 | (1) |
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Another Approach: Monte Carlo Simulation |
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508 | (7) |
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515 | (1) |
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515 | (1) |
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516 | (5) |
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Appendix A Useful Mathematical Relationships |
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521 | (4) |
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521 | (1) |
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521 | (1) |
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521 | (1) |
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Derivative of an Integral |
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521 | (1) |
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522 | (1) |
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522 | (1) |
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522 | (1) |
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522 | (1) |
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522 | (1) |
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A.3 Solution of First-order Linear Differential Equation |
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523 | (2) |
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Appendix B Binomial Failure Probability Charts |
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525 | (4) |
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Appendix C Φ(z): Standard Normal CDF |
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529 | (4) |
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Appendix D Nonparametric Methods and Probability Plotting |
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533 | (22) |
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533 | (1) |
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D.2 Nonparametric Methods for Probability Plotting |
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533 | (4) |
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533 | (1) |
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533 | (2) |
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535 | (1) |
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536 | (1) |
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537 | (10) |
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Weibull Distribution Plotting |
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540 | (3) |
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Extreme-Value Distribution Plotting |
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543 | (2) |
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Lognormal Distribution Plotting |
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545 | (2) |
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547 | (8) |
Bibliography |
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555 | (2) |
3rd Ed Answers to Odd -- Numbered Exercises |
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557 | (50) |
Index |
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607 | |