The Weibull Distribution: A Handbook - Index of

Contents
Preface XIII
List of Figures XVII
List of Tables XXI
I Genesis, theory and description 1
1 History and meaning of the WEIBULL distribution 3
1.1 Genesis of the WEIBULL distribution . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Origins in science . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Origins in practice . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1.2.1 Grinding of material — ROSIN, RAMMLER and SPERLING 9
1.1.2.2 Strength of material — WEIBULL . . . . . . . . . . . . . 12
1.2 Physical meanings and interpretations of the WEIBULL distribution . . . . 15
1.2.1 The model of the weakest link . . . . . . . . . . . . . . . . . . . . 15
1.2.2 Two models of data degradation leading to WEIBULL distributed
failures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.2.3 The hazard rate approach . . . . . . . . . . . . . . . . . . . . . . . 22
1.2.4 The broken-stick model . . . . . . . . . . . . . . . . . . . . . . . 24
2 Definition and properties of the WEIBULL distribution 27
2.1 Functions describing lifetime as a random variable . . . . . . . . . . . . . 27
2.2 Failure density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.1 Three-parameter density . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.2 Two- and one-parameter densities . . . . . . . . . . . . . . . . . . 34
2.2.3 Analysis of the reduced WEIBULL density . . . . . . . . . . . . . . 36
2.2.4 Differing notations . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.3 Failure distribution (CDF) and reliability function (CCDF) . . . . . . . . . 43
2.4 Hazard rate (HR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.5 Cumulative hazard rate (CHR) . . . . . . . . . . . . . . . . . . . . . . . . 49
2.6 Mean residual life function (MRL) . . . . . . . . . . . . . . . . . . . . . . 51
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