Transcription of The Weibull Distribution - GBV
1 The Weibull Distribution A handbook Horst Rinne Justus-Liebig-University Giessen, Germany @ CRC Press Taylor &. Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group an informa business A CHAPMAN & HALL BOOK Contents Preface XIII List of Figures XVII
2 List of Tables XXI I Genesis, theory and description 1 1 History and meaning of the Weibull Distribution 3 Genesis of the Weibull Distribution 3 Origins in science 4
3 Origins in practice 9 Grinding of material ROSIN, RAMMLER and SPERLING 9 Strength of material Weibull 12 Physical meanings and interpretations of the Weibull Distribution .. 15 The model of the weakest link 15 Two models of data degradation leading to Weibull distributed failures 19 The hazard rate approach 22
4 The broken-stick model 24 2 Definition and properties of the Weibull Distribution 27 Functions describing lifetime as a random variable 27 Failure density 30 Three-parameter density 30 Two- and one-parameter densities 34 Analysis of the reduced Weibull density 36 Differing notations
5 41 Failure Distribution (CDF) and reliability function (CCDF) 43 Hazard rate (HR) 46 Cumulative hazard rate (CHR) 49 Mean residual life function (MRL)
6 51 IV Contents Aging criteria 58 Percentiles and random number generation 68 Percentiles 68 Weibull random numbers 70 Moments.
7 Cumulants and their generating functions 71 General formulas 71 Mean and its relation to mode and median 85 Variance, standard deviation and coefficient of variation 89 Skewness and kurtosis 91 3 Related distributions 98 Systems of distributions and the Weibull Distribution 98
8 PEARSON system 98 BURR system 101 JOHNSON system 103 Miscellaneous 105 Weibull distributions and other familiar distributions 108 Weibull and exponential distributions 108 Weibull and extreme value distributions 108 Weibull and gamma distributions
9 Ill Weibull and normal distributions 112 Weibull and further distributions 115 Modifications of the Weibull Distribution 119 Discrete Weibull Distribution 119 Reflected and double Weibull distributions 125 Inverse Weibull Distribution 129 Log- Weibull Distribution 131
