Weibull Distributions and Their Applications

Abstract

Weibull models are used to describe various types of observed failures of components and phenomena. They are widely used in reliability and survival analysis. In addition to the traditional two-parameter and three-parameter Weibull distributions in the reliability or statistics literature, many other Weibull-related distributions are available. The purpose of this chapter is to give a brief introduction to those models, with the emphasis on models that have the potential for further applications. After introducing the traditional Weibull distribution, some historical development and basic properties are presented. We also discuss estimation problems and hypothesis-testing issues, with the emphasis on graphical methods. Many extensions and generalizations of the basic Weibull distributions are then summarized. Various applications in the reliability context and some Weibull densitydistribution functionempirical modelingestimationfailure rate (FR)graphicalhazard plothistoricalhypothesis testingmomentsreliabilityWeibull probability plotWeibull distributionWeibull derived analysis software are also provided.