Technical Note: Relationship between Weibull and double exponential distributions in evaluating quality of ceramics

Abstract

At present Weibull probability law is exclusively applied all over the world for analysis of the flexural strength data of fine ceramics. However, a few misunderstandings on the Weibull distribution seem to devalue the universal method. One of these misunderstandings is the common opinion that the greater the value of the shape parameter of the distribution is, the less the standard deviation of stochastic variable or dispersion of flexural strength data becomes. This Note aims to remove such an obstacle by proposing an unprejudiced approach to the problem. The intention is to correct the prevailing misapprehension, specifically through a study on the statistical relationship between Weibull and double exponential (or extreme–value) distributions.