ABSTRACT
In many areas of statistical application, the natural starting point to model a random variable of interest is the Normal distribution. This may result from purely pragmatic considerations or from a theoretical argument based on the Central Limit Theorem, which says that if the random variable is the sum of a large number of small effects, then its distribution is approximately Normal. In the context of reliability, the case for Normality is much less compelling. For one thing, lifetimes and strengths are inherently positive quantities. In addition, from a modelling point of view, it is perhaps natural to begin with the Poisson process ideas, which lead to the exponential distribution. Whilst this distribution is of limited applicability in practice, generalizations of the exponential distribution, such as the gamma and Weibull distributions have proved to be valuable models in reliability. Many other statistical models have been applied to reliability data, though the above models are the most commonly encountered in practice.
