Back to and beyond Weibull – The hazard function approach

Abstract

Weilbull studied in 1939 systematically deviations from his classical model, for the case of multiple flaw distributions. This was based on operations with classical Weibull distributions, for the cases of mixed and concurrent flaw distributions. For modeling a further case, he had to drop the weakest-link assumption. The present paper uses the cumulative hazard function, which makes understanding simple and opens the way for further models. Weibull’s example can now be described in the framework of weakest-link theory, by means of a composite hazard function, with sectional Weibull components. Some examples illustrate the approach, which is based on the classical Weibull plot and uses least squares estimation.