Assessing Material Aging from Doubly Censored Data : Weibull Distribution vs. Poisson Process
Résumé
The versatile Weibull distribution is popular for modeling aging in failure time problems. However, in some situations the only available data are right or left censored data and estimating the Weibull distribution parameters is made much more difficult. In this paper, we consider the performance of estimating a Weibull distribution in such a doubly censored context from the maximum likelihood approach and from a non informative Bayesian point of view. Moreover, we propose an alternative model for assessing aging. It consists in assuming that left censored data arise from a Poisson process. This model can appear to provide more reliable results from such poorly informative failure time data. Both approaches are compared on the basis of numerical experiments.