An imprecise statistical method for accelerated life testing using the power-Weibull model

Abstract

Accelerated life testing provides an interesting challenge for quantification of the uncertainties involved, in particular due to the required linking of the units’ failure times, or failure time distributions, at different stress levels. This paper provides an initial exploration of the use of statistical methods based on imprecise probabilities for accelerated life testing. We apply nonparametric predictive inference at the normal stress level, in combination with an estimated parametric power-Weibull model linking observations at different stress levels. To provide robustness with regard to this assumed link between different stress levels, we introduce imprecision by considering an interval around the parameter estimate, leading to observations at stress levels other than the normal level to be transformed to intervals at the normal level. The width of such intervals is increasing with the difference between the stress level at which a unit is tested and the normal level. The resulting inference method is predictive, so it explicitly considers the random failure time of a future unit tested at the normal level. We perform simulation studies to investigate the performance of our imprecise predictive method and to get insight into a suitable amount of imprecision for the linking between levels. We also explain how simulation studies can assist in choosing imprecision in order to provide robustness against specific biases or model misspecifications.