On Imprecise Statistical Inference for Accelerated Life Testing

Abstract

Accelerated life testing provides an interesting challenge for quantification of the uncertainties involved, in particular due to the required linking of items’ 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, with explicit emphasis on prediction of a future observation at the actual stress level of interest. We apply nonparametric predictive inference at that stress level, in combination with an estimated parametric form for the function linking different levels. For the latter aspect imprecision is introduced, leading to observations at stress levels other than the actual level of interest, to be transformed to intervals at the latter level. We believe that this is the first attempt to apply imprecise probability methods to accelerated life testing scenarios, and argue in favour of doing so. The paper concludes with a discussion of related research topics.

Yi-Chao Yin gratefully acknowledges financial support from the China Scholarship Council to visit Durham University