Decelerated Testing: A Hierarchical Bayes Approach

The problem discussed here has arisen from an industrial scenario involving the potential failure of an element of building structures. The element carries with it a warranty of several years. The scenario considered is not specific to buildings and occurs under other circumstances; it goes under the label “product stewardship.” Its statistical content, however, is inference from accelerated tests in reverse, that is, testing at low stress levels and making predictions at high use conditions ones. Inference under stress testing for lifetimes is a well-discussed topic in the statistical literature, but what is different here are three features: not using time-transformation functions relating parameters of failure models with stress, using material strength instead of lifetimes as a metric for reliability, and fusing information consisting of test data and expert testimonies about the degradation of strength with cumulative stress. Because stress testing is also germane to survival analysis, with immunity replacing strength, the scope of this work could extend to biometry. All of the data used here are real, including that pertaining to expert testimonies. However, in the interest of avoiding potential lawsuits, the owners of the data have mandated that neither their source nor their nature be made public.