Validation of a Link-Function Assumption in Type-II Censored Constant Stress Experiments

Link functions of distributional and model parameters, such as linear, log-linear, or inverse linear functions, are commonly utilized in accelerated life testing to include expert knowledge and to reduce the number of unknown parameters. Although, there might be some evidence in choosing a specific link function in the analysis of an experiment, it should be verified by data. In a constant stress test with only a few different stress levels, a verification is impossible or at least problematic. On the other hand, there are technical as well as statistical arguments against a large number of lifetime experiments under different stress levels. Thus, a compromise is needed. In constant-stress tests with type-II censored exponentially distributed lifetimes, leading to a scale-accelerated failure time model, statistical tests concerning a link function are provided, and an experimental setup is proposed in this article, which allows for validating the particular choice of a link function via a regression approach. The procedure is illustrated by a data set known from the reliability literature as well as by simulations.