Modeling Accelerated Degradation Data Based on the Uncertain Process

Accelerated degradation testing (ADT) aids the reliability and lifetime evaluations for highly reliable products. In engineering applications, the number of test items is generally small due to finance or testing resource constraints, which leads to the rare knowledge to evaluate reliability and lifetime. Consequently, the epistemic uncertainty is embedded in ADT data and the large-sample based probability theory is no longer appropriate. In this paper, we introduce the uncertainty theory, which is a theory different from the probability theory, to account for such uncertainty due to small samples and build up a framework of ADT modeling. In this framework, an uncertain accelerated degradation model is first proposed based on the arithmetic Liu process. Then, the uncertain statistics for parameter estimations are presented correspondingly, which is completely constructed on objectively observed ADT data. An application case and a simulation case are used to illustrate the proposed methodology. With further comparisons to the Wiener process based accelerated degradation model (WADM) and the Bayesian-WADM, the sensitivities of these models to sample sizes are explored and the results show that the proposed model is superior to the other two probability-based models under the small sample size.