Exploring Initiation-Growth Correlation in Accelerated Degradation Testing Data: Both Classical and Bayesian Approaches

For many industrial products, accelerated degradation tests (ADTs) serve as an efficient approach to their reliability prediction. Modeling and analyzing the ADT data involves assessing the accelerating effect brought by stress variables, as well as accounting for multiple variation sources. In many situations, in addition to unit-to-unit variabilities seen in both the initial performance levels and degradation rates, an intriguing observation is that these two factors exhibit a strong correlation. Motivated by a real application of optical media, this article proposes a general Wiener process for modeling such ADT data, and it provides a closed-form lifetime distribution. An expectation-maximization algorithm is developed to infer the unknown parameters. An extension to the Bayesian approach under Stan framework is made to enable practitioners to seamlessly incorporate prior domain knowledge into their analysis. Simulation studies and a case application demonstrate the good performance of the proposed methodology.