Reliability modeling and statistical inference of accelerated degradation data with memory effects and unit-to-unit variability

Accelerated degradation testing (ADT) is an effective way to evaluate the lifetime and reliability of highly reliable products. Markovian stochastic processes are usually applied to describe the degradation process. However, the degradation processes of some products are non-Markovian due to the interaction with environments. Besides, owing to the differences in materials and manufacturing processes, products from the same population exhibit diverse degradation paths. Motivated by this issue, an ADT model with memory effects and unit-to-unit variability (UtUV) is proposed in this article. The memory effect in the degradation process is captured by the fractional Brownian motion (FBM) and the UtUV is considered in the acceleration model. Then, the lifetime and reliability under the normal operating condition are presented. To give an accurate estimation of the memory effect, a statistical inference method is devised based on the expectation maximization (EM) algorithm. The effectiveness of the proposed method is verified by a simulation case and a microwave case. It is shown that the estimation of the memory effect obtained by the EM algorithm is much more accurate than the traditional method. Moreover, without considering UtUV in the ADT model, the estimation of the memory effect can be highly biased. The proposed ADT model is superior in both deterministic degradation trend predictions and degradation boundary quantification compared to existing models.