Reliability modeling and statistical analysis of accelerated degradation process with memory effects and unit-to-unit variability

Abstract

A reasonable description of the degradation process is essential for credible reliability assessment in accelerated degradation testing. Existing methods usually use Markovian stochastic processes to describe the degradation process. However, degradation processes of some products are non-Markovian due to the interaction with environments. Misinterpretation of the degradation pattern may lead to biased reliability evaluations. Besides, owing to the differences in materials and manufacturing processes, products from the same population exhibit diverse degradation paths, further increasing the difficulty of accurate reliability estimation. To address the above issues, this paper proposes an accelerated degradation model incorporating memory effects and unit-to-unit variability. The memory effect in the degradation process is captured by the fractional Brownian motion, which reflects the non-Markovian characteristic of degradation. The unit-to-unit variability is considered in the acceleration model to describe diverse degradation paths. Then, lifetime and reliability under normal operating conditions are presented. Furthermore, to give an accurate estimation of the memory effect, a new statistical analysis method based on the expectation maximization algorithm is devised. The effectiveness of the proposed method is verified by a simulation case and a real-world tuner reliability analysis case. The simulation case shows that the estimation of the memory effect obtained by the proposed statistical analysis method is much more accurate than the traditional one. Moreover, ignoring unit-to-unit variability can lead to a highly biased estimation of the memory effect and reliability. From the tuner reliability analysis case, the proposed model is superior in both deterministic degradation trend predictions and degradation boundary quantification compared to existing models, which can provide more credible reliability assessment.