A new class of mechanism-equivalence-based Wiener process models for reliability analysis

Abstract

It is quite common to see that a unit of a product with a higher degradation rate also presents a more prominent dispersion. This phenomenon has motivated studies on developing new degradation models. In particular, a variety of Wiener process models have been developed by correlating the drift parameter and the diffusion parameter based on the statistical features of data. However, no insightful explanations are provided for such interesting correlations. In this article, degradation mechanism equivalence is first introduced based on the acceleration factor invariant principle, and the correlation between degradation rate and variation is explained using basic principles. Then, mechanism-equivalence-based Wiener process models, including a basic model and a random-effects model, are proposed to characterize such degradation behavior of a product. Analytical solutions for both point estimation and interval estimation of unknown model parameters are obtained using the maximum likelihood estimation method and an expectation–maximization algorithm. An extension of the proposed model that is able to handle accelerated degradation tests is developed. A simulation study and two real-world applications are provided to illustrate the effectiveness of the proposed models in product reliability estimation based on degradation data.