Unified stochastic modeling and reliability assessment for coupled degradation mechanisms

Abstract

Engineered systems often experience coupling effects with multiple degradation mechanisms during their operation. A well-tuned modeling process of such complex degradation mechanisms is crucial for accurate reliability assessment of engineered systems. This study puts forth a unified stochastic process model for (accelerated) degradation data with coupled mechanisms in a form of weighted mixture. The weighted hybrid degradation process is based mainly on the Tweedie exponential dispersion process (TEDP) as a unified model of traditional stochastic processes for a unique degradation mechanism via a continuously adjustable shape parameter and nonlinear time transformation. By assigning proper weights to quantify the contributions of coupled degradation effects, the weighted mixture model permits flexible modeling of complex degradation mechanisms. Under the proposed degradation modeling framework, we propose a new accelerated degradation test (ADT) model to extrapolate lifetime distribution at normal use condition through the relationship between stress and degradation rate. To derive maximum likelihood estimates (MLEs) of the model parameters, we newly design the expectation-maximization (EM) algorithm and compare the performance of widely adopted numerical optimizers in terms of convergence rate and computational efficiency. A variety of simulation studies and analyses of two real-world cases validate the effectiveness of the proposed degradation modeling and reliability assessment framework.