Reliability Analysis for Degradation-Shock Processes with State-Varying Degradation Patterns Using Approximate Bayesian Computation (ABC) for Parameter Estimation

The degradation of products is an integral part of their life-cycle, often following predictable trajectories. However, sudden, unexpected events, termed ’shocks’, can substantially alter these degradation paths. Shocks can significantly influence the pace of degradation, leading to accelerated system failure. Moreover, they may initiate changes in degradation patterns, transitioning from linear to non-linear or random trajectories. To address this challenge, we present a novel multi-state reliability model for competing failure processes that account for degradation-shock dependencies by considering the state-varying degradation pattern. The degradation process is divided into s-states, with each state treated according to its pattern based on the time-transform Wiener process. The reliability function is derived based on soft failure caused by continuous degradation involving the s-states, the sudden increase in degradation caused by random shocks, and hard failure due to some shock processes. Additionally, we performed a sensitivity analysis to determine which parameters have the most significant impact on product reliability. Due to the complexity of the likelihood function, we adopted the ABC method to estimate the model parameters. A simulation study and a practical application with micro-electro-mechanical systems (MEMS) degradation results are used to demonstrate the efficiency and effectiveness of the proposed approach.