Efficient Bayesian reliability assessment for step-stress accelerated Wiener degradation model

Step-stress accelerated degradation testing (SSADT) plays a critical role in evaluating the reliability of high-performance industrial products under harsh conditions, where performance deterioration is not significant under normal operating conditions. However, existing Bayesian inference methods for SSADT models face significant challenges due to computational inefficiency, particularly in achieving convergence and handling complex stochastic processes. These limitations hinder practical applications where rapid and precise reliability assessment is essential. To address this, we propose a novel iterative integrated nested Laplace approximation framework combined with a fixed-point iteration technique. By reformulating the Wiener-process-based SSADT model into a latent Gaussian model via Taylor linearization, our approach leverages quadratic polynomial approximation and expansion-and-contraction strategies to optimize computational efficiency. Simulation studies demonstrate that the proposed method achieves comparable accuracy to traditional Bayesian methods like Gibbs sampling while significantly reducing computational costs, even for moderate sample sizes. Additionally, empirical validation using two real-world datasets confirms its applicability and effectiveness in practical reliability analysis.