Inferences for Skew-Wiener Degradation Model: Approximate Bayesian Computation via Gibbs-Step and Model Selection

The Skew-Wiener Degradation (SKWD) model presents a novel approach for addressing unit-to-unit variability in degradation processes by integrating the skew-normal distribution into the Wiener process. This study introduces a robust parameter estimation method for the Skew-Wiener model using Approximate Bayesian Computation with Gibbs sampling (ABC-Gibbs), providing an alternative to the Expectation-Maximization (EM) algorithm. ABC-Gibbs offers a computationally efficient, likelihood-free inference approach, particularly well-suited for high-dimensional parameter spaces where direct likelihood calculations are computationally expensive. Through extensive simulations and real-world applications, including laser and LED degradation datasets, the efficiency and practical utility of the proposed method were validated. Additionally, an ABC model choice (ABC-MC) procedure is implemented to compare linear and nonlinear SKWD models, identifying the most suitable model for specific degradation datasets. The findings demonstrate that ABC significantly enhances parameter estimation accuracy, and ABC-MC effectively distinguishes between competing models, making the approach highly valuable for reliability analysis.