A random-effect Wiener process degradation model with transmuted normal distribution and ABC-Gibbs algorithm for parameter estimation

Degradation modeling is a widely used technique for evaluating the reliability of high-quality products. However, unit-to-unit variability, stemming from material fluctuations during manufacturing and environmental factors, can significantly impact the accuracy of this assessment. To tackle this issue, we propose a novel time-transformed Wiener process with a transmuted normal distribution to represent unit-to-unit variability. This distribution extends the normal distribution, offering greater flexibility by capturing a wide range of non-normal, asymmetric behaviors in unit-to-unit variability. We derive closed-form expressions for the probability density function and reliability function for the model in two scenarios: (i) assuming the degradation process observations remain unaffected by measurement errors, and (ii) assuming the degradation process observations influenced by measurement errors. Due to the complexity of the likelihood functions, we employ the Gibbs version of approximate Bayesian computation (ABC-Gibbs) for parameter estimation. The effectiveness and application of the proposed method were demonstrated through numerical examples and practical application with light-emitting diode degradation data. Moreover, we use approximate Bayesian computation model choice (ABC-MC) for model comparison studies. The results indicated that our model offers improved approximations to observed degradation results compared to existing models, showcasing its superiority in generating data under the smallest tolerance threshold.