A Wiener process model for accelerated degradation analysis considering measurement errors

Accelerated degradation analysis plays an important role in assessing reliability and making maintenance schedule for highly reliable products with long lifetime. In practical engineering, degradation data, especially measured under accelerated condition, are often compounded and contaminated by measurement errors, which makes the analysis more challenging. Therefore, a Wiener process model simultaneously incorporating temporal variability, individual variation and measurement errors is proposed to analyze the accelerated degradation test (ADT). The explicit forms of the probability distribution function (PDF) and the cumulative distribution function (CDF) are derived based on the concept of first hitting time (FHT). Then, combining with the acceleration models, the maximum likelihood estimations (MLE) of the model parameters are obtained. Finally, a comprehensive simulation study involving two examples and a practical application are given to demonstrate the necessity and efficiency of the proposed model.