An Extended Gamma Process for Accelerated Destructive Degradation Test: Modeling and Optimal Design

Accelerated destructive degradation testing (ADDT) has become an invaluable method in reliability analysis, especially for highly reliable products. A common characteristic in many degradation studies is the presence of randomness in the initial degradation levels of testing units. Products with poor initial degradation levels tend to fail earlier. This study proposes an extended gamma process model that accommodates the random initial degradation value to accurately describe the degradation process over time. Under this modeling approach, we propose approximation methods for the conditional mean-time-to-failure (MTTF) and conditional variance of failure times to evaluate the impacts of initial degradation levels on product quality and reliability. We adopt a maximum likelihood approach to estimate the model parameters and MTTF under normal use conditions. In addition, we determine the optimal initial degradation threshold for removing poor-quality products and the proportion of products below this threshold. Based on the proposed model, the optimal ADDT plan is derived by minimizing the asymptotic variance of estimated MTTF under normal use conditions. A Monte Carlo simulation is conducted to assess the performance of the proposed inferential methods. Finally, a real-world ADDT dataset is analyzed to illustrate the proposed model and methodologies for making informed decisions on quality and reliability management.