A Bayesian hierarchical framework for multifactor accelerated degradation modeling

Accelerated degradation tests involving multiple stress factors are essential for timely product reliability assessment, yet modeling multifactor degradation data remains statistically challenging. This work proposes a Bayesian hierarchical framework for accelerated degradation modeling under multiple stress conditions. The framework jointly incorporates all degradation observations and accommodates key data complexities–such as nonlinear degradation paths, stress interactions, and unit-to-unit variability–through a flexible hierarchical specification. Parameter estimation is carried out using a data-augmentation MCMC strategy, which facilitates sampling from the high-dimensional posterior distribution and yields full posterior inference for all model parameters and reliability metrics. The methodology is illustrated with a two-factor degradation experiment on C-phycocyanin, an antioxidant pigment, subjected to varying temperature and light levels. The proposed model effectively captures the combined influence and interaction of both stressors on the degradation paths and provides credible-interval-based failure-time distributions under a range of operating conditions. These results demonstrate the framework’s potential for improving reliability assessment in settings where multiple stress factors jointly influence degradation.