Bayesian analysis of accelerated life test under constrained randomization

Abstract

Reliability engineers typically prioritize the lower percentiles. Accurately assessing these lower percentiles enables engineers to delve deeper into early product failures, paving the way for enhanced product reliability. In the manufacturing realm, many accelerated life tests (ALTs) veer away from completely randomized designs (CRDs) due to constraints in time and budget. Within ALTs, alterations in stress can lead to shifts in the failure mechanism of products. To accurately discern product lifetime percentiles, there is an imperative need to account for these varying failure mechanisms and random effects. Our approach introduces a re-parameterization model encapsulating random effects and disparate failure mechanisms. In this model, a specific percentile is employed as a stand-in for the scale parameter, laying the groundwork for a regression model interlinking the percentile, acceleration stress, and random effect. Concurrently, a separate regression model is designed for shape parameters in relation to acceleration stresses. Leveraging the Bayesian method, we ascertain the estimated values for the model parameters. The model is applied to an ALT example focusing on glass capacitors. The simulations underline the model’s prowess in delivering a more precise estimation of lower lifetime percentiles. Additionally, the Bayesian method further refines the accuracy of the lifetime percentile estimations.