A Bayesian framework for accelerated reliability growth testing with multiple sources of uncertainty

Reliability growth tests are often used for achieving a target reliability for complex systems via multiple test-fix stages with limited testing resources. Such tests can be sped up via accelerated life testing (ALT) where test units are exposed to harsher-than-normal conditions. In this paper, a Bayesian framework is proposed to analyze ALT data in reliability growth. In particular, a complex system with components that have multiple competing failure modes is considered, and the time to failure of each failure mode is assumed to follow a Weibull distribution. We also assume that the accelerated condition has a fixed time scaling effect on each of the failure modes. In addition, a corrective action with fixed ineffectiveness can be performed at the end of each stage to reduce the occurrence of each failure mode. Under the Bayesian framework, a general model is developed to handle uncertainty on all model parameters, and several special cases with some parameters being known are also studied. A simulation study is conducted to assess the performance of the proposed models in estimating the final reliability of the system and to study the effects of unbiased and biased prior knowledge on the system-level reliability estimates.