Planning Bayesian reliability demonstration tests via a generalized test statistic

Reliability demonstration testing (RDT) has been extensively employed to verify whether a product meets specific reliability requirements at a desired confidence level. Driven by intense market competition and constrained test resources, manufacturers are motivated to seek effective strategies to reduce the testing efforts required for RDT. In this paper, we propose a method that utilizes existing knowledge and information obtained from the product design and development phase to construct a Bayesian prior distribution of the product’s reliability. Based on this prior, a preliminary disposition decision on whether to accept or reject the product is made. A subsequent demonstration test is needed only when the prior information is deemed insufficient for an immediate disposition. A RDT planning method is developed based on the posterior distribution of the product’s reliability, which is applicable to general cases involving non-conjugate priors. We study two types of demonstration testing: binomial and exponential. For each, we prove the existence of an optimal test plan and develop an efficient searching algorithm to determine it. Numerical studies are conducted to demonstrate the effectiveness of the proposed method, supplemented by a case study on RDT for systems of different configurations. Overall, this work provides a unified and effective framework for reliability demonstration under the Bayesian paradigm.