Optimal binomial reliability demonstration tests design under acceptance decision uncertainty

Binomial reliability demonstration tests (BRDTs) are widely adopted demonstration tests in reliability engineering to safeguard product quality over time. Based on the testing results, a BRDT will be either accepted and the product will be released to market or a test will be rejected and the product continues into the reliability growth stage. While designing a BRDT, the actual testing results (e.g., the number of failures to be observed) are uncertain, which lead to the uncertainty associated with the acceptance/rejection decision. Conventional optimal BRDTs mainly focus on minimizing the cost at the testing phase without taking account the uncertainty of the decision and the expected cost of subsequent reliability assurance activities, typically including the reliability growth and warranty services. In this paper, a Bayesian optimal BRDT design is proposed by explicitly quantifying the test uncertainty and further integrating the BRDT testing cost with the expected reliability growth and warranty service costs. The nonlinear relationships among different BRDT design parameters, the likelihood of accepting/rejecting the test and different cost components are investigated. A comprehensive sensitivity analysis is further carried out to evaluate the expected overall cost of the proposed design under different scenarios of the cost structure. A case study is provided to illustrate the proposed method and demonstrate its advantages over the conventional BRDT designs. By incorporating the informative prior knowledge into the proposed Bayesian design, it is possible to reduce the overall cost and the sample size of a test plan.