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.

二项式可靠性论证测试（BRDT）是可靠性工程中被广泛采用的论证测试，可以长期保护产品质量。根据测试结果，BRDT将被接受，产品将投放市场，或者测试将被拒绝，产品将继续进入可靠性增长阶段。在设计BRDT时，实际测试结果（例如，要观察的故障数量）是不确定的，这导致与接受/拒绝决定相关的不确定性。常规的最佳BRDT主要集中在使测试阶段的成本最小化，而不考虑决策的不确定性以及后续可靠性保证活动（通常包括可靠性增长和保修服务）的预期成本。在本文中，通过明确量化测试不确定性，并将BRDT测试成本与预期的可靠性增长和保修服务成本进一步整合，提出了贝叶斯最优BRDT设计。研究了不同BRDT设计参数之间的非线性关系，接受/拒绝测试的可能性以及不同的成本构成。进一步进行了综合敏感性分析，以评估在成本结构的不同情况下拟议设计的预期总成本。提供了一个案例研究来说明所提出的方法，并证明其相对于传统BRDT设计的优势。通过将信息丰富的先验知识整合到建议的贝叶斯设计中，可以降低总成本和测试计划的样本量。