Assurance for Sample Size Determination in Reliability Demonstration Testing

Manufacturers are required to demonstrate that products meet reliability targets. A way to achieve this is with reliability demonstration tests (RDTs), where a number of products are put on test and the test is passed or failed according to a decision rule based on the observed outcomes. There are various methods for determining the sample size for RDTs, typically based on the power of a hypothesis test following the RDT or risk criteria. Bayesian risk criteria approaches combine the choice of sample size with the analysis of the test data while relying on the specification of acceptable and rejectable reliability levels. In this article, we offer an alternative approach to sample size determination based on the idea of assurance. This approach chooses the sample size to provide a specified probability that the RDT will result in a successful outcome. It separates the design and analysis of the RDT, allowing different priors for the producer and consumer. We develop the assurance approach for sample size calculations in RDTs for binomial and Weibull likelihoods and propose appropriate prior distributions for the design and analysis of the test. In each case, we illustrate the approach with an example based on real data.

制造商需证明其产品达到可靠性指标要求。实现这一目标的常用方法之一是开展可靠性验证试验（Reliability Demonstration Tests, RDTs）：将一定数量的产品投入试验，依据观测结果制定决策规则，以此判定试验通过与否。当前存在多种确定RDT样本量的方法，这类方法通常基于试验后假设检验的功效，或是风险准则。贝叶斯风险准则方法将样本量选择与试验数据分析相结合，同时需预先设定可接受与不可接受的可靠性水平。本文提出一种基于保障概率理念的RDT样本量确定新方法：该方法通过选取合适样本量，使RDT获得成功结果的概率达到预设水平。该方法将RDT的设计与分析环节分离，允许为生产方与使用方设定不同的先验分布。本文针对服从二项分布与威布尔分布似然的RDT样本量计算，完善了保障概率方法，并为该试验的设计与分析环节提出了适配的先验分布。针对上述两类分布场景，本文均结合真实数据集通过示例对该方法进行了演示说明。