Abstract

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.

摘要

制造商需要证明产品满足可靠性目标。实现这一目标的一种方法是使用可靠性演示测试 (RDT)，其中对许多产品进行测试，根据基于观察结果的决策规则，测试通过或失败。有多种方法可用于确定 RDT 的样本量，通常基于遵循 RDT 或风险标准的假设检验的功效。贝叶斯风险标准方法将样本大小的选择与测试数据的分析相结合，同时依赖于可接受和可拒绝的可靠性水平的规范。在本文中，我们提供了一种基于保证思想的样本量确定替代方法。此方法选择样本量以提供 RDT 产生成功结果的指定概率。它将 RDT 的设计和分析分开，允许生产者和消费者使用不同的先验。我们为 RDT 中二项式和威布尔似然的样本量计算开发了保证方法，并为测试的设计和分析提出了适当的先验分布。在每种情况下，我们都会通过一个基于真实数据的示例来说明该方法。