ABSTRACT

Bayesian statistics has been widely utilized as an approach that can incorporate prior knowledge into statistical inference. Tolerance intervals (TI) are the most commonly used statistical methods for product quality assurance. There are two main Bayesian approaches for calculating statistical tolerance intervals: Hamada and Wolfinger. A simulation-based approach was implemented to compare two-sided Wolfinger, Hamada, and frequentist tolerance intervals which control the probability content at a specified level of confidence. As sample sizes increase, compared to frequentist, Hamada TI become more conservative while Wolfinger TI are more liberal. To address this issue, we propose an empirical weighted Bayesian TI approach that is a compromise between Hamada and Wolfinger approaches. The proposed Bayesian TI result in narrower limits in certain scenarios while ensuring the confidence content coverage remains comparable to frequentist.

摘要

贝叶斯统计已被广泛用作一种可以将先验知识纳入统计推理的方法。公差区间 (TI) 是最常用的产品质量保证统计方法。有两种主要的贝叶斯方法用于计算统计公差区间：Hamada 和 Wolfinger。实施了一种基于模拟的方法来比较两侧 Wolfinger、Hamada 和频率主义者的容差区间，这些区间将概率内容控制在指定的置信水平。随着样本量的增加，与常客相比，Hamada TI 变得更加保守，而 Wolfinger TI 更加自由。为了解决这个问题，我们提出了一种经验加权贝叶斯 TI 方法，它是 Hamada 和 Wolfinger 方法之间的折衷方案。