Tran Hong
Product Quality Management, Janssen Pharmaceuticals, Titusville, New Jersey, USA.
J Biopharm Stat. 2021 Mar;31(2):180-190. doi: 10.1080/10543406.2020.1814801. Epub 2020 Sep 30.
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.
贝叶斯统计作为一种能够将先验知识纳入统计推断的方法，已被广泛应用。公差区间（TI）是产品质量保证中最常用的统计方法。计算统计公差区间主要有两种贝叶斯方法：滨田法和沃尔芬格法。实施了一种基于模拟的方法来比较双侧沃尔芬格法、滨田法和频率论者公差区间，这些方法在指定的置信水平下控制概率内容。随着样本量的增加，与频率论者相比，滨田公差区间变得更加保守，而沃尔芬格公差区间则更加宽松。为解决这一问题，我们提出了一种经验加权贝叶斯公差区间方法，该方法是滨田法和沃尔芬格法之间的一种折衷。所提出的贝叶斯公差区间在某些情况下会产生更窄的界限，同时确保置信内容覆盖率与频率论者相当。
