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Constructing exact tolerance intervals for the exponential distribution based on record values
Quality and Reliability Engineering International ( IF 2.3 ) Pub Date : 2020-07-10 , DOI: 10.1002/qre.2704
Baocai Guo, Naifan Zhu, Wei Wang, Hsiuying Wang

Recently, with the wide application of tolerance intervals (TIs), especially in quality management, the construction of TIs has attracted increasing attention. However, TIs applied to record data have not been well established as they have been for complete data. In many industrial stress tests, only record data are stored instead of complete data, which leads to the fact that the developments of methods based on record data are as important as those based on complete data. In this paper, we propose the exact two‐sided TIs for the exponential distribution based on record values from the frequentist and Bayesian perspectives. The accuracy of each type of TIs is quantified. The results show that the Bayesian approach is superior to the frequentist approach in terms of the accuracy. A real data example is used to illustrate the constructions and implementations of the proposed TIs.

中文翻译:

根据记录值构造指数分布的精确公差区间

近年来,随着公差间隔(TI)的广泛应用,尤其是在质量管理中,TI的构建引起了越来越多的关注。但是,用于记录数据的TI尚未完善,因为它们已经用于完整数据。在许多工业压力测试中,仅存储记录数据而不是存储完整数据,这导致以下事实:基于记录数据的方法的开发与基于完整数据的方法一样重要。在本文中,我们从频繁主义者和贝叶斯主义者的观点出发,根据记录值为指数分布提出精确的两面TI。每种类型的TI的准确性都得到了量化。结果表明,在准确性方面,贝叶斯方法优于频繁方法。
更新日期:2020-07-10
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