Constructing exact tolerance intervals for the exponential distribution based on record values

Abstract

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.

Prediction of record values by using quantile regression curves and distortion functions

“…In several practical situations, the usual point predictions obtained with linear regression do not provide good record predictions. The basic tools in this field can be seen in Dunsmore (1983), Raqab and Nagaraja (1995), Awad and Raqab (2000) and Nevzorov (2001) and the recent advances in Paul and Thomas (2016), Guo et al (2020), Volovskiy and Kamps (2020a, b). Specific results for records from exponential distributions can be found in Awad and Raqab (2000), Basak and Balakrishnan (2003), Raqab (2007), Volovskiy and Kamps (2020a, b) and the references therein.…”

Determining sample size for specification limits verification with tolerance intervals

“…In Guo et al, 20 the authors developed a tolerance interval for the exponential distribution, while in Wang and Tsung, 21 two types of data with different accuracy levels are combined to construct tolerance intervals.…”

Tolerance limits for mixture‐of‐normal distributions with application to COVID‐19 data

“…TIs based on the combination of high-resolution and low-resolution data were proposed (Wang & Tsung, 2017). In many cases, only record values can be observed, and an exact two-sided TI based on record values for the exponential distribution was constructed (Guo et al, 2020). The equal-tailed and shortest Bayesian TIs that could control percentages in both tails of the exponential distribution based on k-record values were built (Kiapour & Qomi, 2017).…”