Equal-tailed and shortest Bayesian tolerance intervals based on exponential<font><i>k</i></font>-records

Kiapour, Azadeh; Qomi, Mehran Naghizadeh

doi:10.1080/03610926.2015.1076476

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…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). Simultaneous tolerance limits and TIs for several normal populations with a common unknown variance were proposed (Krishnamoorthy & Chakraberty, 2022).…”

Section: Type Of Tolerance Intervalmentioning

confidence: 99%

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

Wang

2023

WIREs Computational Stats

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Tolerance intervals (TIs) are widely used in various applications including manufacturing engineers, clinical research, and pharmaceutical industries. TIs can be used to construct limits of control charts for monitoring quality characteristics. For manufacturing processes where multiple factors may contribute to defects or multiple‐stream processes, a mixture distribution of several suitable probabilistic models may be a better choice than a simple distribution for modeling the data. TIs for the normal mixture distribution have been studied in the literature. This article reviews the TIs of the normal mixture distribution, the applications of the mixture distribution, and the control charts of the mixture distribution. A rule for constructing modified two‐sided TIs of the normal mixture distribution is summarized, and this rule may be extended to construct modified two‐sided TIs for general mixture distributions. The feasibility of using TIs to build control charts for mixture distributions is also discussed. A real data example of coronavirus disease 2019 is used to illustrate the method by linking the TI to control charts.This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification

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Section: Type Of Tolerance Intervalmentioning

confidence: 99%

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

Wang

2023

WIREs Computational Stats

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“…Ahmadi and Arghami 24 put forward distribution‐free TIs based on record values. Qomi and Kiapour 20 and Kiapour and Qomi 25 proposed methods to calculate TIs controlling both tails of the exponential distribution to contain no more than β 1 in the lower tail and no more than β 2 in the upper tail of the distribution based on record values. The exponential distribution is one of the most widely used statistical models, especially in many industrial lifetime tests.…”

Section: Introductionmentioning

confidence: 99%

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

Guo

Zhu

Wang

et al. 2020

Quality & Reliability Eng

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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.

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A note on computing Bayesian tolerance intervals in exponential distribution based on $k$-record values

MirMostafaee

Qomi

2018

Novi Sad J. Math.

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Equal-tailed and shortest Bayesian tolerance intervals based on exponentialk-records

Cited by 3 publications

References 14 publications

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

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

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

A note on computing Bayesian tolerance intervals in exponential distribution based on $k$-record values

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