On the confidence intervals of process capability index Cpm based on a progressive type‐II censored sample

Akdoğan, Yunus

doi:10.1002/qre.3111

Cited by 5 publications

(1 citation statement)

References 40 publications

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“…After the later papers by Efron and Gong (1983), Efron and Tibshirani (1986), Diaconis and Efron (1983) that the statistical and scientific community began began to take these ideas into account, to appreciate the extensions and broad applicability of the methods, and to recognize their importance (Chernick 2008). There are so many studies used the bootstrap method with a view to make statistical inference by the help of confidence intervals: see also Efron and Tibshirani (1986), Diaconis and Efron (1983), Efron (1987), Carpenter, and Bithell (2000), Park (2011), DiCiccio andEfron (1996), DiCiccio and Tibshirani (1987), Efron and Tibshirani (1993), Chesneau et al (2022) and Akdoğan (2022).…”

Section: Introductionmentioning

confidence: 99%

Shrinkage Estimation and Bootstrap Confidence Interval for Scale Parameter of Laplace Distribution

ÖZDEMİR,

EBEGİL

2023

Afyon Kocatepe University Journal of Sciences and Engineering

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In this study, a biased estimator is proposed for the scale parameter of Laplace distribution. First, it is theoretically shown that the mean square error of the biased estimator is smaller than that of the maximum likelihood estimator. Then the maximum likelihood estimator is compared with the obtained biased estimator by means of a simulation study using the relative efficiency of these estimators. In addition, confidence intervals are constructed for the scale parameter of Laplace distribution with bootstrap method in order to compare them with each other in a different way.

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Section: Introductionmentioning

confidence: 99%

Shrinkage Estimation and Bootstrap Confidence Interval for Scale Parameter of Laplace Distribution

ÖZDEMİR,

EBEGİL

2023

Afyon Kocatepe University Journal of Sciences and Engineering

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Bayesian and non‐Bayesian inference of the process capacity index Spk′$S^{\prime }_{pk}$ under progressive type‐II right censored scheme

Saha,

Dutta

2024

Quality & Reliability Eng

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Process capability indices (PCIs), are widely used to gauge how well a process performs within its requirements. While greater PCIs are indicative of improved process “quality,” they do not necessarily translate into lower rejection rates. Therefore, using a loss‐based PCI to gauge process capability makes more sense. In this paper, the PCI has been considered for normal random variable. The article attempts to study the classical and the Bayesian estimation of for type‐II progressive right censored sample under symmetric as well as asymmetric loss functions, namely squared error loss function, and LINEX loss function, respectively. The Markov chain Monte Carlo simulation technique has been efficiently used here to have the approximate solution for . Through an extensive Monte Carlo simulation study along with two real life examples related to electronic industry, we compare the performances of the classical and the Bayes estimates based on symmetric and asymmetric loss functions and compared among the asymptotic confidence interval and highest posterior density credible intervals, in terms of average width and corresponding coverage probabilities of , respectively.

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Classical and Bayesian inference of Cpc$\mathcal {C}_{pc}$ for Wilson–Hilferty distribution under progressively first‐failure type‐II censoring samples

Al‐Mosawi,

Dey

2024

Quality & Reliability Eng

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This study uses two frequentist approaches and the Bayesian method of estimation using progressively first‐failure type‐II censored data to estimate process capability index (PCI), , for the Wilson–Hilferty (WH) distribution. A competitive maximum product of spacing (MPS) method for estimation of is proposed in the frequentist method as an alternative to conventional likelihood (LK)‐based estimation. We have also taken into account the PS function in the Bayesian setup as an alternative to the conventional LK function, and both LK and PS‐based Bayesian estimates are given for . Further, the Bayes estimates are evaluated by applying Tierney–Kadane (TK) approximation method and Markov chain Monte Carlo (MCMC) method with the help of both LK and PS functions and Jeffrey's prior. Additionally, the approximate confidence intervals based on the suggested frequentist techniques as well as the Bayes highest posterior density (HPD) credible intervals are built for the index . In addition, two bootstrap confidence intervals are obtained. In the simulation exercise, the performance of the Bayes and traditional estimates of is assessed in terms of their mean squared errors, and the average width and coverage probabilities of the CIs and HPD intervals are compared. An actual data set from the electronic industries is reanalyzed in order to show the efficacy of the proposed index and estimation methodology.

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On the confidence intervals of process capability index Cpm based on a progressive type‐II censored sample

Cited by 5 publications

References 40 publications

Shrinkage Estimation and Bootstrap Confidence Interval for Scale Parameter of Laplace Distribution

Shrinkage Estimation and Bootstrap Confidence Interval for Scale Parameter of Laplace Distribution

Bayesian and non‐Bayesian inference of the process capacity index Spk′$S^{\prime }_{pk}$ under progressive type‐II right censored scheme

Classical and Bayesian inference of Cpc$\mathcal {C}_{pc}$ for Wilson–Hilferty distribution under progressively first‐failure type‐II censoring samples

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