Bootstrap confidence intervals of generalized process capability indexCpykusing different methods of estimation

Dey, Sanku; Saha, Mahendra

doi:10.1080/02664763.2019.1572721

Cited by 27 publications

(12 citation statements)

References 39 publications

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“…where ζ 1 (α, β) and ζ 2 (α, β) are defined in equations (15) and (16), respectively. Substituting the MPSEs in equations (6) and (7), we can get the estimator of S pmk and S pmkc as…”

Section: Cramèr-von Mises Estimatorsmentioning

confidence: 99%

“…Since then, several researchers have developed numerous techniques for constructing CIs. In this regard, readers may refer to [8][9][10][11][12][13][14][15][16][17][18][19] and the references cited therein. e objective of this paper is three fold: First, the estimates of S pmk using seven different classical methods of estimation are obtained.…”

Section: Introductionmentioning

confidence: 99%

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Classical Estimation of the Index Spmk and Its Confidence Intervals for Power Lindley Distributed Quality Characteristics

Alomani

Alotaibi

Dey³

et al. 2020

Mathematical Problems in Engineering

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The process capability index (PCI) has been introduced as a tool to aid in the assessment of process performance. Usually, conventional PCIs perform well under normally distributed quality characteristics. However, when these PCIs are employed to evaluate nonnormally distributed process, they often provide inaccurate results. In this article, in order to estimate the PCI Spmk when the process follows power Lindley distribution, first, seven classical methods of estimation, namely, maximum likelihood method of estimation, ordinary and weighted least squares methods of estimation, Cramèr–von Mises method of estimation, maximum product of spacings method of estimation, Anderson–Darling, and right-tail Anderson–Darling methods of estimation, are considered and the performance of these estimation methods based on their mean squared error is compared. Next, three bootstrap confidence intervals (BCIs) of the PCI Spmk, namely, standard bootstrap, percentile bootstrap, and bias-corrected percentile bootstrap, are considered and compared in terms of their average width, coverage probability, and relative coverage. Besides, a new cost-effective PCI, namely, Spmkc is introduced by incorporating tolerance cost function in the index Spmk. To evaluate the performance of the methods of estimation and BCIs, a simulation study is carried out. Simulation results showed that the maximum likelihood method of estimation performs better than their counterparts in terms of mean squared error, while bias-corrected percentile bootstrap provides smaller confidence length (width) and higher relative coverage than standard bootstrap and percentile bootstrap across sample sizes. Finally, two real data examples are provided to investigate the performance of the proposed procedures.

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Section: Cramèr-von Mises Estimatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Classical Estimation of the Index Spmk and Its Confidence Intervals for Power Lindley Distributed Quality Characteristics

Alomani

Alotaibi

Dey³

et al. 2020

Mathematical Problems in Engineering

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show abstract

“…Usually, for monitoring a process using a PCI, quality control engineers and statisticians employ two estimation techniques, namely, point estimation and confidence intervals (CIs) (see Chan et al 3 ). For more information on CIs, readers may refer to the works of Peng, 14 Leiva et al, 15 Pearn et al, 16 Kashif et al, 17 Weber et al, 18 Rao et al, 19 Dey et al, 20 Wu, 21 , Dey and Saha, 22,23 Saha et al, [24][25][26][27][28][29] Alomani et al, 30 and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Modified estimation and confidence intervals of an asymmetric loss‐based process capability index Cpm′$\mathcal {C}^{\prime }_{pm}$

Dey¹,

Wang

Saha

2022

Quality & Reliability Eng

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In this article, we are interested to estimate a new capability index scriptCpm′$\mathcal {C}^{\prime }_{pm}$, which is based on asymmetric loss function (linear‐exponential) when the underlying process follows normal distribution. We estimate the parameters of the model using maximum likelihood method, bias‐corrected maximum likelihood method and bootstrap bias‐corrected maximum likelihood method and subsequently the process capability index (PCI) scriptCpm′$\mathcal {C}^{\prime }_{pm}$ using the cited methods. Through extensive simulation studies, we compare the performances of the aforementioned methods of estimation for the PCI scriptCpm′$\mathcal {C}^{\prime }_{pm}$ in terms of their absolute bias (AB) and MSEs. Besides, four bootstrap methods are employed for constructing the confidence intervals for the index scriptCpm′$\mathcal {C}^{\prime }_{pm}$ by using the considered methods of estimation. The performances of the bootstrap confidence intervals (BCIs) are also compared in terms of average widths (AWs) and coverage probabilities (CPs) using Monte Carlo simulation. Finally, for illustrating the effectiveness of the proposed methods of estimation and BCIs, two real data sets from electronic industries are analyzed. All these data sets show that width of bias‐corrected accelerated bootstrap interval is minimum among all other considered BCIs.

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“…Since then, several researchers have developed numerous techniques for constructing CIs. In this regard, readers may refer to Peng 16,17 ; Leiva et al 18 ; Pearn et al 19,20 ; Kashif et al 21,22 ; Weber et al 23 ; Pina-Monarrez et al 24 ; Rao et al 25 ; Dey et al 26 ; Dey and Saha 27,28 ; Park et al 29 ; Saha et al [30][31][32] , Alomani et al 33 and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Parametric inference of the loss based index Cpm for normal distribution

Saha

Dey²,

Wang

2021

Quality & Reliability Eng

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The process capability index (PCI) has been introduced as a tool to aid in the assessment of process performance and most of the traditional PCIs performed well when process follows the normal behavior. In this article, we consider a PCI,  𝑝𝑚 for normal random variables. The objective of this article is five fold: First, six different methods of estimation of the PCI  𝑝𝑚 are addressed from frequentist approaches and compare them in terms of their mean squared errors using extensive numerical simulations. Second, we compare three bootstrap confidence intervals (BCIs) of the PCI  𝑝𝑚 including standard bootstrap, percentile bootstrap, and bias-corrected percentile bootstrap. Third, Bayesian estimation is considered under four loss functions (symmetric as well as asymmetric) using normal prior for location parameter and inverse gamma prior for the scale parameter for the considered model. Also, we obtain highest posterior density (HPD) credible intervals of the PCI  𝑝𝑚 . Fourth, a new cost effective PCI, namely,  𝑝𝑚𝑐 is introduced by incorporating tolerance cost function in the index  𝑝𝑚 . Fifth, the power of the test is obtained, and Monte Carlo simulation study has been carried out to compare the performances of the classical BCIs and HPD credible intervals of PCIs  𝑝𝑚 and  𝑝𝑚𝑐 in terms of average widths and coverage probabilities. Finally, two real data sets have been analyzed for illustrative purposes.

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Bootstrap confidence intervals of generalized process capability indexC_pykusing different methods of estimation

Cited by 27 publications

References 39 publications

Classical Estimation of the Index Spmk and Its Confidence Intervals for Power Lindley Distributed Quality Characteristics

Classical Estimation of the Index Spmk and Its Confidence Intervals for Power Lindley Distributed Quality Characteristics

Modified estimation and confidence intervals of an asymmetric loss‐based process capability index Cpm′$\mathcal {C}^{\prime }_{pm}$

Parametric inference of the loss based index Cpm for normal distribution

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