Bootstrap confidence intervals of CpTk for two parameter logistic exponential distribution with applications

Saha, Mahendra; Dey, Sanku; Maiti, Sudhansu S.

doi:10.1007/s13198-019-00789-7

Cited by 21 publications

(11 citation statements)

References 30 publications

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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%

“…35 With attention to the importance of the Bayesian estimation of the PCIs, several authors have considered conventional PCIs as well as generalized PCIs under symmetric and asymmetric loss functions using informative as well as non-informative priors. Notable among them are: Saxena and Singh 36 ; Huiming et al 37 ; Miao et al 38 ; Maiti and Saha 39 ; Kargar et al 40 ; Ali and Riaz 41 ; Pearn et al 42 ; Seifi and Nezhad 43 ; Saha et al 31 and many others.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Parametric inference of the loss based index Cpm for normal distribution

Saha

Dey²,

Wang

2021

Quality & Reliability Eng

Self Cite

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“…The point estimator is normally employed for evaluation of a process performance, whereas it is not practically useful in making reasonable decisions due to inherent variability associated with a single estimate. One may thus prefer the use of the CIs as they are capable of providing greater information about the process; see, for example, Peng 8 ; Leiva et al 9 ; Pearn et al 10 ; Kashif et al 11 ; Weber et al 12 ; Rao et al 13 ; Dey et al 14 ; Dey and Saha 15,16 ; Saha et al [17][18][19][20][21][22][23] ; Alomani et al, 24 Kumar et al 25 and many others.…”

Section: Introductionmentioning

confidence: 99%

Classical and objective Bayesian estimation and confidence intervals of an asymmetric loss based capability index Cpmk′$\mathcal {C}^{\prime }_{pmk}$

Dey¹,

Saha

Zhang

et al. 2021

Quality & Reliability Eng

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In this paper, we introduce a new process capability index, scriptCpmk′$\mathcal {C}^{\prime }_{pmk}$ based on an asymmetric loss function (linear exponential) for normal process. To estimate scriptCpmk′$\mathcal {C}^{\prime }_{pmk}$, we first obtain eight different classical methods of estimation and then consider objective Bayesian methods of estimation under the squared error loss function and the linear exponential loss function. Extensive simulations are carried out to investigate the performance of these estimation methods in terms of the mean squared errors. In addition, we compare the performance of four bootstrap confidence intervals and the highest posterior density interval of scriptCpmk′$\mathcal {C}^{\prime }_{pmk}$ in terms of average width and coverage probability. Finally, three real‐data applications from electronic industries are provided for illustrative purposes.

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“…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%

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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Bootstrap confidence intervals of CpTk for two parameter logistic exponential distribution with applications

Cited by 21 publications

References 30 publications

Parametric inference of the loss based index Cpm for normal distribution

Parametric inference of the loss based index Cpm for normal distribution

Classical and objective Bayesian estimation and confidence intervals of an asymmetric loss based capability index Cpmk′$\mathcal {C}^{\prime }_{pmk}$

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

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