Approximately Unbiased Estimator for Non-Normal Process Capability Index <i>CNpk</i>

Pearn, W. L.; Tai, Y. T.; Hsiao, I. F.; Ao, Yin

doi:10.1520/jte20130125

Cited by 27 publications

(8 citation statements)

References 26 publications

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“…e MLEs of α and β denoted by α mle and β mle can be obtained by solving the above equations simultaneously or by maximizing the log-likelihood function given in equation (10) with respect to α and β. Substituting the MLEs (α mle , β mle ) of (α, β) and by using the invariance property of MLE, we can get the estimators of S pmk and S pmkc as…”

Section: Maximum Likelihood 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: Maximum Likelihood 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

View full text Add to dashboard Cite

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“…For non-normal processes, considerable evidence has indicated that the basic PCIs will mislead managers into making uninformed decisions. Studies of the effects of non-normality on PCIs can be found in English and Taylor, 17 Chen and Pearn, 18 Shore, 19 Wu and Swain, 20 Vännman and Albing, 21 Pearn et al 22 and Wu et al 23 Hence, the main purpose of this study was to provide an alternative method of assessing the C pm values of non-normal processes. The Markov chain Monte Carlo (MCMC) technique was incorporated into Bayesian models in this study.…”

Section: Introductionmentioning

confidence: 99%

“…For non‐normal processes, considerable evidence has indicated that the basic PCIs will mislead managers into making uninformed decisions. Studies of the effects of non‐normality on PCIs can be found in English and Taylor, Chen and Pearn, Shore, Wu and Swain, Vännman and Albing, Pearn et al . and Wu et al …”

Section: Introductionmentioning

confidence: 99%

Efficient Technique for Assessing Actual Non‐normal Quality Loss: Markov Chain Monte Carlo

Liao

2016

Quality & Reliability Eng

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Markov chain Monte Carlo (MCMC) techniques have been extensively developed and are accepted for solving various real‐world problems. However, process capabilities are rarely analyzed with the means of MCMC. This study integrates the MCMC technique into Bayesian models for assessing the well‐known quality loss index Cpm for gamma and Weibull process distributions. After the MCMC iterations are completed, the quality manager can make reliable decisions via the proposed credible intervals. Furthermore, this study provides performance comparisons of the estimators of Cpm obtained by the MCMC and bootstrap techniques. Simulations show that the MCMC technique performs better than the bootstrap technique in most of the cases that were considered. Copyright © 2016 John Wiley & Sons, Ltd.

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“…As the process is abnormal, much evidence has indicated that the standard PCIs will mislead the manager into making uninformed decisions. Studies of the effects of nonnormality on PCIs can be found in English and Taylor (1993), Shore (1998), Wu and Swain (2001), Pearn et al (2014), and Wu et al (2014).…”

Section: Introductionmentioning

confidence: 99%

Markov chain Monte Carlo in Bayesian models for testing gamma and lognormal S-type process qualities

Liao

2016

International Journal of Production Research

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The process capability index C pu is widely used to measure S-type process quality. Many researchers have presented adaptive techniques for assessing the true C pu assuming normality. However, the quality characteristic is often abnormal, and the derived techniques based on the normality assumption could mislead the manager into making uninformed decisions. Therefore, this study provides an alternative method for assessing C pu of non-normal processes. The Markov chain Monte Carlo, an emerging popular statistical tool, is integrated into Bayesian models to seek the empirical posterior distributions of specific gamma and lognormal parameters. Afterwards, the lower credible interval bound of C pu can be derived for testing the non-normal process quality. Simulations show that the proposed method is adaptive and has good performance in terms of coverage probability.

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Approximately Unbiased Estimator for Non-Normal Process Capability Index CNpk

Cited by 27 publications

References 26 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

Efficient Technique for Assessing Actual Non‐normal Quality Loss: Markov Chain Monte Carlo

Markov chain Monte Carlo in Bayesian models for testing gamma and lognormal S-type process qualities

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