Estimating process capability indexCpk: classical approach versus Bayesian approach

Pearn, W. L.; Wu, Chin Chieh; Wu, Chia Huang

doi:10.1080/00949655.2014.914211

Cited by 22 publications

(11 citation statements)

References 23 publications

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“…Among the PCIs existing in the literature, C pk is the most widely accepted among practitioners and hence the study of the distribution and inferential properties of C pk and its plug-in estimator are of particular interest for several eminent statisticians (refer [9] and the references there-in). Pearn et al [17] have extensively studied the estimation procedure of C pk from both the classical and Bayesian perspective.…”

Section: Example 2 (Based On Leone Et Al's [1] Data)mentioning

confidence: 99%

“…It is easy to observe that the statistical distribution ofĈ pk involves folded normal distribution [9] and [17]. Hence, the methodology for obtaining (μ, σ ) from (μ f , σ f ) along with the cdf values of folded normal distribution can be used in hypothesis testing and in obtaining confidence interval (in particular, to obtain the so-called upper and lower α points for certain values of α, say α = 0.01, 0.05 and so on) forĈ pk values.…”

Section: Example 2 (Based On Leone Et Al's [1] Data)mentioning

confidence: 99%

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A simple algorithm for calculating values for folded normal distribution

Chatterjee

Chakraborty

2015

Journal of Statistical Computation and Simulation

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Folded normal distribution originates from the modulus of normal distribution. In the present article, we have formulated the cumulative distribution function (cdf) of a folded normal distribution in terms of standard normal cdf and the parameters of the mother normal distribution. Although cdf values of folded normal distribution were earlier tabulated in the literature, we have shown that those values are valid for very particular situations. We have also provided a simple approach to obtain values of the parameters of the mother normal distribution from those of the folded normal distribution. These results find ample application in practice, for example, in obtaining the so-called upper and lower α-points of folded normal distribution, which, in turn, is useful in testing of the hypothesis relating to folded normal distribution and in designing process capability control chart of some process capability indices. A thorough study has been made to compare the performance of the newly developed theory to the existing ones. Some simulated as well as real-life examples have been discussed to supplement the theory developed in this article. Codes (generated by R software) for the theory developed in this article are also presented for the ease of application.

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Section: Example 2 (Based On Leone Et Al's [1] Data)mentioning

confidence: 99%

Section: Example 2 (Based On Leone Et Al's [1] Data)mentioning

confidence: 99%

A simple algorithm for calculating values for folded normal distribution

Chatterjee

Chakraborty

2015

Journal of Statistical Computation and Simulation

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“…Although the estimates of the parameters can be derived directly from these control charts for a statistically stable method, they are not used in the subsequent stages of capability assessment in practice. Instead, new samples are drawn to approximate the same parameters, rendering the method extremely inefficient see [37], [38] devised Cp estimators based on R X and S X control chart details, as well as the corresponding testing process. They've also proposed a step-by-step approach to help practitioners for determine whether the process is capable or not [39], argued in favor of estimating Cpk using control chart info.…”

Section: Volume … 2021mentioning

confidence: 99%

Comparative Analysis Four Different Ways of Calculating Yield Index SSS_pk Based on Information of Control Chart, and Six Sigma, to Measuring the Process Performance in Industries: Case Study in Aden’s Oil Refinery, Yemen

et al. 2021

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Process capability index PCIs have long been used to assess process efficiency in the manufacturing. While PCIs assess the process stability and efficiency, real measurements of product quality depended on estimate the standard deviation for a short-term variance was calculated as the base approach in several previous studies for measuring PCIs. Studies in recent years seek to estimate shift of the process mean from target. In today's smart manufacturing production climate, manufacturers keep track of production performance. Since the deviance of process mean comparative to the target is different. This allows a more robust norm to be implemented by estimate the relative shift to describe the variance of process in Six Sigma (SS). For that purpose, this paper suggests an evaluation method by comparative analysis to four different ways of calculating yield indexes Spk based on six sigma and control information, of S X chart. Moreover, this paper extends the univariate process index yield SSSpk to a multi-generalized yield index is called SSMSpk. An established an updated approach to assess univariate and multi-characteristic, based on understanding variation which is critical to quality (CTQ) and focusing on the position and actions of natural process tolerance between defined tolerances limits. To demonstrate the trueness verification proficiency of this approach, this paper includes an industrial case study to assess the process efficiency in Aden's oil refinery, Yemen. The findings of this study indicated that the indexes which are calculating based on six sigma outperformed existing indices and that this study has important implications for industrial practitioners, researchers and quality control experts interested in the evaluation of process performance.

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“…They are typically a set of formulas which uses the mean and variance of a particular product characteristic to determine whether the process that makes that product is capable of meeting production tolerance. In addition to providing numerical measures of whether or not a manufacturing process is capable of producing consistent products based on predetermined specification limits, PCIs are also convenient and an effective tools to facilitate communication among engineers (Allam, Becker, Baudouin, Bigot, & Krumpipe, 2014;Pan, Li, & Shih, 2016;Parchami, Sadeghpour, Nourbakhsh, & Mashinchi, 2014;Pearn, Wu, & Chia, 2014;Pham, 2015;Srinivasan et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

TITLE YIELD INDEX BASED ON CONCEPT OF SIX- SIGMA SSCpk FOR ASSESSMENT PROCESS PERFORMANCE IN INDUSTRIES

Ali¹,

Ghaffar²,

Al‐Swidi³

et al. 2022

PES

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Process quality is a key factor in facilitating product sales, (PCIs), which determine the relationship between the manufacturing specifications and the actual process performance by quantifying process potential. Although Cp, Cpk indices are the most popular and important criteria used in manufacturing industries to measure process performance reported extensively in the literature, in the literature, the majority of previous studies neglected the idea of Six Sigma (SS). However, existing PCIs based on SS presented only a range of quality levels rather than a specific quality level value. The purpose of this study is to measure and enhance the precision of performance evaluation for processes industrial, through the use of (PCIs) and (SS) concept. In light of this, this study introduces new performance index based on the idea SS which are SSCpk by extending the indices Cp, Cpk and calculating the sigma process level directly to measure yield process based on idea SS. To demonstrate the effectiveness applicability of the SSCpk index, this study presents an industrial case study to assess the process performance of Aden oil refinery in Yemen. Toward this end, the data for essential quality characteristic of petroleum products namely octane number was collected randomly from Aden refinery. The findings of this study indicated that the proposed index SSCpk outperformed on the existing indices Cpk as the shows at the results and discussion. Finally, the proposed process yield index based on SS concept is a promising approach and thus can be utilized by other industries and practitioners to assess process performance in the aspect of precision and quality control.

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Estimating process capability indexC_pk: classical approach versus Bayesian approach

Cited by 22 publications

References 23 publications

A simple algorithm for calculating values for folded normal distribution

A simple algorithm for calculating values for folded normal distribution

Comparative Analysis Four Different Ways of Calculating Yield Index SSS_pk Based on Information of Control Chart, and Six Sigma, to Measuring the Process Performance in Industries: Case Study in Aden’s Oil Refinery, Yemen

TITLE YIELD INDEX BASED ON CONCEPT OF SIX- SIGMA SSCpk FOR ASSESSMENT PROCESS PERFORMANCE IN INDUSTRIES

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Estimating process capability indexCpk: classical approach versus Bayesian approach

Cited by 22 publications

References 23 publications

A simple algorithm for calculating values for folded normal distribution

A simple algorithm for calculating values for folded normal distribution

Comparative Analysis Four Different Ways of Calculating Yield Index SSSpk Based on Information of Control Chart, and Six Sigma, to Measuring the Process Performance in Industries: Case Study in Aden’s Oil Refinery, Yemen

TITLE YIELD INDEX BASED ON CONCEPT OF SIX- SIGMA SSCpk FOR ASSESSMENT PROCESS PERFORMANCE IN INDUSTRIES

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Product

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About

Estimating process capability indexC_pk: classical approach versus Bayesian approach

Comparative Analysis Four Different Ways of Calculating Yield Index SSS_pk Based on Information of Control Chart, and Six Sigma, to Measuring the Process Performance in Industries: Case Study in Aden’s Oil Refinery, Yemen