A Control Chart for the Multivariate Coefficient of Variation

Yeong, Wai Chung; Khoo, Michael B. C.; Teoh, Wei Lin; Castagliola, Philippe

doi:10.1002/qre.1828

Cited by 64 publications

(119 citation statements)

References 30 publications

(75 reference statements)

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“…The in‐control MCV, γ 0 , needs to be estimated from the phase I data. According to Yeong et al, there are three methods of estimating γ 0 , ie, the (1) mean

\overset{γ}{true} = \frac{\sum_{t = 1}^{m} {\overset{truê}{γ}}_{t}}{m}

, (2) weighted root mean square, and (3) maximum likelihood estimation. Among these three methods, the statistical efficiency of

\overset{γ}{true}

is found to be quite low.…”

Section: Distribution Of the Sample Multivariate CV Statisticmentioning

confidence: 99%

“…The root mean square method has a high level of statistical efficiency when compared with the other two methods of estimation. In addition, this method also provides easy computation and has an explicit form (Yeong et al). Thus, the in‐control sample MCV,

{\overset{truê}{γ}}_{0}

, is obtained by adopting the root mean square estimator, given as follows:

{\overset{truê}{γ}}_{0} = \sqrt{\frac{1}{m} \sum_{i = 1}^{m} {\hat{γ}}_{i}^{2}},

where m is the number of in‐control phase I multivariate samples adopted to estimate γ 0 and

{\overset{truê}{γ}}_{i}^{2}

is the squared MCV for the i th phase I sample.…”

Section: Distribution Of the Sample Multivariate CV Statisticmentioning

confidence: 99%

“…In a contrary, research works on monitoring the MCV arise. Yeong et al were the pioneers in developing the standard MCV chart. Subsequently, Lim et al and Khaw et al proposed the run sum (RS) MCV chart and adaptive MCV charts, respectively.…”

Section: Introductionmentioning

confidence: 99%

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A proposed variable parameter control chart for monitoring the multivariate coefficient of variation

Chew

Khoo

Khaw

et al. 2019

Quality & Reliability Eng

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An efficient process monitoring system is important for achieving sustainable manufacturing. The control charting technique is one of the most effective techniques to monitor process quality. In certain processes where the process mean and variance are not independent of one another, the coefficient of variation (CV), which measures the ratio of the standard deviation to the mean, should be monitored. In line with industrial settings, where at least two or more variables are monitored simultaneously in most processes, this paper proposes a variable parameter (VP) chart to monitor the multivariate CV (MCV). Formulae and algorithms to optimize the various performance measures are discussed. The proposed VP MCV chart is designed based on a Markov chain approach. The performance comparison shows that the proposed VP MCV chart prevails over the existing MCV charts, in terms of the average time to signal (ATS), standard deviation of the time of signal (SDTS), and expected average time to signal (EATS) criteria. An example is presented to illustrate the implementation of the proposed VP MCV chart.

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“…The in‐control MCV, γ 0 , needs to be estimated from the phase I data. According to Yeong et al, there are three methods of estimating γ 0 , ie, the (1) mean

\overset{γ}{true} = \frac{\sum_{t = 1}^{m} {\overset{truê}{γ}}_{t}}{m}

, (2) weighted root mean square, and (3) maximum likelihood estimation. Among these three methods, the statistical efficiency of

\overset{γ}{true}

is found to be quite low.…”

Section: Distribution Of the Sample Multivariate CV Statisticmentioning

confidence: 99%

{\overset{truê}{γ}}_{0}

, is obtained by adopting the root mean square estimator, given as follows:

{\overset{truê}{γ}}_{0} = \sqrt{\frac{1}{m} \sum_{i = 1}^{m} {\hat{γ}}_{i}^{2}},

where m is the number of in‐control phase I multivariate samples adopted to estimate γ 0 and

{\overset{truê}{γ}}_{i}^{2}

is the squared MCV for the i th phase I sample.…”

Section: Distribution Of the Sample Multivariate CV Statisticmentioning

confidence: 99%

See 1 more Smart Citation

A proposed variable parameter control chart for monitoring the multivariate coefficient of variation

Chew

Khoo

Khaw

et al. 2019

Quality & Reliability Eng

Self Cite

View full text Add to dashboard Cite

show abstract

“…Therefore, many researchers employed the expected ARL (EARL) as a viable performance indicator when the shift size is unknown. A vast majority of existing literatures considered the EARL for the Case‐K control charts, for example, see Celano, Castagliola et al, and Yeong et al To the best of the authors' knowledge, very limited literature on Case‐U control charts investigated the application of the expected ANOS (EANOS) criterion as a performance metric. Hence, in this article, 2 optimal designs are considered for the Case‐U SSMGR

\overset{X}{true}

chart, ie, by minimizing (i) the OOC ANOS (ANOS 1 ) and (ii) the OOC expected ANOS 1 (EANOS 1 ), for known and unknown shift sizes, respectively.…”

Section: Introductionmentioning

confidence: 99%

Optimal design of the side‐sensitive modified group runs (SSMGR) chart when process parameters are estimated

Chong

Khoo

Teoh

et al. 2018

Quality & Reliability Eng

Self Cite

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A side‐sensitive modified group runs (SSMGR) trueX¯ chart is commonly examined under the assumption of known process parameters (denoted as Case‐K). However, in practical situations, the process parameters are seldom known, and it is essential to estimate them from in‐control (IC) phase I samples. From the study of the minimum amount of phase I samples, m that is required by the SSMGR trueX¯ chart when the process parameters are estimated (represented as Case‐U), to achieve practically the same performance as that of the Case‐K, it was found that a huge number of IC phase I samples are needed. Due to time and cost factors, accumulating a substantial amount of IC phase I samples is difficult. To circumvent this problem, we study the optimal designs of the Case‐U SSMGR trueX¯ chart, based on both the zero and steady states' average number of observations to signal (ANOS) and expected ANOS (EANOS). Tables containing optimal charting parameters are provided to ease the implementation of the Case‐U SSMGR trueX¯ chart. By using these optimal parameters specifically designed for the Case‐U SSMGR trueX¯ chart, we can obtain similar zero and steady states' ANOS and EANOS performances to that of the Case‐K. The use of the optimal Case‐U SSMGR trueX¯ chart is demonstrated with real data taken from a hard‐bake process in a manufacturing company.

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“…However, in certain scenarios, the practitioner is not interested in the changes in the mean or the standard deviation but is instead interested in the relative variability compared with the mean (see for Yeong et al 2015). This relative variability is called the CV.…”

Section: Introductionmentioning

confidence: 99%

Designing a multiple dependent state sampling plan based on the coefficient of variation

2016

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A multiple dependent state (MDS) sampling plan is developed based on the coefficient of variation of the quality characteristic which follows a normal distribution with unknown mean and variance. The optimal plan parameters of the proposed plan are solved by a nonlinear optimization model, which satisfies the given producer’s risk and consumer’s risk at the same time and minimizes the sample size required for inspection. The advantages of the proposed MDS sampling plan over the existing single sampling plan are discussed. Finally an example is given to illustrate the proposed plan.

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A Control Chart for the Multivariate Coefficient of Variation

Abstract: International audienc

Cited by 64 publications

References 30 publications

A proposed variable parameter control chart for monitoring the multivariate coefficient of variation

A proposed variable parameter control chart for monitoring the multivariate coefficient of variation

Optimal design of the side‐sensitive modified group runs (SSMGR) chart when process parameters are estimated

Designing a multiple dependent state sampling plan based on the coefficient of variation

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