A study of multivariate $(\bar{X},S)$ control chart based on Kullback–Leibler information

Takemoto, Yasuhiko

doi:10.1007/s00170-003-1947-9

Cited by 13 publications

(3 citation statements)

References 15 publications

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“…Kanagawa et al 38 and Watakabe and Arizono 39 first used the Kullback‐Leibler information to design an

((),, \overset{false¯}{x}, s)

chart. Takemoto and Arizono 40 extended that work to a multivariate

((),, \overset{false¯}{x}, s)

chart. Alwan et al 41 introduced an information‐theoretic framework for process control, allowing the process to assume a variety of distributions in the exponential family.…”

Section: Introductionmentioning

confidence: 99%

A Kullback‐Leibler information control chart for linear profiles monitoring

Chang

Chen

2020

Quality & Reliability Eng

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Profile monitoring is referred to as monitoring the functional relationship between the response and explanatory variables. Traditionally, process control charts monitor the mean and/or the variance of a univariate quality characteristic. For several correlated quality characteristics, multivariate process control charts monitor the mean vector and/or the covariance matrix. However, monitoring the functional relationship between variables is sometimes more beneficial. One example is the power output of a Diesel engine and the amount of fuel injected should be related. In this paper, we propose a Kullback-Leibler information (KLI) control chart for linear profiles monitoring in Phase II. The plotted statistics of the KLI chart are calculated based on a backward procedure. The functional relationship is described by linear regression. The performance of the proposed KLI

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“…Kanagawa et al 38 and Watakabe and Arizono 39 first used the Kullback‐Leibler information to design an

((),, \overset{false¯}{x}, s)

chart. Takemoto and Arizono 40 extended that work to a multivariate

((),, \overset{false¯}{x}, s)

chart. Alwan et al 41 introduced an information‐theoretic framework for process control, allowing the process to assume a variety of distributions in the exponential family.…”

Section: Introductionmentioning

confidence: 99%

A Kullback‐Leibler information control chart for linear profiles monitoring

Chang

Chen

2020

Quality & Reliability Eng

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“…Watakabe and Arizono 28 proposed several approximations for the plotted statistic (PS) of the aforementioned

(\overset{x}{true}, s)

chart. The multivariate

(\overset{x}{true}, s)

chart is discussed in Takemoto and Arizono 29 . A visualization of the

(\overset{x}{true}, s)

chart is presented in Takemoto and Arizono 30 .…”

Section: Introductionmentioning

confidence: 99%

Designing a parameter‐free Kullback‐Leibler information control chart for monitoring process mean shift

Chang

Mastrangelo

2020

Quality & Reliability Eng

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This paper proposes a parameter‐free Kullback‐Leibler information control chart for monitoring sustained shifts in the process mean of a normally distributed process in phase II. Two plotted statistics are provided. One is based on our backward empirical sequential test, the other is based on the maximum log‐likelihood ratio change point method. These two achieve similar performances for the control chart. The performance of the proposed chart is compared with those of the cumulative sum chart, the exponentially weighted moving average chart, and the generalized likelihood ratio (GLR) chart. The results show that our proposed chart and the GLR chart have similar performances. Both can detect a wide range of shifts in the process mean, and neither requires design parameters other than the control limits. The proposed chart outperforms GLR when the size of the shift is below 1.24 standard deviations, while GLR outperforms the proposed chart when the size of the shift is above 1.24 standard deviations.

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“…Chou et al (2002) have considered the multivariate control chart for monitoring the process mean vector and covariance matrix for the related quality characteristics simultaneously by using log-likelihood ratio statistics. Takemoto and Arizono (2005) considered the multivariate (X, S) control chart for monitoring the mean vector m and the covariance matrix Σ simultaneously based on the Kullback-Leibler information as the test statistic. Khoo (2005) proposed a control chart based on the T 2 and |S| statistics for monitoring bivariate…”

Section: Introductionmentioning

confidence: 99%

Monitoring the mean vector and the covariance matrix of multivariate processes with sample means and sample ranges

Costa¹,

Machado²

2011

Prod.

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The joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and R charts and the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and S² charts are the most common charts used for monitoring the process mean and dispersion. With the usual sample sizes of 4 and 5, the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and R charts are slightly inferior to the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and S² charts in terms of efficiency in detecting process shifts. In this article, we show that for the multivariate case, the charts based on the standardized sample means and sample ranges (MRMAX chart) or on the standardized sample means and sample variances (MVMAX chart) are similar in terms of efficiency in detecting shifts in the mean vector and/or in the covariance matrix. User's familiarity with the computation of sample ranges is a point in favor of the MRMAX chart. An example is presented to illustrate the application of the proposed chart.

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A study of multivariate $(\bar{X},S)$ control chart based on Kullback–Leibler information

Cited by 13 publications

References 15 publications

A Kullback‐Leibler information control chart for linear profiles monitoring

A Kullback‐Leibler information control chart for linear profiles monitoring

Designing a parameter‐free Kullback‐Leibler information control chart for monitoring process mean shift

Monitoring the mean vector and the covariance matrix of multivariate processes with sample means and sample ranges

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