Economic-Statistical Design of Multivariate Control Charts Using Quality Loss Function

Chou, Chao‐Yu; Liu, H.-R.; Huang, Xuan; Chen, C.-H.

doi:10.1007/s001700200215

Cited by 31 publications

(15 citation statements)

References 18 publications

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“…Serel et al 80 proposed the use of independentX-charts, one for each of the p variables, with unequal probabilities, which the test statistic plots beyond the control limits under an in-control state, while Molnau et al 81 showed that the economic statistical design of a MEWMA gives better statistical properties without significantly increasing optimal total costs. Chou et al 82 have developed a procedure for the economicstatistical design of multivariate control charts by using a quality-loss function for monitoring the process mean vector and covariance matrix simultaneously. Noorossana et al 83 summarized the assumptions as well as the consequences made regarding the out-of-control process shift in the economic design of multivariate control charts, while Love and Linderman 84 discussed the economic design of the MEWMA control chart.…”

Section: Economic Modelsmentioning

confidence: 99%

Multivariate statistical process control charts: an overview

Bersimis

Psarakis

Panaretos

2006

Quality & Reliability Eng

512

313

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In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewharttype control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial least squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.

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Section: Economic Modelsmentioning

confidence: 99%

Multivariate statistical process control charts: an overview

Bersimis

Psarakis

Panaretos

2006

Quality & Reliability Eng

512

313

View full text Add to dashboard Cite

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“…The loss function approach in the economic design of control charts have been applied by several researchers (see, e.g., [16][17][18][19][20][21] and [27][28][29][30]). Among the existing literature, Taguchi et al [27] provided an economic design to determine the diagnosis interval and control limits for on-line production processes applying the loss function.…”

Section: Economical-statistical Design and Quality Loss Functionmentioning

confidence: 99%

Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function

Safaei

Kazemzadeh

Niaki

2011

Int J Adv Manuf Technol

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Shewhart charts are the most popular control charts that can be used to monitor variable quality characteristics in a production process. In this paper, a multi-objective model of the economic statistical design of the X-bar control chart is first proposed by incorporating the Taguchi loss function and the intangible external costs. The model minimizes the mean hourly loss cost while minimizing out-of-control average run length and maintaining reasonable in-control average run length. A multiobjective evolutionary algorithm, namely NSGA-II, is then developed and used to obtain the Pareto optimal solution of the model. Some sensitivity analyses are next performed to investigate the effect of parameter estimation on the chart performances. Finally, a comparison study with a traditional economic design model reveals that the proposed multiple objective design of the X-bar control chart offers a better approach and more practical outcomes for the practitioners.

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“…As mentioned before, Chou et al [11] have given approximately the distribution function based on the chi-square series expression of the moment generating function of 2λ under the incontrol state. However, because the sample size is usually small in the practical operation of control charts, the control limit by their procedure requires the complicated calculation based on the expression with the Bernoulli polynomials of degrees r ≥ 30 in order to assure sufficient accuracy.…”

Section: Derivation Of Control Limits and Powermentioning

confidence: 99%

“…4 corresponds to the moment generating function of 2λ in the article of Chou et al [11]. Based on Eqs.…”

Section: Derivation Of Control Limits and Powermentioning

confidence: 99%

“…Recently, Chou et al [11] have proposed the multivariate control chart based on the log-likelihood ratio statistics for monitoring the mean vector and covariance matrix simultaneously. As a detail, Chou et al have approximately given the distribution function based on the chi-square series expression of the moment-generating function of the test statistic under the incontrol state and obtained the control limit of the multivariate control chart.…”

Section: Introductionmentioning

confidence: 99%

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

Takemoto

2004

Int J Adv Manuf Technol

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Recently, Chou et al. [11] 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. They have computed the approximation formula described with Bernoulli polynomials of degrees r ≥ 30 by using software MATHEMATICA 4.0 for obtaining the control limit with sufficient accuracy for the specified type I error probability in the chart. However, they cannot have obtained the approximation formula for the power evaluation. By the way, Kanagawa et al. [12] have proposed the (x, s)control chart for monitoring the mean and variance simultaneously based on Kullback-Leibler information when quality characteristics obey a univariate normal distribution. In this article, by adopting the procedure by Kanagawa et al., we propose the other approximation formula for determining simply the control limit with sufficient accuracy for the specified type I error probability. Furthermore, the power evaluation for the chart is also considered in theory.

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Economic-Statistical Design of Multivariate Control Charts Using Quality Loss Function

Cited by 31 publications

References 18 publications

Multivariate statistical process control charts: an overview

Multivariate statistical process control charts: an overview

Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function

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

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