A multivariate exponentially weighted moving average control chart

Cynthia A. Lowry; William H. Woodall; Charles W. Champ; Steven E. Rigdon

doi:10.2307/1269551

A multivariate exponentially weighted moving average control chart

Cynthia A. Lowry
, William H. Woodall
, Charles W. Champ
, Steven E. Rigdon

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1065 Scopus citations

Abstract

A multivariate extension of the exponentially weighted moving average (EWMA) control chart is presented, and guidelines given for designing this easy-to-implement multivariate procedure. A comparison shows that the average run length (ARL) performance of this chart is similar to that of multivariate cumulative sum (CUSUM) control charts in detecting a shift in the mean vector of a multivariate normal distribution. As with the Hotelling's χ² and multivariate CUSUM charts, the ARL performance of the multivariate EWMA chart depends on the underlying mean vector and covariance matrix only through the value of the noncentrality parameter. Worst-case scenarios show that Hotelling's χ² charts should always be used in conjunction with multivariate CUSUM and EWMA charts to avoid potential inertia problems. Examples are given to illustrate the use of the proposed procedure.

Original language	English
Pages (from-to)	46-53
Number of pages	8
Journal	Technometrics
Volume	34
Issue number	1
DOIs	https://doi.org/10.2307/1269551
State	Published - Feb 1992

Scopus Subject Areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Keywords

Average run length
Hotelling's T chart
Multivariate CUSUM
Statistical process control

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10.2307/1269551

Cite this

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title = "A multivariate exponentially weighted moving average control chart",

abstract = "A multivariate extension of the exponentially weighted moving average (EWMA) control chart is presented, and guidelines given for designing this easy-to-implement multivariate procedure. A comparison shows that the average run length (ARL) performance of this chart is similar to that of multivariate cumulative sum (CUSUM) control charts in detecting a shift in the mean vector of a multivariate normal distribution. As with the Hotelling's χ2 and multivariate CUSUM charts, the ARL performance of the multivariate EWMA chart depends on the underlying mean vector and covariance matrix only through the value of the noncentrality parameter. Worst-case scenarios show that Hotelling's χ2 charts should always be used in conjunction with multivariate CUSUM and EWMA charts to avoid potential inertia problems. Examples are given to illustrate the use of the proposed procedure.",

keywords = "Average run length, Hotelling's T chart, Multivariate CUSUM, Statistical process control",

author = "Lowry, \{Cynthia A.\} and Woodall, \{William H.\} and Champ, \{Charles W.\} and Rigdon, \{Steven E.\}",

year = "1992",

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doi = "10.2307/1269551",

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T1 - A multivariate exponentially weighted moving average control chart

AU - Lowry, Cynthia A.

AU - Woodall, William H.

AU - Champ, Charles W.

AU - Rigdon, Steven E.

PY - 1992/2

Y1 - 1992/2

N2 - A multivariate extension of the exponentially weighted moving average (EWMA) control chart is presented, and guidelines given for designing this easy-to-implement multivariate procedure. A comparison shows that the average run length (ARL) performance of this chart is similar to that of multivariate cumulative sum (CUSUM) control charts in detecting a shift in the mean vector of a multivariate normal distribution. As with the Hotelling's χ2 and multivariate CUSUM charts, the ARL performance of the multivariate EWMA chart depends on the underlying mean vector and covariance matrix only through the value of the noncentrality parameter. Worst-case scenarios show that Hotelling's χ2 charts should always be used in conjunction with multivariate CUSUM and EWMA charts to avoid potential inertia problems. Examples are given to illustrate the use of the proposed procedure.

AB - A multivariate extension of the exponentially weighted moving average (EWMA) control chart is presented, and guidelines given for designing this easy-to-implement multivariate procedure. A comparison shows that the average run length (ARL) performance of this chart is similar to that of multivariate cumulative sum (CUSUM) control charts in detecting a shift in the mean vector of a multivariate normal distribution. As with the Hotelling's χ2 and multivariate CUSUM charts, the ARL performance of the multivariate EWMA chart depends on the underlying mean vector and covariance matrix only through the value of the noncentrality parameter. Worst-case scenarios show that Hotelling's χ2 charts should always be used in conjunction with multivariate CUSUM and EWMA charts to avoid potential inertia problems. Examples are given to illustrate the use of the proposed procedure.

KW - Average run length

KW - Hotelling's T chart

KW - Multivariate CUSUM

KW - Statistical process control

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U2 - 10.2307/1269551

DO - 10.2307/1269551

M3 - Article

SN - 0040-1706

VL - 34

SP - 46

EP - 53

JO - Technometrics

JF - Technometrics

IS - 1

ER -

A multivariate exponentially weighted moving average control chart

Abstract

Scopus Subject Areas

Keywords

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