Some analytical results on CUSUM and EWMA control charts

Gabriel Mititelu; Yupaporn Areepong; Saowanit Sukparungsee; Alexander A. Novikov

Some analytical results on CUSUM and EWMA control charts

Gabriel Mititelu, Yupaporn Areepong, Saowanit Sukparungsee, Alexander A. Novikov

Western Sydney University

Research output: Chapter in Book / Conference Paper › Conference Paper › peer-review

Abstract

The control charts CUSUM (CUmulative SUM) and EWMA (Exponentially Weighted Moving Average) are widely used in a great variety of practical applications such as economics, finance, medicine, and engineering. The Average Run Length (ARL) is the most common characteristic used to design EWMA and CUSUM. Here we use the Fredholm type integral equations to derive analytical closed form representations for the ARL for some special cases. In particular, we derive a closed form representation for the ARL of CUSUM chart assuming that the random observations have a hyperexponential distribution. For EWMA we solve the corresponding ARL integral equation when the observations have the Laplace distribution.

Original language	English
Title of host publication	Contributions in Mathematics and Applications III: ICMA-MU 2009, December 17-19, 2009, Bangkok, Thailand: Refereed Papers Presented at the International Conference in Mathematics and Applications
Publisher	Mahidol University
Pages	233-242
Number of pages	10
Publication status	Published - 2009
Event	International Conference in Mathematics and Applications - Duration: 17 Dec 2009 → …

Conference

Conference	International Conference in Mathematics and Applications
Period	17/12/09 → …

Keywords

integral equations
CUSUM technique
exponentially weighted moving average

Cite this

@inproceedings{6e661c13243a4c68839892cc1b585389,

title = "Some analytical results on CUSUM and EWMA control charts",

abstract = "The control charts CUSUM (CUmulative SUM) and EWMA (Exponentially Weighted Moving Average) are widely used in a great variety of practical applications such as economics, finance, medicine, and engineering. The Average Run Length (ARL) is the most common characteristic used to design EWMA and CUSUM. Here we use the Fredholm type integral equations to derive analytical closed form representations for the ARL for some special cases. In particular, we derive a closed form representation for the ARL of CUSUM chart assuming that the random observations have a hyperexponential distribution. For EWMA we solve the corresponding ARL integral equation when the observations have the Laplace distribution.",

keywords = "integral equations, CUSUM technique, exponentially weighted moving average",

author = "Gabriel Mititelu and Yupaporn Areepong and Saowanit Sukparungsee and Novikov, {Alexander A.}",

year = "2009",

language = "English",

pages = "233--242",

booktitle = "Contributions in Mathematics and Applications III: ICMA-MU 2009, December 17-19, 2009, Bangkok, Thailand: Refereed Papers Presented at the International Conference in Mathematics and Applications",

publisher = "Mahidol University",

note = "International Conference in Mathematics and Applications ; Conference date: 17-12-2009",

}

Mititelu, G, Areepong, Y, Sukparungsee, S & Novikov, AA 2009, Some analytical results on CUSUM and EWMA control charts. in Contributions in Mathematics and Applications III: ICMA-MU 2009, December 17-19, 2009, Bangkok, Thailand: Refereed Papers Presented at the International Conference in Mathematics and Applications. Mahidol University, pp. 233-242, International Conference in Mathematics and Applications, 17/12/09.

Some analytical results on CUSUM and EWMA control charts. / Mititelu, Gabriel; Areepong, Yupaporn; Sukparungsee, Saowanit et al.
Contributions in Mathematics and Applications III: ICMA-MU 2009, December 17-19, 2009, Bangkok, Thailand: Refereed Papers Presented at the International Conference in Mathematics and Applications. Mahidol University, 2009. p. 233-242.

Research output: Chapter in Book / Conference Paper › Conference Paper › peer-review

TY - GEN

T1 - Some analytical results on CUSUM and EWMA control charts

AU - Mititelu, Gabriel

AU - Areepong, Yupaporn

AU - Sukparungsee, Saowanit

AU - Novikov, Alexander A.

PY - 2009

Y1 - 2009

N2 - The control charts CUSUM (CUmulative SUM) and EWMA (Exponentially Weighted Moving Average) are widely used in a great variety of practical applications such as economics, finance, medicine, and engineering. The Average Run Length (ARL) is the most common characteristic used to design EWMA and CUSUM. Here we use the Fredholm type integral equations to derive analytical closed form representations for the ARL for some special cases. In particular, we derive a closed form representation for the ARL of CUSUM chart assuming that the random observations have a hyperexponential distribution. For EWMA we solve the corresponding ARL integral equation when the observations have the Laplace distribution.

AB - The control charts CUSUM (CUmulative SUM) and EWMA (Exponentially Weighted Moving Average) are widely used in a great variety of practical applications such as economics, finance, medicine, and engineering. The Average Run Length (ARL) is the most common characteristic used to design EWMA and CUSUM. Here we use the Fredholm type integral equations to derive analytical closed form representations for the ARL for some special cases. In particular, we derive a closed form representation for the ARL of CUSUM chart assuming that the random observations have a hyperexponential distribution. For EWMA we solve the corresponding ARL integral equation when the observations have the Laplace distribution.

KW - integral equations

KW - CUSUM technique

KW - exponentially weighted moving average

UR - http://hdl.handle.net/1959.7/uws:57761

M3 - Conference Paper

SP - 233

EP - 242

BT - Contributions in Mathematics and Applications III: ICMA-MU 2009, December 17-19, 2009, Bangkok, Thailand: Refereed Papers Presented at the International Conference in Mathematics and Applications

PB - Mahidol University

T2 - International Conference in Mathematics and Applications

Y2 - 17 December 2009

ER -

Some analytical results on CUSUM and EWMA control charts

Abstract

Conference

Keywords

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