Adaptive CUSUM procedures with EWMA-based shift estimators

Wei Jiang; Lianjie Shu; Daniel W. Apley

doi:10.1080/07408170801961412

Adaptive CUSUM procedures with EWMA-based shift estimators

Wei Jiang^*, Lianjie Shu, Daniel W. Apley

^*Corresponding author for this work

Industrial Engineering and Management Sciences

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

139 Scopus citations

Abstract

Adaptive Cumulative SUM charts (ACUSUM) have been recently proposed for providing an overall good detection over a range of mean shift sizes. The basic idea of the ACUSUM chart is to first adaptively update the reference value based on an Exponentially Weighted Moving Average (EWMA) estimate and then to assign a weight on it using a certain type of weighting function. A linear weighting function is proposed that is motivated by likelihood ratio testing concepts and that achieves superior detection performance. Moreover, in view of the lower efficiency in tracking relative large mean shifts of the EWMA estimate, a generalized EWMA estimate is proposed as an alternative. A comparison of run length performance of the proposed ACUSUM scheme and other control charts is shown to be favorable to the former.

Original language	English (US)
Pages (from-to)	992-1003
Number of pages	12
Journal	IIE Transactions (Institute of Industrial Engineers)
Volume	40
Issue number	10
DOIs	https://doi.org/10.1080/07408170801961412
State	Published - 2008

Funding

Daniel W. Apley is an Associate Professor of Industrial Engineering and Management Sciences at Northwestern University, Evanston, IL, where he serves as the Director of the Manufacturing and Design Engineering Program. He obtained B.S., M.S. and Ph.D. degrees in Mechanical Engineering and an M.S. degree in Electrical Engineering from the University of Michigan. Prior to joining Northwestern University in 2003, he served on the faculty of Texas A&M University for 5 years. His primary research interests are manufacturing variation reduction and quality control, with a focus on processes in which advanced measurement, data collection and automatic control technologies are prevalent. He received the NSF CAREER award for his research and teaching in this area in 2001. He is a past chair of the Quality, Statistics & Reliability Section of INFORMS, and currently serves as an Associate Editor for Technometrics and is on the Editorial Board of the Journal of Quality Technology.

Keywords

Average run length
Change-point detection
EWMA
Markov chain

ASJC Scopus subject areas

Industrial and Manufacturing Engineering

Access to Document

10.1080/07408170801961412

Cite this

@article{805785daab29427693c88305c59f2925,

title = "Adaptive CUSUM procedures with EWMA-based shift estimators",

abstract = "Adaptive Cumulative SUM charts (ACUSUM) have been recently proposed for providing an overall good detection over a range of mean shift sizes. The basic idea of the ACUSUM chart is to first adaptively update the reference value based on an Exponentially Weighted Moving Average (EWMA) estimate and then to assign a weight on it using a certain type of weighting function. A linear weighting function is proposed that is motivated by likelihood ratio testing concepts and that achieves superior detection performance. Moreover, in view of the lower efficiency in tracking relative large mean shifts of the EWMA estimate, a generalized EWMA estimate is proposed as an alternative. A comparison of run length performance of the proposed ACUSUM scheme and other control charts is shown to be favorable to the former.",

keywords = "Average run length, Change-point detection, EWMA, Markov chain",

author = "Wei Jiang and Lianjie Shu and Apley, {Daniel W.}",

note = "Funding Information: Daniel W. Apley is an Associate Professor of Industrial Engineering and Management Sciences at Northwestern University, Evanston, IL, where he serves as the Director of the Manufacturing and Design Engineering Program. He obtained B.S., M.S. and Ph.D. degrees in Mechanical Engineering and an M.S. degree in Electrical Engineering from the University of Michigan. Prior to joining Northwestern University in 2003, he served on the faculty of Texas A&M University for 5 years. His primary research interests are manufacturing variation reduction and quality control, with a focus on processes in which advanced measurement, data collection and automatic control technologies are prevalent. He received the NSF CAREER award for his research and teaching in this area in 2001. He is a past chair of the Quality, Statistics & Reliability Section of INFORMS, and currently serves as an Associate Editor for Technometrics and is on the Editorial Board of the Journal of Quality Technology.",

year = "2008",

doi = "10.1080/07408170801961412",

language = "English (US)",

volume = "40",

pages = "992--1003",

journal = "IIE Transactions (Institute of Industrial Engineers)",

issn = "0740-817X",

publisher = "Taylor and Francis Ltd.",

number = "10",

}

TY - JOUR

T1 - Adaptive CUSUM procedures with EWMA-based shift estimators

AU - Jiang, Wei

AU - Shu, Lianjie

AU - Apley, Daniel W.

N1 - Funding Information: Daniel W. Apley is an Associate Professor of Industrial Engineering and Management Sciences at Northwestern University, Evanston, IL, where he serves as the Director of the Manufacturing and Design Engineering Program. He obtained B.S., M.S. and Ph.D. degrees in Mechanical Engineering and an M.S. degree in Electrical Engineering from the University of Michigan. Prior to joining Northwestern University in 2003, he served on the faculty of Texas A&M University for 5 years. His primary research interests are manufacturing variation reduction and quality control, with a focus on processes in which advanced measurement, data collection and automatic control technologies are prevalent. He received the NSF CAREER award for his research and teaching in this area in 2001. He is a past chair of the Quality, Statistics & Reliability Section of INFORMS, and currently serves as an Associate Editor for Technometrics and is on the Editorial Board of the Journal of Quality Technology.

PY - 2008

Y1 - 2008

N2 - Adaptive Cumulative SUM charts (ACUSUM) have been recently proposed for providing an overall good detection over a range of mean shift sizes. The basic idea of the ACUSUM chart is to first adaptively update the reference value based on an Exponentially Weighted Moving Average (EWMA) estimate and then to assign a weight on it using a certain type of weighting function. A linear weighting function is proposed that is motivated by likelihood ratio testing concepts and that achieves superior detection performance. Moreover, in view of the lower efficiency in tracking relative large mean shifts of the EWMA estimate, a generalized EWMA estimate is proposed as an alternative. A comparison of run length performance of the proposed ACUSUM scheme and other control charts is shown to be favorable to the former.

AB - Adaptive Cumulative SUM charts (ACUSUM) have been recently proposed for providing an overall good detection over a range of mean shift sizes. The basic idea of the ACUSUM chart is to first adaptively update the reference value based on an Exponentially Weighted Moving Average (EWMA) estimate and then to assign a weight on it using a certain type of weighting function. A linear weighting function is proposed that is motivated by likelihood ratio testing concepts and that achieves superior detection performance. Moreover, in view of the lower efficiency in tracking relative large mean shifts of the EWMA estimate, a generalized EWMA estimate is proposed as an alternative. A comparison of run length performance of the proposed ACUSUM scheme and other control charts is shown to be favorable to the former.

KW - Average run length

KW - Change-point detection

KW - EWMA

KW - Markov chain

UR - http://www.scopus.com/inward/record.url?scp=49249101687&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49249101687&partnerID=8YFLogxK

U2 - 10.1080/07408170801961412

DO - 10.1080/07408170801961412

M3 - Article

AN - SCOPUS:49249101687

SN - 0740-817X

VL - 40

SP - 992

EP - 1003

JO - IIE Transactions (Institute of Industrial Engineers)

JF - IIE Transactions (Institute of Industrial Engineers)

IS - 10

ER -

Adaptive CUSUM procedures with EWMA-based shift estimators

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this