Estimating the Standard Deviation in Quality-Control Applications

Mahmoud, Mahmoud A.; Henderson, G. Robin; Epprecht, Eugenio K.; Woodall, William H.

doi:10.1080/00224065.2010.11917832

Cited by 76 publications

(54 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Mahmoud et al (2010) showed that this estimator is more efficient than the mean of the subgroup standard deviations and the mean of the subgroup ranges when the data are normally distributed. We also evaluate a robust estimator proposed by Tatum (1997).…”

Section: Estimators Of the Standard Deviationmentioning

confidence: 99%

A Robust Standard Deviation Control Chart

Schoonhoven

Does

2012

Technometrics

View full text Add to dashboard Cite

A robust standard deviation control chart Schoonhoven, M.; Does, R.J.M.M. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden.The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. This article studies the robustness of Phase I estimators for the standard deviation control chart. A Phase I estimator should be efficient in the absence of contaminations and resistant to disturbances. Most of the robust estimators proposed in the literature are robust against either diffuse disturbances, that is, outliers spread over the subgroups, or localized disturbances, which affect an entire subgroup. In this article, we compare various robust standard deviation estimators and propose an algorithm that is robust against both types of disturbances. The algorithm is intuitive and is the best estimator in terms of overall performance. We also study the effect of using robust estimators from Phase I on Phase II control chart performance. Additional results for this article are available online as Supplementary Material.

show abstract

Section: Estimators Of the Standard Deviationmentioning

confidence: 99%

A Robust Standard Deviation Control Chart

Schoonhoven

Does

2012

Technometrics

View full text Add to dashboard Cite

show abstract

“…In the case of Shewhart charts, see for example, Schoonhoven et al (2011); for the CUSUM chart, see Nazir et al (2013); and for the EWMA chart, see Zwetsloot, Schoonhoven, and Does (2014). Furthermore, Mahmoud et al (2010) provided an overview and comparison of estimators for the standard deviation. Here we use, as estimator for μ 0 , the overall sample mean based on the Phase I data defined bŷ…”

Section: Defining the Shewhart Cusum And Ewma Control Chartsmentioning

confidence: 99%

A head-to-head comparative study of the conditional performance of control charts based on estimated parameters

Zwetsloot

Woodall

2016

Quality Engineering

Self Cite

View full text Add to dashboard Cite

General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. ABSTRACTImplementation of the Shewhart, CUSUM, and EWMA charts requires estimates of the in-control process parameters. Many researchers have shown that estimation error strongly influences the performance of these charts. However, a given amount of estimation error may differ in effect across charts. Therefore, we perform a pairwise comparison of the effect of estimation error across these charts. We conclude that the Shewhart chart is more strongly affected by estimation error than the CUSUM and EWMA charts. Furthermore, we show that the general belief that the CUSUM and EWMA charts have similar performance no longer holds under estimated parameters.

show abstract

“…Another result worth noting is thatS performs worst in this situation (with comparable bad performance like S and R). While others (e.g., Mahmoud et al (2010)) recommend using this estimator because it is most e cient in the absence of contaminations, we see that its performance decreases most quickly when there are outliers. The estimators G and ADM are e cient when no contaminations are present and perform better than the traditional estimators (S, S, and R) in the case of occasional outliers.…”

Section: E Ciency Of Proposed Estimatorsmentioning

confidence: 85%

“…The traditional estimators are of course the pooled and the meansample standard deviation and the mean-sample range. Mahmoud et al (2010) studied the relative e ciencies of these estimators for di↵erent sample sizes n and number of samples k. In deriving estimates of the in-control standard deviation, we will look at these as well as nine other estimators.…”

Section: Estimators Of the Standard Deviationmentioning

confidence: 99%

Design and Analysis of Control Charts for Standard Deviation with Estimated Parameters

Schoonhoven

Riaz

Does³

2011

Journal of Quality Technology

View full text Add to dashboard Cite

Design and analysis of control charts for standard deviation with estimated parametersSchoonhoven, M.; Riaz, M.; Does, R.J.M.M. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. This paper concerns the design and analysis of the standard deviation control chart with estimated limits. We consider an extensive range of statistics to estimate the in-control standard deviation (Phase I) and design the control chart for real-time process monitoring (Phase II) by determining the factors for the control limits. The Phase II performance of the design schemes is assessed when the Phase I data are uncontaminated and normally distributed as well as when the Phase I data are contaminated. We propose a robust estimation method based on the mean absolute deviation from the median supplemented with a simple screening method. It turns out that this approach is e cient under normality and performs substantially better than the traditional estimators and several robust proposals when contaminations are present.

show abstract

Estimating the Standard Deviation in Quality-Control Applications

Cited by 76 publications

References 5 publications

A Robust Standard Deviation Control Chart

A Robust Standard Deviation Control Chart

A head-to-head comparative study of the conditional performance of control charts based on estimated parameters

Design and Analysis of Control Charts for Standard Deviation with Estimated Parameters

Contact Info

Product

Resources

About