Guaranteed Conditional Performance of Control Charts via Bootstrap Methods

Gandy, Axel; Kvaløy, Jan Terje

doi:10.1002/sjos.12006

Cited by 127 publications

(154 citation statements)

References 50 publications

(94 reference statements)

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“…For the effect of estimation error on the Shewhart chart see, for example, Saleh et al (2015b). For the effect of estimation error on the CUSUM chart see, for example, Gandy and Kvaløy (2013) or Saleh et al (2016). For the effect of estimation error on the EWMA chart see, for example, Jones, Champ, and Rigdon (2001) or Saleh et al (2015a).…”

Section: Introductionmentioning

confidence: 99%

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

Zwetsloot

Woodall

2016

Quality Engineering

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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.

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Section: Introductionmentioning

confidence: 99%

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

Zwetsloot

Woodall

2016

Quality Engineering

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“…1), CARL tol = 1/α tol = 1/0.0055 = 182. For comparison purposes, the boxplots also show the results of using the bootstrap method of Gandy and Kvaløy (2013) and Faraz et al (2015) and of the chart with unadjusted limits. The minimum tolerated CARL of 182 is indicated with a vertical dashed line, and the p-quantile of the CARL distribution is indicated in each boxplot with an added short vertical line.…”

Section: Use Of Different Estimators In Phase IImentioning

confidence: 99%

“…Thus, from a practical standpoint, another approach is necessary. One such recent proposal is to adjust the control limits to guarantee a minimum in-control chart performance based on the CFAR (or CARL; see, e.g., Albers and Kallenberg (2004), Gandy and Kvaløy (2013), and Goedhart et al (2017)) with a given probability. This is the idea pursued in this article.…”

Section: Introductionmentioning

confidence: 99%

“…This is the idea pursued in this article. Note that in this context, bootstrap methods have already been proposed (e.g., Gandy and Kvaløy (2013), Faraz et al (2015), Salah, Mahmoud, Jones-Farmer, Zwetsloot, and Woodall (2015), and Saleh, Mahmoud, Keefe, and Woodall (2015)) to find the adjusted control limits. Although this computer-intensive method eventually leads to the desired results and is more broadly applicable, analytical expressions give more insight into the required adjustments and are, in general, easier to implement.…”

Section: Introductionmentioning

confidence: 99%

“…As previously mentioned, Faraz et al (2015) also considered the problem of adjusting the S and S 2 chart control limits. They used the bootstrap method of Gandy and Kvaløy (2013) to obtain the adjusted coefficients. However, their out-of-control performance analysis was restricted to a pair of boxplots of the distribution of a chart's out-of-control CARL with the adjusted and unadjusted control limits.…”

Section: Introductionmentioning

confidence: 99%

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Shewhart control charts for dispersion adjusted for parameter estimation

et al. 2017

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Shewhart control charts for dispersion adjusted for parameter estimationGoedhart, R.; da Silva, M.M.; Schoonhoven, M.; Epprecht, E.K.; Chakraborti, S.; Does, R.J.M.M.; Veiga , A. 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. ABSTRACTSeveral recent studies have shown that the number of Phase I samples required for a Phase II control chart with estimated parameters to perform properly may be prohibitively high. Looking for a more practical alternative, adjusting the control limits has been considered in the literature. We consider this problem for the classic Shewhart charts for process dispersion under normality and present an analytical method to determine the adjusted control limits. Furthermore, we examine the performance of the resulting chart at signaling increases in the process dispersion. The proposed adjustment ensures that a minimum in-control performance of the control chart is guaranteed with a specified probability. This performance is indicated in terms of the false alarm rate or, equivalently, the in-control average run length. We also discuss the tradeoff between the in-control and out-of-control performance. Since our adjustment is based on exact analytical derivations, the recently suggested bootstrap method is no longer necessary. A real-life example is provided in order to illustrate the proposed methodology.

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2018

An Introduction to Discrete‐Valued Time Series

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Guaranteed Conditional Performance of Control Charts via Bootstrap Methods

Cited by 127 publications

References 50 publications

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

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

Shewhart control charts for dispersion adjusted for parameter estimation

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