Another Look at the EWMA Control Chart with Estimated Parameters

Saleh, Nesma A.; Mahmoud, Mahmoud A.; Jones‐Farmer, L. Allison; Zwetsloot, Inez Maria; Woodall, William H.

doi:10.1080/00224065.2015.11918140

Cited by 132 publications

(169 citation statements)

References 32 publications

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“…Thus, for a practical implementation, we propose the use of adjusted control chart limits for Shewhart control charts for dispersion under normality adopting an alternative point of view. The idea is in line with recent research (e.g., Faraz et al (2015), Salah, Mahmoud, Jones-Farmer, Zwetsloot, and Woodall (2015), Saleh, Mahmoud, Keefe, and Woodall (2015), and Goedhart et al (2017)). The adjusted control limits are determined such that a minimum in-control chart performance is guaranteed with a pre-specified probability.…”

Section: Discussionsupporting

confidence: 67%

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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Section: Discussionsupporting

confidence: 67%

Shewhart control charts for dispersion adjusted for parameter estimation

et al. 2017

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“…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). Although many studies have been conducted to evaluate the effect of estimation error on a specific control chart, none have compared the effect of estimation error across these three types of charts.…”

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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“…studied the Shewhart ( X and

\overset{X}{true}

) control charts using the SDARL metric. In addition, the EWMA control chart with estimated parameters was studied by Saleh et al . Moreover, Aly et al .…”

Section: Introductionmentioning

confidence: 83%

“…Their approach adjusts the control limits of a chart such that the in‐control ARL is greater than or equal a desired value with a certain specified probability. Saleh et al . designed both the EWMA and Shewhart

\overset{X}{true}

charts using Gandy and Kvaløy's approach.…”

Section: Introductionmentioning

confidence: 97%

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A Reevaluation of the Adaptive Exponentially Weighted Moving Average Control Chart When Parameters are Estimated

Aly

Saleh

Mahmoud

et al. 2014

Quality & Reliability Eng

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The performance of control charts can be adversely affected when based on parameter estimates instead of known in‐control parameters. Several studies have shown that a large number of phase I observations may be needed to achieve the desired in‐control statistical performance. However, practitioners use different phase I samples and thus different parameter estimates to construct their control limits. As a consequence, there would be in‐control average run length (ARL) variation between different practitioners. This kind of variation is important to consider when studying the performance of control charts with estimated parameters. Most of the previous literature has relied primarily on the expected value of the ARL (AARL) metric in studying the performance of control charts with estimated parameters. Some recent studies, however, considered the standard deviation of the ARL metric to study the performance of control charts. In this paper, the standard deviation of the ARL metric is used to study the in‐control and out‐of‐control performance of the adaptive exponentially weighted moving average (AEWMA) control chart. The performance of the AEWMA chart is then compared with that of the Shewhart trueX¯ and EWMA control charts. The simulation results show that the AEWMA chart might represent a good solution for practitioners to achieve a reasonable amount of ARL variation from the desired in‐control ARL performance. In addition, we apply a bootstrap‐based design approach that provides protection against frequent false alarms without deteriorating too much the out‐of‐control performance. Copyright © 2014 John Wiley & Sons, Ltd.

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Another Look at the EWMA Control Chart with Estimated Parameters

Cited by 132 publications

References 32 publications

Shewhart control charts for dispersion adjusted for parameter estimation

Shewhart control charts for dispersion adjusted for parameter estimation

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

A Reevaluation of the Adaptive Exponentially Weighted Moving Average Control Chart When Parameters are Estimated

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