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Robustness of the EWMA control chart for individual observations

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  • S. W. Human
  • P. Kritzinger
  • S. Chakraborti
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    Abstract

    The traditional exponentially weighted moving average (EWMA) chart is one of the most popular control charts used in practice today. The in-control robustness is the key to the proper design and implementation of any control chart, lack of which can render its out-of-control shift detection capability almost meaningless. To this end, Borror et al. [5] studied the performance of the traditional EWMA chart for the mean for i.i.d. data. We use a more extensive simulation study to further investigate the in-control robustness (to non-normality) of the three different EWMA designs studied by Borror et al. [5]. Our study includes a much wider collection of non-normal distributions including light- and heavy-tailed and symmetric and asymmetric bi-modal as well as the contaminated normal, which is particularly useful to study the effects of outliers. Also, we consider two separate cases: (i) when the process mean and standard deviation are both known and (ii) when they are both unknown and estimated from an in-control Phase I sample. In addition, unlike in the study done by Borror et al. [5], the average run-length (ARL) is not used as the sole performance measure in our study, we consider the standard deviation of the run-length (SDRL), the median run-length (MDRL), and the first and the third quartiles as well as the first and the 99th percentiles of the in-control run-length distribution for a better overall assessment of the traditional EWMA chart's in-control performance. Our findings sound a cautionary note to the (over) use of the EWMA chart in practice, at least with some types of non-normal data. A summary and recommendations are provided.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664763.2010.545114
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Journal of Applied Statistics.

    Volume (Year): 38 (2011)
    Issue (Month): 10 ()
    Pages: 2071-2087

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    Handle: RePEc:taf:japsta:v:38:y:2011:i:10:p:2071-2087

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    Related research

    Keywords: average run-length; boxplot; distribution-free; median run-length; non-parametric; percentile; run-length; simulation;

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