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Robustness of the EWMA control chart for individual observations

Author

Listed:
  • S. W. Human
  • P. Kritzinger
  • S. Chakraborti

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.

Suggested Citation

  • S. W. Human & P. Kritzinger & S. Chakraborti, 2011. "Robustness of the EWMA control chart for individual observations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2071-2087.
  • Handle: RePEc:taf:japsta:v:38:y:2011:i:10:p:2071-2087 DOI: 10.1080/02664763.2010.545114
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    References listed on IDEAS

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    1. E. Andersson, 2002. "Monitoring cyclical processes. A non-parametric approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(7), pages 973-990.
    2. S. Knoth, 2002. "Monitoring the mean and the variance of a stationary process," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(1), pages 77-100.
    3. David Bock, 2008. "Aspects on the control of false alarms in statistical surveillance and the impact on the return of financial decision systems," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(2), pages 213-227.
    4. Christian Sonesson, 2003. "Evaluations of some Exponentially Weighted Moving Average methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(10), pages 1115-1133.
    5. Bersimis, Sotiris & Psarakis, Stelios & Panaretos, John, 2006. "Multivariate Statistical Process Control Charts: An Overview," MPRA Paper 6399, University Library of Munich, Germany.
    6. Clare Marshall & Nicky Best & Alex Bottle & Paul Aylin, 2004. "Statistical issues in the prospective monitoring of health outcomes across multiple units," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(3), pages 541-559.
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    Cited by:

    1. Graham, M.A. & Mukherjee, A. & Chakraborti, S., 2012. "Distribution-free exponentially weighted moving average control charts for monitoring unknown location," Computational Statistics & Data Analysis, Elsevier, pages 2539-2561.

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