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Skewness correction X̄ and R charts for skewed distributions

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  • Lai K. Chan
  • Heng J. Cui

Abstract

This paper proposes a skewness correction (SC) method for constructing the $\bar{X}$ and R control charts for skewed process distributions. Their asymmetric control limits (about the central line) are based on the degree of skewness estimated from the subgroups, and no parameter assumptions are made on the form of process distribution. These charts are simply adjustments of the conventional Shewhart control charts. Moreover, the $\bar{X}$ chart is almost the same as the Shewhart $\bar{X}$ chart if the process distribution is known to be symmetrical. The new charts are compared with the Shewhart charts and weighted variance (WV) control charts. When the process distribution is in some neighborhood of Weibull, lognormal, Burr or binomial family, simulation shows that the SC control charts have Type I risk (i.e., probability of a false alarm) closer to 0.27% of the normal case. Even in the case where the process distribution is exponential with known mean, not only the control limits and Type I risk, but also the Type II risk of the SC charts are closer to those of the exact $\bar{X}$ and R charts than those of the WV and Shewhart charts. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 555–573, 2003

Suggested Citation

  • Lai K. Chan & Heng J. Cui, 2003. "Skewness correction X̄ and R charts for skewed distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(6), pages 555-573, September.
    • Handle: RePEc:wly:navres:v:50:y:2003:i:6:p:555-573
    DOI: 10.1002/nav.10077
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    1. Choobineh, F. & Branting, D., 1986. "A simple approximation for semivariance," European Journal of Operational Research, Elsevier, vol. 27(3), pages 364-370, December.
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    Cited by:

    1. Fatimah Alshahrani & Ibrahim M. Almanjahie & Majid Khan & Syed M. Anwar & Zahid Rasheed & Ammara N. Cheema, 2023. "On Designing of Bayesian Shewhart-Type Control Charts for Maxwell Distributed Processes with Application of Boring Machine," Mathematics, MDPI, vol. 11(5), pages 1-20, February.
    2. Jing Jia Zhou & Kok Haur Ng & Kooi Huat Ng & Shelton Peiris & You Beng Koh, 2022. "Asymmetric Control Limits for Weighted-Variance Mean Control Chart with Different Scale Estimators under Weibull Distributed Process," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
    3. Pandu R. Tadikamalla & Dana G. Popescu, 2007. "Kurtosis correction method for X̄ and R control charts for long‐tailed symmetrical distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 371-383, June.

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