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Probability Weighted Moments Approach to Quality Control Charts

Author

Listed:
  • Muhammad Faqir

    (Department of Mathematics and Statistics, Allama Iqbal Open University, Islamabad, Pakistan)

  • Riaz Muhammad

    (Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan)

Abstract

A new control chart namely Spw -Chart for monitoring the changes in the process variability is proposed and is based on Probability Weighted Moments (PWMs) and assuming that the quality characteristic follows a normal distribution. The coefficients r 2 and r 3 (similar as the d 2 and d 3 coefficients used for R-Charts) are derived for sample sizes n = 2, 3, . . . , 20, 25, 30, 35, 50, 100 by means of a simulation study. The quantiles of which are used for determining the values of the control limits and the power of the Spw -Chart to detect shifts in process variability, are also derived for n = 2, 3, . . . , 20, 25, 30, 35, 50, 100 by simulation. Each of the simulation studies is based on 10,000 random samples from the corresponding normal distribution. The performance of Spw -Chart is investigated by comparing its power curves with those of R and S Charts. It is observed that the power curves of the Spw -Chart are above those of the R-Chart, while slightly below those of the S-Chart in detecting shifts in the process variability. The effect of non-normality on the designs of S, R, and Spw Charts, is studied by simulating random samples from the exponential and the t distributions. The simulations reveal superiority of the Spw -Chart over both R and S Charts in the sense that the power curve of Spw -Chart is least affected by non-normality among all the three charts under study.

Suggested Citation

  • Muhammad Faqir & Riaz Muhammad, 2006. "Probability Weighted Moments Approach to Quality Control Charts," Stochastics and Quality Control, De Gruyter, vol. 21(2), pages 251-260, January.
    • Handle: RePEc:bpj:ecqcon:v:21:y:2006:i:2:p:251-260:n:8
    DOI: 10.1515/EQC.2006.251
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    References listed on IDEAS

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    1. E. Collani, 1999. "Control of production processes subjectto random shocks," Annals of Operations Research, Springer, vol. 91(0), pages 289-304, January.
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    Cited by:

    1. Muhammad Riaz & Ronald Does, 2009. "A process variability control chart," Computational Statistics, Springer, vol. 24(2), pages 345-368, May.

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