Probability Weighted Moments Approach to Quality Control Charts

Muhammad Faqir and Riaz Muhammad
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Muhammad Faqir: Department of Mathematics and Statistics, Allama Iqbal Open University, Islamabad, Pakistan
Riaz Muhammad: Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan

Stochastics and Quality Control, 2006, vol. 21, issue 2, 251-260

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 r2 and r3 (similar as the d2 and d3 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.

Date: 2006
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DOI: 10.1515/EQC.2006.251

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