Probability Weighted Moments Approach to Quality Control Charts

Abstract A new control chart namely S pw -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 S pw -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 S pw -Chart is investigated by comparing its power curves with those of R and S Charts. It is observed that the power curves of the S pw -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 S pw Charts, is studied by simulating random samples from the exponential and the t distributions. The simulations reveal superiority of the S pw -Chart over both R and S Charts in the sense that the power curve of S pw -Chart is least affected by non-normality among all the three charts under study.