WEIGHTED STANDARD DEVIATION METHOD FOR X AND S CONTROL CHARTS

Abstract

A Shewhart chart based on normality assumption is not appropriate for skewed distributions since its Type-I error rate is ináated. Thisstudy presents X and S control charts for monitoring the process variabilityfor skewed distributions. We propose Weighted Standard Deviation (WSD)X and S control charts. Standard deviation estimator is applied to monitorthe process variability for estimating the process standard deviation, in thecase of the W SD X and S control charts as this estimator is simple and easyto compute. Unlike the Shewhart control chart, the proposed charts provideasymmetric limits in accordance with the direction and degree of skewnessto construct the upper and lower limits. The performances of the proposedcharts are compared with other heuristic charts for skewed distributions by using Simulation study. The Simulation studies show that the proposed controlcharts have good properties for skewed distributions and large sample sizes.