New Skewness Correction S Control Chart for Monitoring Dispersion of Skewed Data with Application in Healthcare

Abstract

A.M.A., Atta, S.S. S. Yahaya, Z. Zain, N. Ahmad.

Control chart is as a highly reputable statistical quality control tool in monitoring process stability. The classical control charts are designed on the basis of normality assumption, which is often not valid for real situations in industry; such violation of normality render the charts less accurate. This paper presents an alternative skewness correction S (SC-S) chart specifically developed to monitor process dispersion (e.g. S for standard deviation) for skewed distributions. Its false alarm rate (Type I error) is compared with those of various heuristics charts and standard S chart, while the probability of out-of-control (OOC) detection is evaluated along with the exact S chart. The proposed charts designed for process variables following Weibull and gamma distributions are assessed alongside the normal distribution. An extensive simulation study affirms that the SC-S chart performs well in regard to false alarm rate at wide range of skewness levels and sample sizes. Meanwhile, its probability of OOC detection is closer to that of the exact S chart in comparison to the established charts. In conclusion, the new SC-S chart outperforms the established ones in monitoring process dispersion for skewed distributions.