New X-bar Control Chart Using Skewness Correction Method for Skewed Distributions with Application in Healthcare

Abstract

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

Control chart has been long-established among the highly reputable tools in statistical process control (SPC) with extensive industrial application. Shewhart chart is one of the most popular charts, but its reliability is arguable when dealing with skewed data, due to inflated false alarm rate (Type I error). In alleviating the problem, this study has developed a new X-bar control chart for monitoring of process mean using skewness correction (SC) method for skewed distributions, thus named as SC- control chart. The SC method is incorporated into the standard Shewhart’s X-bar chart, leading to the proposed univariate SC- to monitor the process mean of skewed data. It offers asymmetric control limits using the usual three sigma and the same known function of the skewness estimated from subgroups without assuming any distribution. The chart’s constants, and skewness correction factor are computed via numerical integration. To evaluate the strength and weakness of the charts, several conditions are created from different types of distributions and subgroup sizes. The SC- performance evaluation based on the false alarm rates (FAR) and probability of out-of-control (OOC) detection are accomplished using Monte Carlo simulation in SAS version 9.4. To illustrate its applicability, a real data on healthcare is employed. Its FAR performance is compared to the established charts: weighted variance X-bar R(WV- ); weighted variance X-bar S(WV- ); and standard X-bar S (ST- ). In aspect of the probability of OOC detection, the SC- is contended by the exact S chart. Extensive simulation study shows that the proposed SC- chart performs well in terms of FAR in almost all the degrees of skewness and sample sizes, n. In terms of the probability of OOC detection, it provides the closest values to those of the exact chart. It offers substantial enhancement over the established charts, and thus signifies as a preferred alternative especially in cases of skewed data.