Robustness of the Variable Sample Size and Control Limit ¯X Chart to Non Normality

Abstract

Recent studies demonstrated that the variable sample size (VSS) ¯X chart is quicker than the standard Shewhart (SS) ¯X chart in detecting small process mean shifts. The usual assumption for designing a control chart is that the data or measurements are normally distributed. However, this assumption may not be tenable in some production processes. The Burr distribution has been used in the literature to represent various non normal distributions. In this article, the Burr distribution will be employed to evaluate the control charts for non normal populations. We first show the VSS and Shewhart ¯X charts are sensitive to non normality. Then we propose a method of varying the sample size and the control limits simultaneously. The variable sample size and control limit VSSCL ¯X chart is shown to be quicker than the VSS ¯X chart in detecting small and moderate shifts in the process. Most importantly, the risk of false alarm for the VSSCL ¯X chart can be substantially decreased. In addition, with proper selection of chart parameters, the VSSCL ¯X chart is more robust to non normality than the VSS and Shewhart ¯X charts.