Adaptive control charts for skew-normal distribution

The standard Shewhart-type X chart, named FSS-X chart, has been widely used to detect the mean shift of process by implementing fixed sample and sampling frequency schemes. The FSS-X chart could be sensitive to the normality assumption and is inefficient to catch small or moderate shifts in the process mean. To monitor nonnormally distributed variables, Li et al [Commun Stat-Theory Meth. 2014; 43(23): 4908-4924] extended the study of Tsai [Int J Reliab Qual Saf Eng. 2007; 14(1): 49-63] to provide a new skew-normal FSS-X (SN FSS-X) chart with exact control limits for the SN distribution. To enhance the sensitivity of the SN FSS-X chart on detecting small or moderate mean shifts in the process, adaptive X charts with variable sampling interval (VSI), variable sample size (VSS), and variable sample size and sampling interval (VSSI) are introduced for the SN distribution in this study. The proposed adaptive control charts include the normality adaptive charts as special cases. Simulation results show that all the proposed SN VSI-X, SN VSS-X, and SN VSSI-X charts outperform the SN FSSX chart on detecting small or moderate shifts in the process mean. The impact of model misspecification on using the proposed adaptive charts and the sample size impact for using the FSS-X chart to monitor the mean of SN data are also discussed. An example about single hue value in polarizer manufacturing process is used to illustrate the applications of the proposed adaptive charts.