Effect of Sample Size on X Chart for Correlated Data

Shewhart X charts are often used in industries to detect the larger shifts in the process mean. One of the assumptions while implementing these charts is that the observations from the process output are Independent and Identically Distributed (IID), but in actual practice, the observations are correlated for many processes. This correlation has a significant effect on the performance of the Shewhart (standard) X chart. The performance of the X chart is studied for the IID and correlated data at different sample sizes. The Average Run Lengths (ARLs) at various sets of parameters of the X chart are computed by simulation, using MATLAB. Various optimal schemes of the X chart for different sample sizes and levels of correlation are suggested in this paper. The larger sample size (n) is recommended to detect the shift in the process mean quickly. The suggested schemes may be very useful at the shop floor level for industries and service sectors.