A model-free design of [X] charts for unknown autocorrelated processes

We consider the design of X macr control charts, assuming that the quality characteristic measurements follow an unknown autocorrelated process and a set of Phase-I in-control data are given. Our X macr -chart procedure sets the centerline at a known in-control (or target) mean and control limits at k standard deviations away from the centerline, where the standard deviation of X macr is estimated by the NBM (nonoverlapping batch means) method using the Phase I data. We propose a model-free method for computing the design parameter values: the batch size, sample size, and factor k. Simulation results show that the model-free design performs well, especially when the correlation is small or when the correlation is large but the mean shift is small or median.