Performance of Conventional X-bar Chart for Autocorrelated Data Using Smaller Sample Sizes

Control charts are used to determine whether or not a manufacturing or business process is in a state of statistical control. Various schemes of the standard (Shewhart) X chart for autocorrelated data at sample sizes of 2 and 3 are developed and compared with the schemes of the same chart for IID data at various process shifts in the process mean. It is clear from the comparison that the in-control ARL of 370 is achieved by employing the X chart for the IID and autocorrelated data but as the level of correlation increases, the performance of conventional (Shewhart) X chart deteriorates. It is concluded that for faster detection in the process mean, the larger sample sizes (n) may be used. Thus the X chart for autocorrelated data should be used with carefully and judiciously.