Performance of Conventional X Chart for Auto-Correlated Data Using Subgroup Size of Ten

Control charts have been used to monitor and control the production process and generate some sort of signal when there are indications to the effect that the process has gone out of control. Conventional (Shewhart) X charts were originally developed by Walter F. Shewhart (1931). The limits of the chart are known as upper control limit (UCL) and lower control limit (LCL). He suggested two control limits i.e. UCL = X + 3σ/√n and LCL = X - 3σ/√n, where X is the target mean, σ is population standard deviation and n is the sample size. In implementing the X chart, it is assumed that the process outputs must be IID but usually there is some correlation among the data. When this correlation builds up automatically in the entire process, this phenomenon is called autocorrelation. It is found that the performance of conventional X chart deteriorates on increasing the level of correlation.