Synthetic X chart for AR(1) autocorrelated processes

Assuming independent observations in the implementation of control charts in Statistical Process Control (SPC) are sometimes violated in practice, especially with high sampling policy. In this paper, we will investigate the properties of the synthetic X chart with data autocorrelation which can be represented as a first-order autoregression AR(1) model. Numerical results show the undesired effect of autocorrelation within subgroups on the chart's performance. In order to reduce this negative effect, a good strategy is to get non-neighboring items in each sample to form a new one. The synthetic control chart's properties are evaluated when applying this new sampling scheme. With the guideline of this paper, the practitioners can choose the appropriate sampling strategy to account for the autocorrelation on the synthetic X chart.