Quality control chart interpretation is usually based on the assumption that successive observations are independent over time. In this article we show the effect of autocorrelation on the retrospective Shewhart chart for individuals, often referred to as the X-chart, with the control limits based on moving ranges. It is shown that the presence of positive first lag autocorrelation results in an increased number of false alarms from the control chart. Negative first lag autocorrelation can result in unnecessarily wide control limits such that significant shifts in the process mean may go undetected. We use first-order autoregressive and first-order moving average models in our simulation of small samples of autocorrelated data.

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The basic assumption underlying statistical control chart criteria is that the process measurements are independent and identically distributed over time.However, autocorrelation and other time-series effects occur frequently in application. In this paper, the effects of autocorrelation are investigated for the frequently advocated supplementary runs rules. For both individual control charts based on the moving range and sample standard deviation, using simulation, the impact of autocorrelation for the AR(1) on in-control average run lengths is given.

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