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The effect of autocorrelation on the retrospective X-chart
Journal article   Peer reviewed

The effect of autocorrelation on the retrospective X-chart

Hazem D. Maragah and William H. Woodall
Journal of statistical computation and simulation, v 40(1-2), pp 29-42
01 Feb 1992
DOI: https://doi.org/10.1080/00949659208811363

Abstract

control chart false alarm Statistical process control
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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