Many processes the observations are autocorrelated, and this autocorrelation can have a significant effect on the performance of the control chart. Many processes such as those found in chemical manufacturing, refinery operations, smelting operations, wood product manufacturing, waste-water processing and the operations of nuclear reactors have been shown to have autocorrelated observations. This paper introduces a autocorrelated cumulative sum (ACUSUM) control chart, a chart for detecting shifts of all kinds in case of first order autocorrelated process with high autocorrelation. This chart is based on standard CUSUM control chart with modified statistic, which is a correction of CUSUM chart statistic. Control chart statistic specially designed under the assumption of autocorrelated observations. The average run length of ACUSUM control chart is found via the Markov chain approach.
ACUSUM, ARMA, Average Run Length, CUSUM, Inertia, Modified CUSUM
