Max-cusum chart for autocorrelated processes

A Cumulative Sum (CUSUM) control chart capable of detecting changes in both the mean and the standard deviation for autocorrelated data, referred to as the Max-CUSUM chart for Autocorrelated Process chart (MCAP chart), is proposed. This chart is based on fitting a time series model to the data, and then calculating the residuals. The observations are represented as a first-order autoregressive process plus a random error term. The Average Run Lengths (ARL's) for fixed decision intervals and reference values, (h, k) are calculated. The proposed chart is compared with the combined Shewhart-EWMA chart for autocorrelated data proposed by Lu and Reynolds (1999). Comparisons are based on the out-of-control ARL's. The MCAP chart detects small shifts in the mean and standard deviation at both low and high levels of autocorrelation more quickly than the combined Shewhart-EWMA chart. This makes the MCAP chart useful to modern production processes where high quality goods are produced with a low fraction of nonconforming products.