Statistica Sinica 15(2005), 527-546
MAX-CUSUM CHART FOR AUTOCORRELATED
PROCESSES
Smiley W. Cheng and Keoagile Thaga
University of Manitoba and University of Botswana
Abstract:
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, 
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.
Key words and phrases:
AR(1) model, autocorrelation, autoregressive,
Markov chain, Max-CUSUM chart, random error and residual.