In statistical process control, it is usually assumed that observations on the process output at
different times are lID. However, for many processes the observations are correlated and control charts for
monitoring these processes have recently received much attention. For monitoring the process level, this
study evaluates the properties of control charts, such as the EWMA chart and the CUSUM chart, based on
the residuals from the forecast values of an ARMA model. It is assumed that the process mean is a ftrst
order autoregressive (AR(l)) model and the observations are the mean plus a random error. Properties of
these charts are evaluated using a Markov chain approach or an integral equation approach. The
performance of control charts based on the residuals is compared to the performance of control charts
based on the original observations. A combined chart using forecasts and residuals as the control statistics
as well as a combined chart using the EWMA of observations and the EWMA of residuals as the control
statistics are also studied by simulation. It is found that no universally "good" chart exists among all the
charts investigated in this study.
In addition, for monitoring the process variance, two kinds of EWMA chart based on residuals are
studied and compared.
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