Control charts for monitoring the mean and variance of autocorrelated processes

In statistical process control it is usually assumed that the observations taken from the process of interest are independent, but in practice the obs ervations in many cases are actually autocorrelated. This paper considers t he problem of monitoring a process in which the observations can be represe nted as a first-order autoregressive process plus a random error. The probl em of detecting special causes which may produce changes in the process mea n and/or variance is considered. Several types of control charts and combin ations of control charts are evaluated for their ability to detect changes in the process mean and variance. Some of these control charts plot the ori ginal observations and have control limits adjusted to account for the auto correlation in the observations, and others plot the residuals from the for ecast values of a fitted time series model. The results of these investigat ions show that there is no combination of charts that gives optimal perform ance across a wide variety of situations, but, for reasonably good overall performance, an exponentially weighted moving average chart of the observat ions used with a Shewhart chart of the residuals can be recommended for pra ctical applications.