Control Charts for Monitoring the Mean and Variance of Autocorrelated Processes

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Abstract
In statistical process control it is usually assumed that the observations taken from the process of interest are independent, but in practice the observations in many cases are actually autocorrelated. This paper considers the problem of monitoring a process in which the observations can be represented as a first-order autoregressive process plus a random error. The problem of detecting special causes which may produce changes in the process mean and/or variance is considered. Several types of control charts and combinations of control charts are evaluated for their ability to detect changes in the process mean and variance. Some of these control charts plot the original observations and have control limits adjusted to account for the autocorrelation in the observations, and others plot the residuals from the forecast values of a fitted time series model. The results of these investigations show that there is no combination of charts that gives optimal performance across a wide variety of situations, but, for reasonably good overall performance, an exponentially weighted moving average chart of the observations used with a Shewhart chart of the residuals can be recommended for practical applications.

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