Control Chart for Autocorrelated Processes with Heavy Tailed Distributions

Standard control charts are constructed under the assumption that the observations taken from the process of interest are independent over time; however, in practice the observations in many cases are actually correlated. This paper considers the problem of monitoring a process in which the observations can be represented as a first-order autoregressive model following a heavy tailed distribution. We propose a chart based on computing the control limits using the process mean and the standard error of the least absolute deviation for the case when the process quality characteristics follows a heavy tailed t-distribution. This chart has narrow control limits since the standard error of the least absolute deviation is smaller than that of the ordinary least square estimator in the case of heavy tailed distributions.