Simultaneous monitoring of sample and group autocorrelations

Abstract

Most statistical process control (SPC) methods for detecting the presence of special causes of variation when process observations are inherently autocorrelated are focused on studying changes in the mean or variance of a time series. It is seldom emphasized in the quality literature that the presence of special causes of variation is manifested not only by the changes in mean or variance of a time series but also by the changes in its stochastic behavior. An approach to detect this type of change can be based on the sample autocorrelation function (ACF) or the Ljung-Box-Pierce portmanteau statistic applied to the residuals of the chosen time series model. In this article, we discuss the reasons why the residual A CF and portmanteau statistic give different sensitivities in terms of testing model adequacy and, hence, of detecting changes in stochastic behavior of a process. The problem is shown to be related to the multivariate SPC problem of deciding whether to monitor the individual observations using separate control charts or Hotelling's T2 statistic. Here, we present a graphical scheme for simultaneously monitoring the residual ACF and the portmanteau statistic.