Performance Comparison of Residual Control Charts for Trend Stationary First Order Autoregressive Processes

Abstract

Data sets collected from industrial processes may have both a particular type of trend and correlation among adjacent observations (autocorrelation). Existing statistical control charts may individually cope with autocorrelated or trending data. Applying the Shewhart, EWMA, CUSUM, or GMA charts to the uncorrelated residuals of an appropriate time series model for a process is a primary method to deal with autocorrelated process data. In the relevant literature, there exists no study that shows how these charts’ performances change by the addition of a particular type of trend in autocorrelated data. In the present paper, average run lengths of these charts are computed; first, for autocorrelated data which does not include an increasing linear trend, and second, for autocorrelated data which includes an increasing linear trend. It is assumed that stationary AR(1) model and trend stationary first order autoregressive (trend AR(1) for short) model, respectively, are suitable models for the test data. ARL performances are compared within the charts and among the charts. Comparisons are made for different magnitudes of the process mean shift and various levels of autocorrelation. 

Keywords

• statistical process control
• autocorrelation
• linear trend
• trend AR(1).