For the purpose of process control, quality assurance engineers in a vegetable oil factory wonder the
performance of the Shewhart, CUSUM, and EWMA residual control charts for peroxide values that show
both serial autocorrelation between adjacent observations (autocorrelation) and upward linear trend. To
deal with autocorrelated process data, a primary method is to apply these charts to the uncorrelated
residuals of an appropriate time series model fitted to the data. In the relevant literature, although
performances of the residual charts have been widely studied for autocorrelated processes, there
exists no study that shows how these charts’ performances change by the addition of a particular type
of trend in the autocorrelated data. In the present paper, average run length performances of these
charts are computed for peroxide data from two batches, for which trend stationary first order