ARL performance of residual control charts for trend AR(1) process: A case study on peroxide values of stored vegetable oil

Abstract

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 autoregressive (trend AR(1) for short) model is a representative model. Key words: Statistical process control, autocorrelation, peroxide value, vegetable oil, trend AR(1) model.