Artificial neural networks in applying MCUSUM residuals charts for AR(1) processes

The usual key assumptions in designing quality control charts are the normality and independency of serial samples. While the normality assumption holds in most cases, in many continuous-flow processes such as the chemical processes, serial samples have some degrees of autocorrelation associated with them. Ignoring the autocorrelation structure in constructing control charts, results in decreasing the in-control run length, and so increasing the false alarms. Moreover, when the object is to detect small shifts in the mean vector of a process, the performance of Cumulative Sum (CUSUM) control charts is dramatically better than Schewhart control charts. One of the methods, which have been developed to deal with autocorrelation, is to use the residuals charts, the residuals being the difference between the real and the predicted values of the mean vector of the process variables. In this paper we design a neural network-based model to forecast and construct residuals CUSUM chart for multivariate Auto-Regressive of order one, AR(1), processes. We compare the performance of the proposed method with the time series-based residuals chart and the auto-correlated MCUSUM chart and report the results.