Moving -window spectral model based statistical process control

Statistical process control by a simple control chart of a process variable is based on the assumption that the process variable is an independent identically distributed random variable. In practice the process variable typically contains significant correlations due to common cause effects. These common cause effects become confounded with special cause effects. The objective of time series model based statistical process control is to separate the process variable into two components, namely the systematic variation due to common cause (contained in the fitted values) and the purely random variation (contained in the residuals). The moving-window spectral (MWS) time series model is a frequency domain approach. It is an extension of the time series concept to a generalized automatic system that further decomposes the process variable into trend, periodic components and residuals. The MWS model is applied to simulated autoregressive process variable series containing multiple periodic components and randomness. The proposed dual chart MWS method outperforms the standard X chart and the time domain exponentially weighted moving average (EWMA) model. The MWS method is the only one to correctly classify and detect special cause and common cause effects for small and large process shifts with no increase in false alarms.