Cross-correlation and X-bar -trend control charts for processes with linear shift

We developed a cross-correlation control chart to detect linear trends in a process. The observations from the process were collected at fixed intervals in a sampling period and were available as a batch at the end of the sampling period. The cross-correlation chart utilized two series: the average of the observations in a sampling period and the slope of the line fitted to those observations. The performance of two formulations of the cross-correlation chart was compared with an appropriately designed CUSUM chart and X-bar -trend chart in which the average of the most recent p observations in a sampling period was plotted. The conditions that result in better performance of either the X-bar -trend, CUSUM or the cross-correlation control chart are discussed.