Unified CUSUM Charts for Monitoring Process Mean and Variability

Abstract

In this paper, we propose two new CUSUM control charts which are based on the probability integral transformation. The CUSUM M-chart is specifically designed for detecting small shifts in process mean, while the CUSUM V-chart is specifically designed for detecting small changes in process variability. They can be thought of as the CUSUM version of the X¯ chart and S -chart. Besides that the proposed control charts can be readily extended to non-normal distributions, a special feature is that both charts can be visualized as a single chart to provide simultaneous monitoring of the process mean and variability. An example and simulations are used to compare the existing optimal CUSUM control charts with the proposed CUSUM control charts. It is demonstrated that the CUSUM M-chart, the CUSUM V-chart and the combined CUSUM M- and V-charts are comparable to the existing optimal CUSUM procedures.