Influence of the Sampling Interval, Decision Limit and Autocorrelation on the Average Run Length in Cusum Charts

Abstract

This paper shows how the average run length (ARL) for a one-sided Cusum chart varies as a function of the length of the sampling interval between consecutive observations, the decision limit for the Cusum statistic, and the amount of autocorrelation between successive observations. It is shown that the rate of false alarms can be decreased considerably, without modifying the rate of valid alarms, by decreasing the sampling interval and appropriately increasing the decision interval. Also that this can be done even when the shorter sampling interval induces moderate autocorrelation between successive observations.