Alarm rates for quality control charts

There is a direct relationship between a single alarm probability and the average run length only for basic Shewhart charts such as the . Alarm rates are defined in this paper that can be applied with charts such as the cumulative sum (CUSUM) chart and the exponentially weighted moving average (EWMA) chart that base decisions on several observations, not just the most recent one. Methods for determining EWMA chart limits are compared on the basis of their false alarm rates. It is shown how control charts can be more flexibly and carefully defined by considering a desired pattern of in-control false alarm rates in conjunction with a desired in-control average run length.