Designs of One- and Two-Sided Exponential EWMA Charts

Exponentially weighted moving average (EWMA) control charts are developed for monitoring the rate of occurrences of rare events based on the interarrival times of these events. The average run lengths of the EWMA charts are determined exactly based on the solution of a set of differential equations. The effects of using boundaries on the one-sided EWMA charts are examined, and reasonable choices of boundaries are proposed. A simple design procedure is provided for determining the chart parameters of a one-sided or a two-sided EWMA chart. The chart obtained using the design procedure is optimal within the class of EWMA charts. The cumulative sum (CUSUM) and EWMA charts are compared based on the average run length. The CUSUM chart is found to be optimal in detecting the intended mean, while the EWMA chart is found to be slightly less sensitive.