Control charts for monitoring the ratio of two Poisson rates

Abstract In this paper, we are concerning in monitoring the ratio ρ of two Poisson rates by control charts. Let X and Y be two independent Poisson random variables with means λ1 and λ2=λ1/ρ, respectively. The study considers that only individual observations Xi and Yi are available at each sampling time i. The performance in detecting shifts on the ratio ρ using several statistics, some based on normalized transformations, is evaluated by an extensive simulation study. Two types of control charts, Shewhart and exponentially weighted moving average (EWMA), are considered. The one‐sided control chart with upper control limit (UCL) is applied so that we are focusing on detecting when the ratio ρ shifted to higher rate in this paper. The results pointed out that EWMA control chart is a better alternative. Some guidelines indicating which statistics yield best performance are proposed for the practitioners.