Control chart for monitoring the ratio of two Poisson rates. - Yamauchi, Tsubasa (2019)
In this study we are concerning in monitoring the ratio p of two Poisson rates by the control chart. Let X and Y be two independent Poisson random variables with means ?1 and ?2 = ?1/p 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 p by several statistics, some based on normalized transformations are evaluated by an extensive simulation study. Two types of control charts, Shewhart and EWMA are considered. The one-sided control limit with UCL is applied so that we are focusing on detecting when the ratio p shifted to higher rate in this dissertation. Our focus is on monitoring the ratio p and not on the inference of means of ?1 and ?2. The results pointed out that EWMA control chart is better alternative. Some guidelines indicating which statistics yield best performance are proposed for the practitioners. In general, the combination of statistics W0 and Z4** are recommended once EWMA control chart is applied. In case the difference between ?1 and ?2 is small, the statistic W*4 could be used instead of W0. Numerical example illustrates an application.