Self-starting monitoring scheme for Poisson count data with varying population sizes

In this paper we consider the problem of monitoring Poisson rates when the population sizes are time-varying and the nominal value of the process parameter is unavailable. Almost all previous control schemes for the detection of increases in the Poisson rate in Phase II are constructed based on assumed knowledge of the process parameters, e.g., the expectation of the count of a rare event when the process of interest is in control. In practice, however, this parameter is usually unknown and not able to be estimated with a sufficiently large number of reference samples. A self-starting EWMA control scheme based on a parametric bootstrap method is proposed. The success of the proposed method lies in the use of probability control limits, which are determined based on the observations during rather than before monitoring. Simulation studies show that our proposed scheme has good in-control and out-of-control performance under various situations. In particular, our proposed scheme is useful in rare event studies during the start-up stage of a monitoring process.