Weighted CUSUM control charts for monitoring Poisson processes with varying sample sizes

Monitoring inhomogeneous Poisson processes with varying sample sizes has attracted considerable attention recently in both industrial quality control and public-health surveillance. One of the key challenges in these applications is that a change in incidence rate may be masked by changes of sample sizes. The conventional Poisson cumulative sum (CUSUM) chart designed for detecting a prespecified change in the incidence rate could perform poorly when the actual change is different from the prespecified one. This phenomenon is especially prominent when the sample size is nonconstant and varies over time. To efficiently detect changes in the incidence rate with varying sample sizes, this paper proposes a class of weighted CUSUM (WCUSUM) schemes with general weight functions applied to the likelihood-ratio statistic. The comparison results with the traditional Poisson CUSUM method and other alternatives favor the proposed method. An example in health-care surveillance is used to illustrate the application of the proposed method.