Surveillance of Nonhomogeneous Poisson Processes

The use of varying sample size monitoring techniques for Poisson count data has drawn a great deal of attention in recent years. Specifically, these methods have been used in public health surveillance, manufacturing, and safety monitoring. A number of approaches have been proposed, from the traditional Shewhart charts to cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) methods. It is convenient to use techniques based on statistics that are invariant to the units of measurement since in most cases these units are arbitrarily selected. A few of the methods reviewed in our expository article are not inherently invariant, but most are easily modified to be invariant. Most importantly, if methods are invariant to the choice of units of measurement, they can be applied in situations where the in-control Poisson mean varies over time, even if there is no associated varying sample size. Several examples are discussed to highlight the promising uses of invariant Poisson control charting methods in this much broader set of applications, which includes risk-adjusted monitoring in healthcare, public health surveillance, and monitoring of continuous time nonhomogeneous Poisson processes. A new chart design method based on extensive online simulation is highlighted.