The Effect of Aggregating Data When Monitoring a Poisson Process

Abstract

The aggregation of event counts is a common, and often necessary, practice in many applications. When working with large numbers of events, it may be more practical to consider the number of events occurring during time intervals of a given length rather than the individual interarrival times between successive events. However, when data collection or summarization is done only at the end of aggregation periods, e.g., days, weeks, months, or quarters, there is the potential for significant information loss. In public-health and safety applications, this data lag could lead to unnecessary injuries and deaths because of a delay in detecting an increased risk. In our paper, we assume an underlying Poisson process and study the effect of aggregation by investigating the relative performance of the cumulative sum (CUSUM) control chart for monitoring with Poisson-distributed aggregated data and the CUSUM chart based on exponentially distributed time-between-events data. By comparing steady-state chart performance for varying aggregation periods, we show that the adverse effect of aggregation can be significant.

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