The Relationship Between the Recurrence Interval and Time-to-Signal Properties of Surveillance Schemes
by
Shannon Fraker and William H. Woodall
Department of Statistics, Virginia Tech, USA

In the literature there is often some confusion between the definitions of the in-control average time-to-signal (ATS) and the recurrence interval, defined as the number of time periods for which the expected number of false alarms is one. The recurrence interval is typically used in public health surveillance whereas time-to-signal measures are used in industrial statistical process control. In this paper, we compare the recurrence interval and measures based on the time-to-signal properties for the temporal monitoring case using scan statistics, exponentially weighted moving average (EWMA) charts, cumulative sum (CUSUM) charts, and Markov dependent signaling processes. The in-control average time-between-signals (ATBS) and the in-control average signaling event length (ASEL) are introduced as performance measures that are useful when a monitoring process is not reset to its initial state after a signal. We show that the recurrence interval is limited in its applicability and often fails to summarize important information about the performance of the monitoring process. We, therefore, recommend that measures based on the time-to-signal properties be used instead of the recurrence interval to evaluate the performance of surveillance schemes.

Date received: February 20, 2007