Multivariate time-between-events monitoring: an overview and some overlooked underlying complexities

We review methods for monitoring multivariate time-between-events (TBE) data. We present some underlying complexities that have been overlooked in the literature. It is helpful to classify multivariate TBE monitoring applications into two fundamentally different scenarios. One scenario involves monitoring individual vectors of TBE data. The other involves the monitoring of several, possibly correlated, temporal point processes in which events could occur at different rates. We discuss performance measures and advise the use of time-between-signal based metrics for the design and comparison of methods. We re-evaluate an existing multivariate TBE monitoring method, offer some advice and suggest some directions for future research.