Monitoring of Multivariate Time-between-events

In high-quality processes, a quick way to detect a change in the process is to monitor the time-between-events (TBE). We are interested in the monitoring of multivariate TBE data where we consider multiple processes that are related. Existing multivariate TBE charts are limited in the sense that they only signal after an event occurred for each of the individual processes. This results in slow delayed times (i.e., long time to signal), especially if it is of interest to detect a change in one or a few of the processes. In this talk, we propose a multivariate TBE monitoring method which has the ability to signal after each observed event, i.e. there is no need to wait until an event occurred in each individual process. We derive a mathematical framework for monitoring multivariate TBE data using the distribution function of the superimposed process. We illustrate how the resulting control chart is implemented for the Marshall-Olkin bivariate exponential (MOBE) and Gumbel’s bivariate exponential (GBE) distributions. A simulation study is conducted to compare our method with existing methods.