A minimum cost exponential cusum test

A minimum cost CUSUM test for an event rate increase when inter-event times are exponentially distributed is presented. Optimal values of the test decision parameters, h and k, are developed from a renewal reward model of the event cycle by combining a non-linear optimization technique with an exact method for determining exponential average run lengths. Test robustness for event cycle parameter estimates and departures from the assumption of exponentially distributed inter-event times are discussed in the context of an injury monitoring scenario. Robustness to positively serially correlated observations emanating from EAR(1) and EMA(1) processes is also examined.