We investigate performance characteristics of secure group communication systems (GCSs) in mobile ad hoc networks that employ intrusion detection techniques for dealing with insider attacks tightly coupled with rekeying techniques for dealing with outsider attacks. The objective is to identify optimal settings including the best intrusion detection interval and the best batch rekey interval under which the system lifetime (mean time to security failure) is maximized while satisfying performance requirements. We develop a mathematical model based on stochastic Petri net (SPN) to analyze tradeoffs between security and performance properties, when given a set of parameter values characterizing operational and environmental conditions of a GCS instrumented with intrusion detection tightly coupled with batch rekeying. We compare our design with a baseline system using intrusion detection integrated with individual rekeying to demonstrate the effectiveness.