In a Wireless Sensor Network (WSN), the im portance of individual sensors might not be equal. That is, some nodes might be more important than others due to their proximity to critical regions. A-ANCH is one of the new clustering algorithms for these scenarios which extends the lifetimes of active sensors by sacrificing in-active ones. In this paper, an analytical model for the A-ANCH algorithm is presented in order to predict the number of sensed events (packets) in the network. Our extensive experiments illustrated on average 91.08% accuracy for the proposed mathematical model compared with the results of a simulation study. The analytical model presented here has also revealed that the number of sensed events in the A-ANCH algorithm is sensitive to the number of sensors and the network dimensions. On the other hand, it is almost insensitive to the number of clusters.