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In cluster-based two-tier Wireless Sensor Networks (WSNs), the cluster-head nodes (CHs) gather data from sensors and then transmit to the base station. When these cluster head nodes start to die, the coverage of the respective clusters is lost and it leaves the region unmonitored. Even if the CHs are rotated and reassigned after some time, until the next rotation that cluster in question will be out of cluster head, causing a loss of information and loss of coverage. To select a Backup Cluster Head (BCH) is suggested for those CHs which are close to deplete their energy. When the CH dies, BCH takes over the responsibility and continues to work as a new cluster head. In this paper we present an analytical model of cluster reliability in cluster-based WSN using BCH, based on Markov chain model. We use non-homogeneous Markov process, along with Forward Chapman-Kolmogorov equations to illustrate the cluster monitoring period in a finite three state space model. We test the accuracy of the model by applying the probabilities of failure of CH and BCH nodes, for a fixed number of sensor nodes in a cluster. The results show that the presented model is able to match the behaviour of the cluster state transition accurately and validates the simulation results and analysis published in.