## 2 Related Work  
This section demonstrates the previous studies regarding evaluating the system reliability of WSNs. The different techniques for evaluating WSN reliability are discussed. Moreover, analyzing and calculating WSN reliability-based RBD is illustrated. Studies, evaluations, and analyses of WSNs' reliability have been previously carried out in several studies [26; 27]. Evaluation of the reliability of a WSN can be conducted utilizing different techniques, of which the most well-known are a universal generating function [28], a Markov model [29], a fault tree [30], and a Monte Carlo simulation [31], where the authors utilized an ordered binary decision diagram (OBDD) beside a Monte Carlo simulation, to evaluate the WSN's reliability. The authors of [32] proposed a Monte Carlo Markov chain simulation method to evaluate the reliability, regarding data capacity and coverage area, of mobile WSNs with multi-state nodes, but the power consumption was not taken into account. A Markov model was proposed in [33], to address the reliability of sensor nodes in a WSN-based monitoring strategy, but power consumption was not considered. A modified sum of disjoint products approach was proposed in [34], for evaluating the reliability of WSN with multi-state nodes, where the reliability was evaluated based on the network's dynamic state only. The reliability evaluation of WSNs and compromised node identification was described in [8], where an enhanced way of evaluating reliable nodes was proposed to protect the entire WSN from compromised nodes. A new efficient algorithm-based OBDD was proposed in [6], to evaluate WSN reliability, where the proposed approach executed the recursive construction of OBDD once. A new sum of disjoint products technique (SDP) was proposed in [35] to generate disjoint products and calculate the network reliability. Moreover, probabilistic analysis was utilized to evaluate the network transmission reliability in [36], where the required retransmission was decreased and the transmission reliability was improved. The reliability block diagram paradigm (RBD), is one of the most useful techniques to calculate reliability [37; 38]. The reliability was evaluated via RBD in the following studies: RBD was applied in [37], to analyze the reliability of a mesh network that consisted of different tree and star networks and was classified as a series-parallel system. The authors of [39] evaluated the reliability of star and cluster WSNs with dynamic dependent nodes based on dynamic RBD (DRBD), where it overcame the Markov model's limitations because it considered nonlinear discharge processes. Furthermore, the author in [40] calculated the reliability of star, cluster, and mesh WSNs, with sleep/wake-up interfering nodes-based DRBD and Petri nets, which overcame the Markov model's limitations according to nonlinear processes. Since RBD overcomes the limits of the Markov model, RBD is utilized to evaluate WSNs' reliability in [5], considering the DIRECT, FLOODING, and LEACH routing algorithms and battery level. In [41], the reliability of a mesh WSN was analyzed and evaluated, based on RBD and fault tree analysis. Moreover, the authorsstudied the effects of way redundancy and node arrangements on reliability. The authors in [42] analyzed the reliability of WSN data transport protocols based on RBD and the higher-order logic theorem prover. Reliability is an important factor to consider when evaluating the performance of WSNs since it can be evaluated according to network power, where a dead sensor node is unable to transmit data and affects the entire system. The reliability of different network topologies in WSN-based RBD has been evaluated in a range of studies, except for chain routing, which has not been examined in any studies. All published works have assumed the same concept of probability, where probability is 1 for a working node and 0 for a failure node.