## 1 Introduction  
A wireless sensor network (WSN) is a collection of spatially distributed independent sensors that communicate wirelessly to fetch data about any physical and environmental condition/activity. WSN systems were introduced in the 19 th century and have become a critical technology across various fields. Their growing importance attracts researchers, scholars, and scientists from different domains. In recent decades, the growth of wireless connectivity has been exponential, driven by its potential applications in environmental monitoring, healthcare, medical sciences, military surveillance, agriculture, industry, and smart cities. Moreover, WSNs have become the framework of many IOT applications and act as the backbone in connecting various devices and enabling seamless communication. [PERSON] [1] presented remarkable advantages of WSNs and explained how rapidly evolving technological domains need WSNs. [PERSON] et al. [2] extensively investigated applications of AI in Industry 4.0 and highlighted the vital role of wireless sensor networks in accelerating progress in various fields. [PERSON] et al. [3] explored sensor network architecture that can be used for various applications and also discussed advances in WSNs with machine learning and the IOT. [PERSON] et al. [4] explained various technologies that will drive 6G communications and presented possible applications and the technologies to be deployed for 6G communications. Microcontroller unit-based wireless sensor nodes were investigated by [PERSON] et al. [5], who also reviewed the progress made by industry and academia in designing wireless sensor nodes to avoid redundancy. Analysis conducted by [PERSON] et al. [6] demonstrated the significant progress and potential of WSNs in environmental monitoring. Many researchers and engineers have contributed towards the methodology, which improves the performance of various industrial systems by identifying numerous parameters that affect the performance of the overall system [7; 8; 9]. Consistent and accurate data transmission in complex industrial applications is essential for efficient and safe operations. Therefore, ensuring the reliability of WSNs is vital to maintain the system's integrity and prevent accidents. In critical applications, network disruption can lead to severe consequences, including safety risks and significant financial losses. However, the effectiveness of WSNs and their performance in different environmental conditions are highly dependent on some crucial parameters such as reliability, availability, and sensitivity. [PERSON] et al. [10] developed a model for assessing failure and repair rates in network systems using Markov chains with various preliminary experiments and case studies for demonstrating their application. [PERSON] [11] studied WSN reliability, which is used in environment security services where security is of utmost concern for the end users. [PERSON] and [PERSON] [12] proposed a model to compute reliability under different failure models and environmental conditions. Authors also ensured that the proposed method, to evaluate the reliability of WSNs, is more accurate, even though it uses a lesser number of states. [PERSON] et al. [13] presented a method to evaluate the reliability of WSNs by integrating sensing coverage with network connectivity and impact of common cause failure. This approach is illustrated with a hierarchical clustered WSN. [PERSON] and [PERSON] [14] studied the reliability of sensor nodes in wireless sensor networks within a cyber-physical system. They demonstrated that a sensor node's reliability is affected by its monitoring strategy, with reliability following an unimodal function relative to the test period. The dependability of WSNs in an industrial environment through fault tree analysis has been conducted by [PERSON] et al. [15]. The authors examined dependability issues, estimated redundancy needs, and suggested a network design.