Analysis of a Hybrid System Comprising Four Series-Connected Subsystems Using Reduction Techniques and Copula-Based Modeling

Wireless Sensor Networks (WSNs) deployed in agricultural and industrial environments require high reliability to ensure continuous monitoring and data transmission. This study presents a reliability analysis of a hybrid WSN system comprising four series-connected subsystems: (1) the central processing unit, (2) sensor nodes in cluster A, (3) sensor nodes in cluster B, and (4) communication relay units. The system operates under a k-out-of-n: G mechanism, where subsystems 2 and 3 require at least one operational unit, while subsystem 4 requires at least two. Whereas unit failures follow exponential distributions, repair processes are modeled using either general distributions or Gumbel–Hougaard copula-based approaches to capture dependencies among multiple repair units. Using Laplace transforms and supplementary variable techniques, we evaluate system reliability metrics and demonstrate that copula-based repair strategies significantly improve availability and the expected profit function. Furthermore, we propose a reduction technique governed by a factor ρ that decreases component failure rates, thereby enhancing overall system reliability relative to the baseline configuration.