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This paper aims to compute the efficiency of a complex communication system (double-bridge). In this model, which applies the Path Tracing Method for evaluating the reliability function of the complex communication system, the process of analyzing the system's reliability has been used to lower the failure rate of the complex system in order to optimize its competence. The illustrative system is subdivided into nine minimal paths that are arranged in series-parallel combinations. Using the Path Tracing Method, the system's reliability, minimal signature, tail signature, signature, Barlow-Proschan index, expected time, expected cost, and sensitivity were determined. The results assist in the creation of a probabilistic approach to analyze and probabilistic method to evaluate the system signature and reliability in a way that is highly useful.

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Several fields within the social and technical sciences have identified the importance of theoretical and practical research into complex systems. The sensitivity of these systems is one of the primary focuses. The capsule’s high-pressure oxygen supply system (HPOSS) prepares a complex system with complex interconnections. The reliability of HPOSS cannot be reduced to a single equivalent component or block by combining series and parallel reductions. The aim of this paper is to demonstrate the application of mathematical detection tests to HPOSS in order to assess the sensitivity of the reliability of complex systems. Using the matrix-based minimal cut methodology and the linear sensitivity model of system reliability, the critical system illustrates the suggested methodologies and their relevance to investigating the sensitivity of complex interconnected systems.