Finding General Mathematical Formulas for Extraction the Minimal Path Sets of Complex Parallel-Series Networks

Most real-world technological systems are highly complex, making it challenging to examine their reliability. Many systems can be represented as Complex Parallel-Series Networks (CPSN). The large number of components and subnetworks, along with their intricate connection, complicates the identification, evaluation, and potential failure of the CPSN. The concept of minimal path sets for a CPSN refers to a specific set of components whose failure leads to the failure of the whole CPSN. The primary research problem is to identify these minimal path sets, both for the overall CPSN and for its complex subnetworks. This paper presents a mathematical technique for analyzing subnetworks instead of the whole CPSN to reduce computational effort and simplifies intricate calculations. Specialized algorithms and techniques are presented and used to identify minimal path sets, with numerical results funded by general formulas. Numerical cases show the effectiveness and applicability of this technique for CPSN.