ABSTRACT For ground‐based telecommunication systems demanding constant and reliable signal transmission, assessing performance under uncertain conditions is crucial. This research offers a thorough reliability and availability analysis of a ground‐based circular consecutive 3‐out‐of‐5:G telecommunication relay system, using Fermatean fuzzy sets (FFS) to model uncertainty. A new mathematical framework, leveraging the Sumudu transform and Supplementary Variable Technique (SVT), is developed to analyze this multi‐state system(MSS) performance considering different degradation and repair states, incorporating common cause failures. A Gumbel‐Hougaard copula model captures the dependencies in component repair processes. The application of Triangular Fermatean Fuzzy Numbers (TFFNs) is used to model the uncertainty involved in the failure rate, thereby allowing for the evaluation of fuzzy reliability and sensitivity via ‐cuts. The numerical solutions indicate a steady reduction in availability/reliability over time, where the application of the fuzzy model is more realistic in estimating the system's performance. Additionally, a cost analysis was performed to improve the relevance of the model by considering the financial impact of the system reliability. The entire framework presents a robust, realistic and effective assessment tool for developing a resilient telecommunication relay system, which is ideally applicable in the context of a national communication network.
G et al. (2026) studied this question.