Performance analysis of ( m -out-of- r ) within ( k -out-of- n

This paper presents an advanced reliability analysis of a fault-tolerant cellular base station modeled as a hierarchical (m-out-of-r)-within-(k-out-of-n):G system, incorporating nested redundancy to satisfy the stringent availability demands of modern telecommunication networks. The base station comprises three independent sectors (Alpha, Beta and Gamma) configured in a 2-out-of-3:G arrangement, each containing four critical components: a primary power amplifier (PPA), redundant power amplifier (RPA), primary transceiver unit (PTU) and redundant transceiver unit (RTU), structured as a 3-out-of-4:G system. Component failures within each sector exhibit dependency owing to a shared power supply and environmental factors, which are modeled using a copula function. System behavior is captured using a continuous-time Markov process, with the Sumudu transform applied to derive analytical expressions for subsystem reliability, availability, and state probabilities. The numerical analyses considered both repairable and non-repairable scenarios. The overall system reliability was computed using the universal generating function (UGF) technique, which integrates subsystem reliabilities. A sensitivity analysis was performed to assess the effects of the failure rate, repair rate, copula dependence parameter, and hierarchical structural parameters on system performance. An economic evaluation based on the expected profit assessed the cost effectiveness of the design. The results confirmed that hierarchical redundancy significantly enhances the reliability and profitability of telecommunication infrastructure. The proposed copula-UGF framework effectively models the complex dependencies and nested configurations of cellular networks, offering valuable insights for reliability optimization and strategic decision-making.