ISSN: 1304-7191 | E-ISSN: 1304-7205
Evaluation of reliability and performance in multi-subsystem serial system: Analyzing K-out-of-n redundancy in complex series-parallel configuration using Copula methodology
1Deparment of Mathematics, Federal University, Dutse, 900242, Nigeria; Department of Mathematics, Yusuf Maitama Sule University, Kano, 700282, Nigeria
2Department of Mathematical Sciences, Bayero University, Kano, 700233, Nigeria
3Department of Mathematics, Yusuf Maitama Sule University, Kano, 700282, Nigeria
Sigma J Eng Nat Sci 2026; 44(2): 1048-1068 DOI: 10.14744/sigma.2026.2024
Full Text PDF

Abstract

This paper presents a novel in-depth cost and performance evaluation of a complex serial system comprising five subsystems arranged in a series-parallel configuration. The Subsystems B, C, and D each have one unit, whereas Subsystem A has n units with k-out-of-n redundancy. System E is made up of two units that function in active parallel. The high-performance system that supplies transportation, energy, and manufacturing, the problem of optimizing system dependability and cost effectiveness has been tackled in this study. To obtain a more reliable method than conventional methods and to address dependency in a complete failure, the general repair models and copula methodology are combined in a novel way. The state transition diagram was used to model the system. The system was modeled using a state transition diagram, which leads to a set of partial differential equations that were solved using Laplace transformation and an additional variable. The profit function, mean time to failure (MTTF), and availability of the system, which are the key reliable indicators, were produced by the methodology. Comparing with the usual repair model, our result showed that the copula -based repair method produced a 15% improvement in MTTF and availability, while maintaining a higher profitability index, which was increased by 12%. Our result also shows the trade-off between system profitability and repair costs, with emphasis on systems with optimal maintenance practices might cut off operation expenses by 20%. The results indicate that the copula method for reliability modeling offers engineers, maintenance managers, and system engineers valuable insights into performance and pertinent information. By offering quantitative assessments that can influence useful choices in system maintenance and resource allocation, and incorporating a dependency-aware repair mechanism, this alone surpasses the earlier results. In an attempt to increase cost-effectiveness in crucial applications and dependability, this research paves the way for feature research on sophisticated repair and optimization techniques.