On k-out-of-n systems with homogeneous components and one independent cold standby redundancy

In this note, we study a k-out-of -n system with component lifetimes linked by Archimedean (survival) copula and independent of the lifetime of a cold standby redundancy. We derive the survival function and the residual life function of the redundant system. Also, we examine how the redundancy and the system structure impact the system reliability through developing the usual stochastic order on system lifetime. In particular, for parallel systems we investigate the role played by the component lifetime, the generator of Archimedean copula, and the starting time of the redundancy as well. The present framework well relates to the real situation and thus the main results are instructive to reliability engineers.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This note examines a k-out-of-n system with component lifetimes linked by Archimedean copula and independent of the lifetime of a cold standby redundancy. The survival function and residual life function of the redundant system are derived. The impact of redundancy and system structure on system reliability is analyzed through the development of the stochastic order on system lifetime. The research findings are instructive to reliability engineers, as they relate well to real-world situations.