Reliability of k -out-of- n systems with component lifetimes linked by Archimedean copula and independent of cold standby lifetime

In this study, we investigate redundant k-out-of-n systems with homogeneous component lifetimes linked by Archimedean copula and the single independent cold standby redundancy to be initiated at the time of some component failure before system breakdown. We derive the closed form expressions of both the survival function and the mean residual life of the redundant k-out-of-n system. In particular, for parallel systems with the standby being put into operation at the time of system breakdown, we proved that the redundant system lifetime preserves the reversed hazard rate order, the hazard order and the likelihood ratio order of the standby lifetime, respectively. These results are interesting extensions of recent advances by Li and Li. Numerical examples as well as simulation results are presented to illustrate and confirm the new findings.