Allocations Of Active Redundancies In Random Weighted K-out-of-n Systems

As an extended model of k-out-of-nsystem,random weighted k-out-of-nsystem is general in practice,such as power supply system,auditorium lighting system and queueing system.Redundancy allocation is one of the techniques to extend the lifetime of the system in reliability theory.The current research on redundancy allocation in the literature is limited to the special case of k-out-of-nsystem.However,there is little research on random weighted k-out-of-nsystem.Under the assumption that the system components are independent and the system components are stochastic dependent,the optimal redundancy allocation strategy of the random weighted k-out-of-nsystem is presented by maximizing the system total capacity.First,optimal allocation policies are presented by maximizing the resulting total capacity according to the usual stochastic ordering or the expectation ordering when the system is comprised of independent and heterogeneous components having independent random weights.Second,by maximizing the reliability of system,we investigate the optimal allocation strategy of active redundancy for random weighted k-out-of-nsystems with right [left] tail weakly stochastic arrangement increasing random weights.Finally,numerical examples are provided to highlight our theoretical findings as well.