On Redundant Weighted Voting Systems With Components Having Stochastic Arrangement Increasing Lifetimes

In the study of active redundancy allocation of a weighted k-out-of-n system,the working component and the redundancy work in parallel in the same system.Because they are affected by the same pressure,temperature and other factors,the components depend on each other.In this paper,the optimal active redundancies allocation of n spares(matching allocation)and m spares is studied under the condition that working components and redundancies in the weighted k-out-of-n system have some dependence respectively.Consider the working components lifetimes and the redundancies lifetimes are stochastic increasing arrangement and left tail weakly stochastic increasing arrangement of matching allocation,we build that allocating better redundancy to weaker working component with more weighted tends to enhance the reliability of system.At the same time,if the working components lifetimes with left tail weakly stochastic increasing arrangement and the m redundancies are identically distributed and coupled by Archimedean copula,we find that assigning more redundancies to the working component with larger weight and worse performance will enhance the reliability of system in the sense of usual stochastic order.In addition,this paper also studies the allocation of standby redundancy in series and parallel systems.The optimal allocation problem of n different redundancies for the working components lifetimes is considered to have some dependence.It is found that when the working components lifetimes of series system having weakly stochastic increasing arrangement,the system reliability can be improved by allocating better redundancy to the working components with poorer performance,while it is just the opposite in the parallel system.