On optimal allocation of active redundancies to multi-state r-out-of-n systems

This paper treats the problem of optimally allocating K active redundancies to a multi-state r-out-of-n system, where the system and its components and redundancies have a range of performance levels. When the performances of components are stochastically ordered, we maximize the reliability level of the resulting r-out-of-n system in the usual stochastic order by balancing the allocation of redundancies on the promise of assigning more redundancies to worse components. The optimal allocation policy is also provided in the i.i.d case.