Optimal allocation of active redundancies in weighted k-out-of-n systems

This paper investigates optimal allocation of active redundancies for weighted k-out-of-n systems. Optimal allocation policies are presented for the case of one, two and multiple active redundancies in the sense of the usual stochastic order when the system is comprised of independent and heterogeneous components having different weights. Some allocation policies known for the k-out-of-n system in the literature are generalized to the weighted k-out-of-n system. Numerical examples and applications are provided to highlight these theoretical findings as well.