Shaked and Shanthikumar [1992. Optimal allocation of resources to nodes of series and
parallel systems. Advances in Applied Probability 24, 894–914] and Singh and Singh
[1997a. Optimal allocation of resources to nodes of series systems with respect to failure-
rate ordering. Naval Research Logistics 44, 147–152] considered the problem of optimal
allocation of K active redundancies to n independent and identical components of a series
system with respect to the usual stochastic order and to the hazard rate order, respectively�…

In this note we deal with the allocation of independent and identical active redundancies to a
k-out-of-n system with the usual stochastic order among its independent components. The
optimal policy is proved both to assign more redundancies to the weaker component and to
majorize all other policies. This improves the corresponding one in Hu and Wang (2009)
and serves as a nice supplement to that in Misra, Dhariyal and Gupta (2009) as well.

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�…

This paper deals with the allocation of active redundancies to a k-out-of-n system with
independent and identically distributed (iid) components in the sense of the hazard rate
order. It is shown that the system's hazard rate may be decreased by balancing the
allocation of active redundancies. This generalizes the main result of Singh and Singh
(1997) and improves the corresponding one of Hu and Wang (2009) as well. As an
application, we build the reversed hazard rate order on order statistics from sample having�…