On optimal allocation in coherent systems:A review with an emphasis on some recent developments

It is of great interest to allocate redundant component(s)in a coherent system in order to optimize the lifetime of the resulting system in reliability engineering,and system security.This topic has posed many interesting theoretical problems to which many researchers have devoted themselves in the past decades.In this article,we aim to review some recent results on the problem of optimal allocations of active[standby]redundancies in coherent systems.Some open problems in this research line are posed as well.Here we highlight the stochastic orderings as a powerful tool in our discussion.