Optimal allocation under partial ordering of lifetimes of components

Assembly of systems to maximize reliability when certain components of the systems can be bolstered in different ways is an important theme in reliability theory. This is done under assumptions of various stochastic orderings among the lifetimes of the components and the spares used to bolster them. The powerful techniques of Schur and arrangement increasing functions are used in this paper to pinpoint optimal allocation results in different settings involving active and standby redundancy allocation, minimal repair and shock-threshold models.