Redundancy importance and allocation of spares in coherent systems

Abstract We study the model in which a set of spares is available for redundancy in a coherent system. In some circumstances, parallel (or active) redundancy is used to improve the reliability of the system, while in others series redundancy is used to improve a different measure of utility. Hence we define the two concepts of parallel and series redundancy importance for components in a coherent system relative to an available set of redundant spares. These measures of importance are compared with the structural importance and reliability importance of a component due to Birnbaum. Various results for the optimal allocation of rebundant spares are given, with particular reference to k out of n systems and modules of coherent systems.