A unified way of comparing the reliability of coherent systems

Consider a coherent system S hat has n nodes and a structure function φ. The state of S is determined by the "states of the components allocated at the n nodes" and φ. If the reliabilities of these it components are expressed by an n-dimensional vector p, then the reliability of S is a function of p. Using the concepts of node-criticality introduced by Boland et al. (1989), the main theorem in this paper proposes a unified approach by which the reliabilities of S corresponding to 2 different values of p can be compared. The conditions in the main theorem are both necessary and sufficient for k-out-of-n systems. Application of this theorem to various situations yields a unified approach for obtaining previous results in the literature. Also, the application of this theorem immediately extends the results established for k-out-of-n systems to coherent systems.