Optimal assignment of components to parallel-series and series-parallel systems

This paper deals with the problem of assigning components to parallel-series (PS) and series-parallel (SP) systems so as to maximize the system’s reliability. The authors assume that any component can be assigned to any position of the system and the reliability of component j is ripj if it is assigned to position i. Exploiting the nature of Schur-convex functions, an algorithm is developed to obtain an optimal assignment for PS systems. Also, a simple optimal assignment rule is derived for SP systems with only two positions in each minimal cutset and with component reliabilities invariant of positions.