Jayaram Sethuraman

Optimal assembly of systems using schur functions and majorization

Abstract : This paper considers the optimal assembly of n systems from components of k types. Special cases of such a problem have been studied earlier in the literature. El-Neweihi, Proschan and Sethuraman(1986) studied the case of a single type of components. Derman, Leiberman and Ross(1972) considered the case where each system consisted of one component of each of k types. We generalize the ideas of both of these papers to the case where the systems may consist of varying numbers of components from more than one type. An assembly of the n systems corresponds to a partitioning A of the components to the different systems. For more details see Section 2. When the components act independently, we show in sections 2 and 3 that an intuitively motivated partitioning A* provides the optimal assembly under many different criteria. In Section 3, we allow each system to have dependent components, and under some general conditions on the reliability function we show that the same partitioning A * provides an optimal assembly. The results of this paper are based on the well known techniques of Schur- functions and majorization. This makes them clear and simple and at the same time more general than in the papers cited.