SUPERMODULAR STOCHASTIC ORDERS AND POSITIVE DEPENDENCE OF RANDOM VECTORS

The supermodular and the symmetric supermodular stochastic orders have been cursorily studied in previous literature. In this paper we study these orders more thoroughly. First we obtain some basic properties o f these orders. We then apply these results in order to obtain compari sons of random vectors with common values, but with different levels o f multiplicity. Specifically, we show that if the vectors of the level s of multiplicity are ordered in the majorization order, then the asso ciated random vectors are ordered in the symmetric supermodular stocha stic order. In the non-symmetric case we obtain bounds (in the supermo dular stochastic order sense) on such random vectors. Finally, we appl y the results to problems of optimal assembly of reliability systems, of optimal allocation of minimal repair efforts, and of optimal alloca tion of reliability items. (C) 1997 Academic Press.