STOCHASTIC COMPARISONS AND BOUNDS FOR AGING RENEWAL PROCESS SHOCK MODELS

AND THEIR APPLICATIONS

M. C. BHATTACHARJEE

Center for Applied Mathematics & Statistics, Department of Mathematics, New Jersey Institute of Technology, Newark, NJ 07102, U.S.A.

(Received July 27, 1994; revised October 16, 1995)

Abstract. Sharp comparisons between aging renewal process shock models and the corresponding Esary-Marshall-Proschan (EMP) shock model are considered. The usefulness of such comparisons derive from the simplicity of the latter models. Simple conditions under which such aging renewal process shock models are stochastically ordered relative to a corresponding EMP-model are derived. Applications to renewal functions and single server queues are indicated.

Key words and phrases: Shock models, aging renewal processes, bounds, stochastic comparisons.