Exponential Life Functions with NBU Components

Abstract

Homogeneous nondecreasing functions of independent NBU random variables are studied. Two results of Block and Savits are improved. It is shown that if a coherent system, formed from independent NBU components, has exponential life then it is essentially a series system with exponential components. Also, it is shown that if a strictly increasing homogeneous function of independent NBU random variables has an exponential distribution then it is essentially a univariate function of one of its variables which must, then, be exponential. A new characterization of the MNBU class of distributions of Marshall and Shaked is derived, and a new proof of the closure of the class of NBU distributions under formation of nonnegative homogeneous increasing functions is given.