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.
Moshe Shaked. "Exponential Life Functions with NBU Components." Ann. Probab. 11 (3) 752 - 759, August, 1983. https://doi.org/10.1214/aop/1176993519