SOME CONTRIBUTIONS TO THE STOCHASTIC CHARACTERIZATION OF WEAR.

Abstract : In the paper the authors present some properties of the class of life distributions characterized by the fact that their mean residual life is decreasing (increasing) in time. Bounds are given on the survival function of this class and results are summarized on class closures under mixtures, convolutions, and the formation of coherent structures. Introduced next is a new class, characterized by the fact that some percentile of its residual life decreases (increases) in time. This class will be abbreviated as the DPL (IPL) class. The authors investigate the implications between this class and those that are known in the literature. In addition to this, bounds are obtained on the survival function of the DPL (IPL) class and the results are summarized on the closure properties mentioned above. A family of distributions are given which are characterized by the fact that for some percentile of their residual lives, the distributions are both IPL and DPL. It is noted that this family is not the exponential family. (Modified author abstract)