Multivariate Classes of Life Distributions in Reliability Theory

Four classes of life distributions which have been useful in describing aging where systems are assumed to have independent univariate component lifetimes are: (1) the increasing failure rate (IFR) class; (2) the increasing failure rate average (IFRA) class; (3) the new better than used (NBU) class; and (4) the new better than used in expectation (NBUE) class. These classes together with multivariate analogs of the IFR and IFRA classes are reviewed and discussed. An up to date survey of the literature on this topic is included. New multivariate definitions of the NBU and NBUE classes are introduced.