Multivariate Classes in Reliability Theory.

Abstract : Four classes of lifetimes which have been useful in describing situations where systems are assumed to have independent univariate component lifetimes are: the increasing failure rate (IFR) class; the increasing failure rate average (IFRA) class; the new better than used (NBU) class; and the new better than used in expectation (NBUE) class. These classes are reviewed and also multivariate analogs of the IFR and IFRA cases are discussed. New multivariate definitions of NBU and NBUE are introduced.