8 Multivariate nonparametric classes in reliability

Abstract

Many multivariate versions of the univariate classes are proposed using generalizations of various failure rate functions. These multivariate classes are discussed in Block and Savits (1981). Other classes are proposed by attempting to imitate univariate definitions in a multivariate setting. One of the most important of these extensions is because of Block and Savits (1980) who generalized the increasing failure rate average (IFRA) class. This multivariate class is proposed to parallel the developments of the univariate case where the IFRA class possessed many important closure properties. As in the univariate case the following multivariate class of IFRA, designated the multivariate increasing failure rate average (MIFRA) class, satisfies important closure properties. The chapter discusses the multivariate IFRA, multivariate new better than used distributions (NBU), multivariate new better than used in expectations (NBUE), multivariate IFR, and multivariate decreasing mean residual life (DMRL) and harmonic new better than used in expectations (HNBUE).