A multivariate IFR class

Various univariate classes of life distributions have been introduced in the mathematical theory of reliability. Recently there has been much interest in obtaining multivariate versions of these classes. Although there have been many different approaches, this document mentions only two because of their nice closure properties: the multivariate IFRA class of Block and Savits (1980) and the multivariate NBU class of Marshall and Shaked (1982). Both of these classes are closed under deletion, conjunction, convolution and weak limits. This paper introduces a multivariate IFR class that has similiar closure properties. its spirit also closely parallels that found in the two previously mentioned papers. Other definitions of a multivariate IFR class have been proposed by Marshall (1975), but none possess all desirable closure properties. Section 2 presents some preliminary facts about log concave functions. Section 3 contains new characterization of the (univariate) IFR class. The multivariate genralization and properties thereof are given in Section 4. A useful alternative condition is delineated in Section 5. Finally, this class is compared with the multivariate IFRA class of Block and Savits (1980) in Section 6.