Multivariate conditional hazard rates and the MIFRA and MIFR properties

Abstract

If T = (T 1, · ··, Tn ) is a vector of random lifetimes then its distribution can be determined by a set λof multivariate conditional hazard rates. In this paper, sufficient conditions on λare found which imply that T is Block–Savits MIFRA (multivariate increasing failure rate average) or Savits MIFR (multivariate increasing failure rate). Applications for a multivariate reliability model of Ross and for load-sharing models are given. The relationship between Shaked and Shanthikumar model of multivariate imperfect repair and the MIFRA property is also discussed.