Shock models and the MIFRA property

Marshall and Shaked [6] have shown that some multivariate life distributions obtained from their shock model satisfy the IFRA conditions A and B of Esary and Marshall [5]. Block and Savits [2] have introduced a multivariate IFRA condition which is stronger than Conditions A and B. In this paper it is shown that the multivariate life distributions of Marshall and Shaked actually satisfy the Block-Savits MIFRA condition. As a consequence it follows that the damage processes associated with the Marshall-Shaked shock models are multivariate strongly IFRA in the sense of Block and Savits [3].