In this paper we study the first passage time for a damage process to exceed a given threshold or for the maximal increment of this process to pass a certain critical value. Conditions under which this first passage time possesses the NBU, the IFRA or the IFR properties are studied. An...

The properties of IFR (increasing failure rate) and PF2 (Polya frequency of order 2) are of use and importance in the study of univariate random lifetimes in reliability theory. In this paper these notions are extended to the multivariate setting. The extensions are not just technical, but they...

Consider the lifelengths T1,..., Tk of k components subjected to a randomly varying environment. They are dependent on each other because of their common dependence of the environment. The parameters of the model are the distribution of the random process which describes the environment and a...

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...

A discrete time stochastic process {Xn, N = 0, 1, 2, ...} is said to be temporally convex (concave) if E[theta](Xn) is a nondecreasing convex (concave) function of n whenever [theta] is a nondecreasing convex (concave) function. Similarly one can define temporal convexity and concavity for...

A representation, called the total hazard construction, of dependent random variables by means of independent exponential random variables is studied. Conditions which imply association of nonnegative random variables are found using this construction. Furthermore, new conditions which imply...