A Multivariate New Better than Used Class Derived from a Shock Model

We introduce a new class of multivariate new better than used (MNBU) life distributions based on a shock model similar to that yielding the Marshall-Olkin multivariate exponential distribution. Let T₁, …, T_M be independent new better than used (NBU) life lengths. Let F̄(t₁, …, t_n) be the joint survival function of min_I∈A1T₁, I = 1, …, n, where A₁, …, A_n are nonempty subsets of {1, …, M} and U_r=1ⁿA₁ = {1, …, M} F̄(t₁, …, t_n) is said to be a MNBU survival function. Basic properties of MNBU survival functions are derived. Comparisons and relationships of this new class of MNBU survival functions are developed with earlier classes.