Stochastic comparisons of order statistics under multivariate imperfect repair

A monotone coupling of order statistics from two sets of independent non-negative random Variables X(i), i= 1,...,n, and Y-i, i=1,..., n, means that there exist random variables X(i)', Y-i', i=1,..., n, on a common probability space such that (X(1)',X(2)',..., X(n)') (d) double under bar (X(1), X(2),..., X(n)), (Y-t', Y-2',...,Y-n') (d) double under bar (Y-1, Y-2'..., Y-n) and X((j))'greater than or equal to Y-(j)', a.s. j=1,..., n, where X((1))less than or equal to X((2))less than or equal to ... less than or equal to X((n)) are the order statistics of X(i), i=1,..., n (with the corresponding notations for the X', Y, Y' sample). In this paper, we study the monotone coupling of order statistics of lifetimes in two multi-unit systems under multivariate imperfect repair. Similar results for a special model due to Ross are also given.