Suppose F and G are unknow continuous distributions and one can observe sequential a series of independent random vectors (X1,Y1),(X2,Y2),...such that (Xi,Yi)'s initially have distribution F×F and at some unknow time their distribution may become F×G. Namely,a change in the distribution of the Y observations may occur for some reason, while the X observation maintain their distribution. We coinsider the case where the X observation maintain their distribution We consider the case where the post-change distribution is a Lehmann alternative of F, i.e.., G = Fδfor some δ > 0. The problem is to detect the change as soon as possible after its occurrence, subject to constriant on the rate of false alarms Let Ankdenote the likehood ratio of the ranks of the combined data(X1,...,Xn,Y1,...,Yn) for the test of no change versus na change to a Lehmann alternative at k+1 in the Y sequence. We consider the nonparmetric Shiryaev-Roberts stopping rule based on Ankand compute its average run length to dectection by decoupling method