Nonparametric-type estimation of θ=P( X>Y ) based on ranked set sampling technique with concomitant random variable, is considered. The maximum likelihood estimation of Θ is also considered using RSS (ranked set sampling) and MRSS (median ranked set sampling) techniques with concomitant random variable. The estimators obtained are compared to their counterparts based on simple random sampling (SRS) using bias and MSE (mean square error). It appears that the suggested nonparametric estimator based on RSS is more efficient than that based on SRS and the MLE estimator based on MRSS is more efficient than the MLE based on RSS which is in turn more efficient than the MLE based on SRS.