SUMMARYThe method of ranked set sampling is widely applicable in environmental research mainly in the estimation of the mean and distribution function of the variable of interest, Y. Ranking of the Ys by visual judgment may be imperfect sometimes. When the Ys are expensive to measure, it would be more convenient to determine the 'rankings' of the Ys by a concomitant variable, X, which is relatively easy and cheap to make measurements. The information carried in X is not utilized in all estimation methods available in the literature except in determining the rankings of Ys unless extra distributional or linearity assumptions are made. However, these assumptions may be too stringent in environmental research. Nonparametric estimators for the distribution function and the mean of Y utilizing the concomitant variable and auxiliary information in a ranked set sampling setup are proposed in this article. The estimators are robust to model misspecification, and the performance of the estimators is highly satisfactory, supported by some simulation studies. The estimators are applied to a real data set to estimate the mean and distribution function of plutonium concentration in surface soil on the Nevada Test Site, Nevada, U.S.A.