In this study, two nonparametric estimators of estimating distribution function under dual-rank ranked set sampling (DRSS) are discussed and compared. The first estimator incorporates the information supported by the relationship between ranks of measured sampling items and information from unmeasured sampling items. This estimator is constructed through an iterative algorithm. The second one depends on using the information generated by a concomitant variable. This estimator is derived by the linear interpolation method. Under both perfect and imperfect ranking situations, a series of simulation studies are carried out, and the proposed estimators are then compared with their counterparts using traditional ranked set sampling (RSS). It is concluded that the proposed procedures have dramatically better performance than their competitors at points in the center of the parent distribution, specifically in the case of an appropriate level of ranking quality. Finally, an illustrative example using a real dataset is also used to investigate the performance of the proposed procedures.