Two-stage cluster sampling with unequal probability sampling in the first stage and ranked set sampling in the second stage

Abstract In this research work we introduce a new sampling design, namely two-stage cluster sampling, where probability proportional to size with replacement is used in the first stage unit and ranked set second order address issue of marked variability sizes population units concerned sampling. We obtained an unbiased estimator mean total, as well variance estimator. calculated relative efficiency design simple random stage. The results demonstrated that more efficient than competing when significant variation observed units.