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A new scheme ‘Rhombus Ranked Set Sampling’ (RRSS) is developed in this research together with its properties for estimating the population means. Mathematical validation along with the simulation evaluation is presented. The proposed method is an addition to the family of different sampling methods and generalization of ‘Folded Ranked Set Sampling’ (FRSS). For the simulation process, nine probability distributions are considered for the efficiency comparison of proposed scheme from which four are symmetric and rest are asymmetric among which Weibull and beta distributions which are used twice, unlike parametric values. (Al-Naseer, 2007 and Bani-Mustafa, 2011). Through simulation processes, it is observed that RRSS is competent and more reliable relative to simple random sampling (SRS), ranked set sampling (RSS) and folded ranked set sampling (FRSS). It is noted that for all the underlying distributions, an increase in the efficiency of Rhombus Ranked Set Sampling (RRSS) is achieved via increasing the size of the sample ‘p’. Besides the efficiency comparison, consistency of the proposed method is also valued by using Co-efficient of Variation (CV). Secondary data on zinc (Zn) concentration and lead (Pb) contamination in different parts and tissues of freshwater fish was collected to illustrate the evaluation of RRSS against SRS, RSS, FRSS and ERSS (extreme ranked set sampling). The results obtained through real life illustration defend the simulation study and hence indicates that the RRSS estimator is efficient substitute for existing methods (Al-Omari, 2011).
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