Optimal Allocation for the Mean of the No Overlap k-tuple Ranked Set Samples

We propose an alternative ranked set sampling scheme-no overlap k-tuple ranked set sample, in which k units are quantified in each set and the units in different sets have sample mean and show that the correlations between the k-units and show that the correlations between the k-units in each set decreases the efficiency of the sample mean. The stronger the correlation structure is, the more the efficiency of the sample mean decreases. The purpose of this work is to find the optimal k-tuple ranked set sample and prove that the no overlap k-tuple ranked set sample with the optimal allocation is more efficient than generalized k-tuple ranked set sample and simple sample and simple random sample. Although the statistical efficiency of no overlap k-tuple ranked set sample is not as much as the classic ranked set sample, under the consider of the cost for sampling and ranking, the no overlap k-tuple ranked set sample is more efficient than the classic ranked set sample.