Cost Model And The Related Benefit About The Improved RSS Under The Uniform Distribution

The RSS method was first proposed by McIntyre in 1952 for improving precision in estimation of a population mean. Under the same sample size, it has higher efficiency than simple ranked sample. In recent articles, people compared the efficiency of the RSS with the efficiency of the SRS, when they have the equal cost. Specifically, they compared the cost of sampling,ranking and the cost of quantification. In 2002, Nahhas, Wolfe, and Chen firstly discussed this question, built a cost model, and get the optimal set size in the Normal distribution model. Then You-Gan Wang, ZeHua Chen and Jianbin Liu did more woke about the cost model. They selected more than one element and studied their model when the total cost was fixed.In this article, we will improve the work as follows:we will change the Normal distribution into the Uniform distribution and based on the guidance of uniform distribution’s fully complete statistics to arrange the RSS sampling. Namely, measure the maximum one and the minimum one. And in this model, we will study the set size and the Cost effectiveness. We find that in this conditions the effectiveness is higher than only one element was selected. Which means the Cost effectiveness is higher than the RSS.In the same time,when the ratio of the cost is fixed, the Cost effectiveness is increasing with the increase of n. While when the n is fixed, the Cost effectiveness will change with the change of the ratio. In general, the cost efficiency under this model is higher than the RSS,and much better than the SRS of course.