Abstract

The reliable data analysis in screening for an attribute at the scale of a granulated lot is a critical issue for decision risk regarding an intended application. Practice shows that Sampling Without Replacement (SWR) is habitually used in surveying for mineral resources, for conformity assessment of particulate commodities etc. Errors in estimating expectance and its variance at lot scale may make the difference between profit and loss or between conform versus nonconform status of a batch of commodity. Literature does not clearly show the grounds of the derivations of the expectance and of its variance in case of SWR. Especially, the variance is derived based on unproven correlation in probability among the sampled items. Therefore, the paper addresses a new approach for deriving the mathematical expressions of the expectance and its variance based on irrefutable probabilistic hypotheses, like the law of large number and repeated SWR trials. The derivations posted in the paper help on optimizing the sampling costs by proper choosing the sample size for a given population size. The findings of the paper can be applied in many practical fields where SWR grounds their activity, as conformity assessment, environmental factor monitoring, screening for mineral resources, sampling waste dumps to be classified as secondary resources etc.

Keywords:Sampling without replacement; Expectance; Variance; Particulate lot; Numerical attribute