Independent particle and lot selection of increment samples in the theory of sampling

Abstract

Introduction. The theory of sampling developed by Pierre Gy does not prove the compatibility and consistency of discrete and continuous selection models. Discrete (independent particle) and continuous (lot) selection models are determined by incompatible properties of increment samples, which prevented from creating the consistent theory of sampling. Research methodology. The inconsistencies are removed at assuming the idea that there are differences in both separate ore lumps or mineral-dressing products and any locally selected parts of the rock mass under test called increment samples simultaneously available in any rock mass under test. The said differences are described by independent particle dispersion and increment samples dispersion. Composite sample permissible error formed in both discrete and continuous selection is attained by selection of the number of particles collected into the increment sample or their parts and the number of increment samples. Particle dispersion, increment sample dispersion, the number of particles in an increment sample and the number of increment samples combined in one formula make up the complete formula of the fundamental sampling error. The development of the theory of sampling. Based on the complete formula, the possibility of obtaining minimum masses of various sizes has been shown. Thus, for one and the same preset permissible error and from one and the same massif under test, it is possible to collect minimum mass of 17.55 kg (individual particle selection), minimum mass of 170.3 kg (collecting with the bucket sampler), and minimum mass of 10 g under the individual particle selection of particle parts (which is fulfilled under X-ray fluorescent on-stream analysis of material). Discrete selection of increment samples without particles destruction is an especial case of continuous selection method when it is possible to accept the condition that increment samples dispersion is equal to zero. It is possible under ideal mixing of the massif under test. Discussion. Minimum mass of a sample is not a constant. It is a function of increment sample mass. Minimum mass in individual particle selection can be accepted as a reference value of the minimum mass. In lot selection it can be significantly higher than the reference one, while in case of reducing particle size it can be significantly lower than the reference one.