A new theory of bed-blending derived from the theory of sampling — Development and full-scale experimental check

Abstract The bed-blending process is analyzed in the light of the theory of sampling but the conclusions of this analysis disagree with those of the statistical theory of bed-blending widely accepted by manufacturers and users of blending equipment. For this reason, the sponsors of this study decided to launch a full-scale experiment, the results of which confirmed all the conclusions of our theory, summarized as follows: 1. (1) The reclaiming phase of the bed-blending process can be assimilated to a systematic sampling of the input material and the properties of the output can be expressed in terms of sampling variance. 2. (2) The properties of the input and output materials can be efficiently characterized by their variograms. 3. (3) The effect of bed-blending is to transform any input variogram into a flat output variogram, which means that bed-blending suppresses the continuous or long-range input variations. 4. (4) The sill of the flat output variogram is equal to the punctual variance of the input material, which means that bed-blending has no action on the discontinuous or short-range input variations. 5. (5) The number of layers of the blending pile is relevant only to the second order, which means that it is useless and costly to increase the number of layers beyond a certain limit that in our experiment is of the order of one hundred.