Sampling from a Convevor Belt

Abstract

Stange³³⁾ was the first to point out that the systematic distribution of characteristics must also be taken into account in sampling from a conveyor belt. It is presumed on the basis of what is known about the preparation process that ash contents or metal contents of “closely adjacent” samples are not independent of one another. Values of samples are therefore correlated to a degree which depends on the distance between them. The characteristics X₁, X₂… X_n of elements lying on a belt fluctuate about the expectation P with a total variance of $\sigma_{{tot}}^2$. The correlation coefficient ρ (y) existing between two elements a distance yapart forms a straight line function of the distance y (Figure 13.1.1). The correlation extends in both directions symmetrically over a finite range characterized by the correlation length λ. Outside this range ρ(y) = 0 for │y│ ≧ λ. Let a belt section of length L contain N elements lying on it. The elements are numbered in sequence.