The Grouping and Segregation Error

In Chapter 9 we defined the Grouping and Segregation Error GSE as the complementary part of the Fundamental Sampling Error within the discontinuous Heterogeneity Fluctuation Error HFE 1 . It is important to recall its moments as follows: The average is: m ( GSE ) = m ( HFE 1 ) – m ( FSE ) ≈ 0 The variance is: s 2 ( GSE ) = γξs 2 ( FSE ) Where: γ is a grouping factor, dimensionless, always positive; it characterizes the size of the increments making up a sample. In fact, γ is practically proportional to the size of the increments. ξ is a segregation factor, dimensionless, whose value is always between 0 and 1, and it characterizes the amount of segregation. It is important to note that both factors γ and ξ cannot be dissociated from one another, and it is always their product that we have to take into account. In practice, it would be extremely difficult to estimate the product γξs 2 ( FSE ) and it is never done, mainly due to the transient nature of segregation that changes all the time with particulate materials.