TABLE OF CONTENTS The variance of the fundamental error (FE) is most important in solids sampling. If we could repeat the sampling protocol, it is the smallest sampling-to-sampling variation we can have with a given particle size and sample mass, assuming correct sample definition, extraction, and handling, as discussed in Chapter 3. Its estimation is therefore important to determine the best we can expect with the current sampling protocol. If this variance is unacceptably large, then either a larger sample mass must be taken or else the particle size must be reduced (unless particle size is of interest). Particle size reduction is discussed later in this appendix. Because the mathematics is very complicated, we give here only a sketch of the derivation and how the formula can be approximated. Details are given in Gy (1992) and Pitard (1993).
Gy (1992, p. 57) defines the heterogeneity carried by an individual particle as a function of the relative difference between the chemical or physical measurement of the particle and what the true lot value is. This difference is mathematically weighted by the mass of the unit. In (B.1) below, c i is the content of a given particle, that is, the measurement of the characteristic of interest, such as chemical concentration. It is determined by dividing the mass of the component of interest in the particle by the mass of the particle itself. Using M i for the mass of the particle, the heterogeneity
