Figure shows the species yield error amplification AY,i as a function of the species recovery, Ri, for a fixed yield Y = 0.20 and fixed species feed grade GF,i = 0.05. The data were formed using a Monte-Carlo approach with N = 10 000 simulations with the relative standard deviation of the error in all the raw assay data held at RSDG = 0.001, which implies a very low error in the raw assay data. It is evident there exists a singularity when the value of the recovery equals the overall yield. At this singularity GP = GT = GF and Equation 1 becomes in effect zero divided by zero. This condition is well known and was also previously identified by . When the error in the raw data is small, the error amplification increases in a smooth predictable manner as the singularity is approached. This analysis shows the large amplification in the uncertainty of the calculated yield that can occur near the singularity, even for very low levels of uncertainty in the raw data. Hence the warning by ) that "… there must always be a significant difference between the component values (in this case assays) if reliable results are to be obtained."