Equation 3 assumes the equations are linear, hence, is limited to the effects of relatively small disturbances. Figure shows the results of the Monte-Carlo analysis for the scenario when the raw assay data has an uncertainty of RSDG = 0.10, much larger than in Figure . When the "distance" from the singularity becomes comparable with the error in the raw data, Equation 1 becomes very sensitive to uncertainty in the data and can give spurious yield values that are negative or larger than 100 %. This results in the error amplification factor increasing in an accelerated manner. This increase here appears to be chaotic in nature, but that chaos may be an artefact of the finite number of samples used in the Monte-Carlo method. A more rigorous analysis involving integration across the singularity would be required to determine the exact error amplification for this situation, however that is beyond the scope of this paper. Figure shows how this region of accelerated yield error amplification scales with the error in the raw assay data. It appears that we can approximate the region where Equation 11 (and 12) is valid as being when: