Precision and Bias For Settlements

"The settlements between mines and smelters are based on the mass of metal contained in concentrate lots. The mass of contained metal is a function of the wet mass of a lot, and its moisture content and metal grade while the variance of the mass of contained metal is a function of the same variables and their variances. Uncertainties in the measurement procedure applied to estimate each variable are quantified in terms of precision and bias. The absence of bias and an acceptable degree of precision are the keys to effective risk analysis and loss control.ISO Technical Committee 183-Copper, Lead and Zinc Sulfide Concentrates, has developed standard methods for sampling and weighing, estimating precision and testing for bias, the determination of mass loss on drying, the calculation of the mass of contained metal and its variance, and various analytical methods for major and minor metals. The variance for wet mass is calculated from the precision of the scale while the total variances of moisture and grade are estimated from pairs of interpenetrating primary samples. The variance of contained metal can be calculated either from mine data or from smelter data but the risk associated with the settlement is largely determined by the absence or presence of bias and the variance of differences between exchange assays.ISO/TC 183 does not deal with precision and bias for exchange assays but is developing guidelines to determine realistic splitting limits. Given that the exchange of assays between mines and smelters accounts for a large part of the risk associated with the settlement, precision and bias for exchange assays should be measured and monitored. The need for umpire services can be reduced by applying statistical quality control (SQC).Calibrating static scales, moisture balances and analytical balances, bias testing of sampling methods and sample preparation procedures, estimating the variance of a single variable or the variance of a function that a set of variables defines, and monitoring precision and bias for exchange assays, are the quintessence of metrology, the science of measurement, when applied in mining and metallurgy."