Weighted Least-Squares Approach To Calculating Limits of Detection and Quantification by Modeling Variability as a Function of Concentration

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Abstract
The limit of detection and limit of quantification are current critical issues in environmental testing. In most laboratories, limits are currently calculated on the basis of the standard deviation of replicate analyses at a single concentration. However, since the standard deviation depends on concentration, these single-concentration techniques result in limits that are directly dependent on spiking concentration. A more rigorous approach uses a weighted least-squares regression analysis of replicates spiked at a series of concentrations [Formula: see text] a calibration design. In this work, the use of weighted tolerance intervals is introduced for estimating detection and quantification limits. In addition, models for estimating the weights used in calculating weighted prediction intervals and weighted tolerance intervals are presented. Using this method, detection and quantification limits were calculated for gas chromatographic analyses of 16 polychlorinated biphenyls. Results show that the approach developed provides improved estimates of analytical limits and that the single-concentration approaches currently in wide use are seriously flawed. Future work should reduce the data needed for the calibration design approach so that more rigorous detection and quantification limits can be routinely applied.