Effect of multiple error sources on the calibration uncertainty

The calibration uncertainty associated with the determination of metals at trace levels in a drinking water sample by ICP-MS was estimated when signals were affected by two error contributions, namely instrumental errors and operational condition errors. The calibration uncertainty was studied by using J concentration levels measured I times, as usual in experimental calibration procedures. The instrumental error was random in character whilst the operational error was assumed systematic at each concentration level but random among the J levels. The presence or the absence of the two error contributions was determined with an F-test between the ordinary least squares residual variance of the mean responses at each concentration and a pooled variance of the replicates. The theory was applied to the calibration of 30 elements present in a multi-standard solution and then to the analysis of boron, calcium, lithium, barium and manganese in a real drinking water sample. The need of using the proposed approach as calibration for almost all the analyzed elements resulted evident. The presence or the absence of the two error contributions was determined with an F-test between the ordinary least squares residual variance of the mean responses at each concentration and a pooled variance of the replicates. It was found that in the former instance the uncertainty determined using a two-components variance regression was greater than that obtainable from the one-variance regression.