The Generalized Least Squares (GLS) method estimates the straight-line calibration function by taking into account uncertainties in variables, heteroscedasticity and correlations. However, the efficiency of the method depends on a good knowledge of the method itself and of the calibration process. This paper details the characteristics of the calibration function and introduces the “model with errors in variables” which is more representative of the context. The GLS method is analysed in the three steps of the estimation process: assumption, computation and validation. Propagation of the uncertainty in input data to coefficients of the straight-line calibration function is also discussed. The measurement result is then computed with the estimated curve, directly and by inverse evaluation. The associated uncertainty is given by distinguishing the mean value without uncertainty and an individual value with its associated uncertainty. Two examples are analysed. Uncertainties in variables have little influence on the value of the measurement result and of coefficients of the straight-line calibration function. On the contrary, associated uncertainties are highly affected by them.

Key words

generalised least squares
measurement errors model
calibration curve
straight-line with uncertainty on variables