Model based analysis of key comparison data

摘要

Comparison measurements of physical quantities are sometimes carried out in dependence on a parameter such as frequency or temperature. A parametric model may be available describing the dependence of the measurand on the parameter. In the field of shock and vibration, for example, sensitivities of accelerometers are determined at different frequencies, and a physical model with unknown parameters describing the frequency dependence of the sensitivities is available. The analysis of comparison measurements carried out in dependence on a parameter is treated with the aid of a parametric model describing the dependence on this parameter. In particular, a reference curve can be defined by this model whose parameters are estimated from the comparison data. The task of estimating the model parameters as well as the need to check the conformity of the data and the given model are discussed. Furthermore, it is proposed that the Monte Carlo method be additionally applied in case the underlying model is non-linear. The model based approach is applied to data from a regional key comparison of accelerometer calibrations at different frequencies; the unknown model parameters have been determined by weighted least squares. The conformity of data and model is assessed by a X~(2)-criterion. Application of the Monte Carlo method shows that for this particular non-linear model the propagation of uncertainties is in good agreement with the propagation of probability density functions. The results obtained are compared to those obtained by separate analysis of the data at the individual frequencies. In particular, the results of consistency checks obtained when separately analyzing the data at each frequency are compared to the result of a consistency check offered by the model based approach. Finally, the data are analyzed assuming certain correlation patterns to examine the effects in case correlations of the data are taken into account.