Evaluation of Associated Uncertainties using Linear Least Squares Best-fit Lines for Electro-mechanical Transducers

摘要

The linear least squares best-fit line computation is now well established tool in pressure metrology. However, although important, its use in evaluation of measurement uncertainty, consistent with ISO guide to the expression of uncertainty in measurement, for line parameters, is still not a routine practice. 7he guide stipulates that output quantity can be obtained by a curve that has been fitted to input quantity by method of least square. In the electro-mechanical type direct pressure indicating devices, the applied pressure is directly measured by a sensing element with a suitable mechanism into an analog / digital electrical signalin terms of voltage, current or frequency. A wide range of such pressure measuring instruments is now commercially available and a lot of research is undergoing to improve their performances. It is clear that the transformation of electrical signal to output pressure should be highly linear, reproducible, minimum zero shift and thereby should ensure the highest measurement uncertainty, particularly in the fluid media. The calculation of the calibration results and associated uncertainties is a complex matter involving many influencing quantities. This paper describes a simple method in a worksheet format that enables the uncertainty calculations for best-fit line parameters to be used in the calibrations of electromechanical transducers. The uncertainty components due to slope of the line, the data points of the line, the interpolated points, and the line as a whole, are also covered. The method of evaluation of associated uncertainties is consistent with ISO guide. For the sake of clarity for the readers, an example is prepared and presented as a case study, which is suitable for use as a model.