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Unknown systematic errors and the method of least squares Michael Grabe. alternative error model: true values and biases. Quantity to be measured true value. First Principle. Does metrology exist without a net of true values?. Not likely!. Impact of true values and biases
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Unknown systematic errors and the method of least squares Michael Grabe alternative error model: true values and biases
Quantity to be measuredtruevalue First Principle Does metrology exist without a net of true values? Not likely!
Impact of true values and biases in least squares • Traceability • Gauß-Markoff theorem • Assessment of uncertainties • Key Comparisons
Traceability Least squares adjustment
Mean of means averaging is permitted if and only if the respective true values are identical
mass Adjustment ad hoc ?
A different approach empirical variance-covariance matrix
Gauß-Markoff Theorem The uncertainties are minimal... ...if the system has been weighted appropriately
according to the GUM we should have but we encounter biases abolish the theorem ...
Consequences ... • no more test of consistency • how to weight the system to minimize uncertainties?
more ... and of utmost importance: weightings • shift estimators and • reduce measurement uncertainties
true value reduction shift before after a picture
Traceability: vary the weights by trial and error ... Assessment of uncertainties
true value true value ... true value ... Key Comparison National Standards
... T ... Round Robin Calibration of a Travelling Standard T
Consider the grand mean KCRV and the differences Key comparisons do more ...
and look for where „consistent“ with
against Should we test when constributesto ? Problem: In some cases the GUM may localize the true value of the travelling standard, in others not ...
true value KCRV Differences between KCRV and individual calibrations ...
... true value Individual Calibrations a horizontal line should intersect each of the uncertainties
... KCRV true value KCRV and individual calibrations