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Background

Due to a decision taken by C.F. Gauss himself, the classical error calculus considered random errors only. Remarkably enough, Gauss also discussed what he had called regular or constant errors - perturbation being unknown in magnitude and sign and constant in time. Today the latter are termed unknown systematic errors. Gauss, unfortunately, dismissed suchlike errors arguing that it should be up to the experimenter to remedy them. When the metrological community became aware that this assumption shaped up as wrong, the Gaussian error calculus had to be revised from scratch.

In the late 1970s, the world’s National Measurement Institutes published the

Guide to the Expression of Uncertainty in Measurement,

called GUM for short, in which it is proposed to treat unknown systematic errors on a statistical basis.

Parallel to the GUM the author proposed another view tentatively termed

Generalized Gaussian Error Calculus

in which he proposed to

- amend the treatment of random errors by persistently bringing empirical covariances to bear and to

- handle unknown systematic errors on a worst case basis,

a proceeding which lead to quasi safe measurement uncertainties.

Quasi safe measurement uncertainties are considered the smallest possible measurement uncertainties which localize the true values of the quantities to be measured reliably.

This statement expressing what is called the traceability of the true values of the measurands lies at the heart of metrology.

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