Failure model

An error model classifies measurement errors , here those of metrology . The properties of the measurement errors that flow into the measurement process are determined by the physical mode of operation of the measurement apparatus .

Denote

• ${\displaystyle x_{l}}$that of n repeated measurements ${\displaystyle l.}$
• ${\displaystyle x_{0}}$the true value of the measurand
• ${\displaystyle f}$ the unknown systematic measurement error, which is common to all n repeated measurements
• ${\displaystyle \varepsilon _{l}}$ the random measurement error.

Then the revision of the Gaussian error calculation is based on an error equation of the following form:

${\displaystyle x_{l}=x_{0}+f+\varepsilon _{l};\quad -f_{s}\leq f=const.\leq +f_{s}}$

The measured values of a stationary operating measuring apparatus sprinkle therefore not to the true value of the measured variable, but to the part of the unknown systematic measurement error shifted value . The latter refers to the statistics as polluted or not the unbiased expectation - not expected true to say: the true value has been missed. ${\displaystyle x_{0}}$ ${\displaystyle f}$ ${\displaystyle x_{0}+f}$ ${\displaystyle x_{0}}$

Neither are nor known to the experimenter. ${\displaystyle x_{0}}$ ${\displaystyle x_{0}+f}$

Interpretation of unknown systematic errors

Currently, unknown systematic errors are interpreted differently:

• The ISO-Guide formally assigns them a random variable and this, by postulate , a rectangular density, defined over the interval . It is implicitly assumed that it is permissible to limit the realizations of that random variable essentially to their simple standard deviation , i.e. H. on an interval of length . As can be shown, however, this interpretation brings with it unrecoverable mathematical and physical problems; see measurement uncertainty . ${\displaystyle -f_{s}\ldots f_{s}}$ ${\displaystyle \pm f_{s}/{\sqrt {3}}}$
• The revision of the Gaussian error calculation, which is an alternative to the guide, considers the unknown systematic measurement error - physically more realistic - as a time constant, through a limited variable that is to be brought into play in the sense of a worst-case estimate, i.e. H. in the form of the interval boundaries . This procedure requires a new type of error calculation which cannot be represented by updating the Gaussian error calculation. On the other hand, the new formalism leads to certain measurement uncertainties; in particular, it is free of inconsistencies . ${\displaystyle -f_{s}\ldots f_{s}}$ ${\displaystyle \pm f_{s}}$

See also

• Error (statistics)
• Index error
• drift
• Distortion (empiricism)
• Design effect