FISCHER FISCHERSCOPE X-RAY XDLM 231, Operator'S Manual

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Measurement Uncertainty and Measuring Ranges Meaning of the measurement uncertainty
86 FISCHERSCOPE
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X-RAY
Definition "Measuring range"
Range, where the precision does not exceed a specified limit value.
Precision: random measurement uncertainty due to distribution of
the spectral channel contents of the instrument.
11.1 Meaning of the measurement uncertainty
Measurement uncertainty refers to the unknown difference to the
true value. Physical samples representing the "true value" are
called standards. Their characteristic values are called nominal
values or engraved values. However, they are valid and can be
used for calibrations only if their uncertainty is specified. This is a
measure for the difference to the true value and is, by nature, a
probability statement. Its numeric value

X characterizes a range X
+

X. It depends on the probability of still being able to capture the
true value when using this value.
PTB [German Physical and Technical Institute] uses the term
"Überdeckungswahrscheinlichkeit" [overlapping probability], which
is identical with the term "confidence interval" used in statistics
literature.
Assuming a normal distribution probability density for the difference
to the true value, one identifies its distribution parameter s with the
standard measurement uncertainty u, and using multiples thereof,
can specify well-defined measurement uncertainties. The often
recommended expansion factor k shall be 2, such that a range X +
2*u contains the true value with a 95% probability.
For several reasons, k=1 is meaningful as well, because here the
standard deviation reaches the random portion (see below) of the
measurement uncertainty for a large number of repeat
measurements. However, here the hit rate is only 68%.
Safety conscientious companies and people prefer to allow less
than 1% probability for errors - and select k=3. In the end, however,
it does not matter in what unit the measurement error is specified;
important is that it is known.
To meet different requirements WinFTM allows for the input of k, cf.
picture at the side. The default value is set to k=2.
Expansion factor k. Input of the expansion factor k that determines
the confidence interval of the error specification, using "General >
Measuring Head Parameters > Default Settings".