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

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Random Error Measurement Uncertainty and Measuring Ranges
FISCHERSCOPE
®
X-RAY 87
11.2 Random Error
If a measurement is repeated N times, the single readings will
deviate around a mean value. The cause for this is the random
distribution of the channel contents of the spectrum, whose law of
formation (Poisson distribution) we know. This is a special case in
measurement technology that allows us, or the program,
respectively, to make a prediction about the repeatability precision
from only one single measurement, or one single spectrum,
respectively. The respective value will be displayed or can be
exported (cf. Section 4). In reality, there are, however, additional
causes for random fluctuations that cannot be determined
theoretically, such as the influence of the gas amplification in
connection with the software drift compensation, for example. In
some cases this may lead to the measured deviations (standard
deviation) exceeding the theoretical prognoses. However, they
typically correspond surprisingly well.
NOTE:
Side note: If a measurement application does not cor-
respond to the reality of the measured sample, this
not only leads to an increased mq value but also to
an increase in the deviations). In any case, the ran-
dom portion of the error can be determined using sta-
tistical means. The program computes the
uncertainty of the mean value from the repeatability
deviations, where the numeric value depends on the
setting of the confidence interval k (see above).
WinFTM cannot describe the differences between reproducibility
and repeatability (= precision) described in the literature since they
depend on the way the tests are carried out. Only if, for example,
the individual measurements always include a new positioning of
the sample, and maybe even a new operator, will the deviations of
the measurements reflect these influences as well. In this case, the
confidence interval of the mean value characterizes the
reproducibility concerning the investigated influencing factors. In
any case, these measurement errors are greater than the random
measurement uncertainties due to the Poisson-distributed
deviations of the spectral intensities owed to the X-ray fluorescence
method.