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

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Measurement device monitoring for the Fischerscope X-RAY Variation of measurement readings
110 FISCHERSCOPE
®
X-RAY
15.3 Variation of measurement readings
Repeatability
Conditions
The displayed value of any measuring instrument will not be exactly
the same when repeating a measurement, instead it will vary, even
under otherwise equal measurement conditions (
repeatability
conditions), due to random influences of the instrument. If repeated
measurements do not exhibit variations, either the resolution
(decimal places) is too low such that the variations are not visible
or the instrument is defective and shows the same value at all
times. The resulting deviations are considered
random because it
cannot be predicted whether the next measurement is bigger or
smaller than the result of the test series up to that moment.
The standard deviation of a test series under repeatability
conditions is the general measure for the variations of the readings.
It can be calculated in the known manner from the single readings.
The measurement result (mean value and standard deviation) of a
test series is to a certain degree random as well and exhibits an
unavoidable
measurement uncertainty . This can be seen in that
repeating a test series will lead to a (often only slightly) different
measurement result. However, the variations of the mean values
are smaller (by a factor of 1/

n, where n is the number of the single
readings of the test series) than the variations of the single
readings.
Measurement
Uncertainty u
The measurement uncertainty u of the mean values is derived from
the standard deviation s and the number n of the individual readings
included in the test series:
(1)
u = c(n)
·
s
where c(n) is a factor that is dependent on the number of single
readings and the so-called confidence level 1-

. For n = 5, 10, 20,
30 and 50 (and a confidence level of 95%) the resultant factors are:
c(5) = 1.24 ---- c(10) = 0.71 ---- c(20) = 0.48 ---- c(30) = 0.37 ----
c(50) = 0.28.
Confidence Interval The measurement uncertainty forms the confidence interval when
deducted as difference from and added as sum to the mean value
(plus/minus). It is an interval around the mean value of the test
series that contains with a 95% probability the true (overall) result
that one was to obtain if one were to measure infinite times. In
measurement technology, the results are always displayed
graphically in the same manner by drawing the mean value as a
circle or point and the confidence interval as an ”error bar” from this
point (”bar-bell”). The confidence interval becomes narrower as the
number of single readings that form the mean value increases and
the better the repeatability precision of the instrument, or
respectively, the smaller the standard deviation of the single
readings is (see above equation for the measurement uncertainty u
and the factors c(n)).