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

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Measurement device monitoring for the Fischerscope X-RAY Pre-run for determining the control limits
120 FISCHERSCOPE
®
X-RAY
measurement distance, collimator, etc.) typically used for the
measurement application and should be concluded within a short
period for the instrument to remain stable during this time.
Systematic changes during this period are then negligible. After
each group (not after each measurement!), the reference sample
should be taken from the instrument and re-positioned in order to
simulate as good as possible the subsequent procedure during the
check measurement. With instruments featuring a variable setting
of the measurement distance, such as the Fischerscope XRAY, the
measurement distance must be retained during the pre-run and the
subsequent check measurement because the standard deviation
correlates to the measurement distance. This distance can be
noted and viewed in the ”notepad” of the product that is used for
measurement device monitoring.
At first, the mean values x.
i
of the m groups 1 to 10 are used to
calculate the overall mean value x.. :
(2) x.. = (1/m) ·

x.
i
= x_est
This overall mean value forms the estimated value x_est for the
mean value of the quality control chart.
The standard deviations s
i
of groups 1 to 10 are used to build the
arithmetic mean value s
I
:
(3) s
I
= (1/m) ·

s
i
The index i runs across the number m of the groups.
The estimated value s
I
serves as the ”current” standard deviation of
the individual readings. The variations between the group mean
values due to drift, interference or changes in the position of the
reference samples during the pre-run are taken into account by
calculating the standard deviation of the mean values
s
II
from the
group mean values x.
i
of the m groups 1 to 10:
(4)
s
II
= {

(x.
i
– x..) 2 /(m-1)} ½
s
II
takes into account the ”extraordinary” influences (potentially
present during the pre-run) on the variations of the group mean
values that may come into existence due to sample re-positioning
for a new group or by changing the measurement location or the
operator – as will also occur during subsequent measurements in
the control chart.
Now, the standard deviations
s
I
and s
II
are used to form the
estimated value of the standard deviation s of the population:
(4)
= (s
I
2 + s
II
2 ) ½

ˆ