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

Page: 195 / 236

FISCHERSCOPE ® X-RAY 193
Addendum
23.1.2 Final Result – Fixed Block Definition
Automatic block creation (Block definition fix) is enabled for the product.
Parameter Description Equation
Mean value Mean value of the block mean
values.
is the summation of all
block mean values of a
measurement series, divided by the
number of blocks
: Block mean values
: Number of blocks
Confidence
interval
q
Each measurement device produces
random measurement errors. With a
certain probability (confidence
level), the true value of the
measured parameter lies in an
interval (double-sided confidence
interval) around the measured mean
value
of a measurement series
(block/group). The borders of this
interval are at a distance
q
from the
true value .
q
is calculated according to the
equation below assuming a normal
distribution for a confidence level of
95 %:
t
: Quantile of the Student’s t-distri-
bution (Student’s factor), can be
obtained from tables in
common publications [1]
s
: Standard deviation of the block
mean values
: Numbers of blocks
: Mean value of the block mean
values
: Block mean values
Mean
standard
deviation
s
The mean standard deviation is a
measure of the dispersion of the
individual block standard deviations
of a measurement series about their
common mean value .
: Standard deviations of the
blocks
: Number of blocks
Coefficient of
variation
V [%]
Standard deviation referring to the
mean value
: Mean standard deviation
: Mean value of the block mean
values
x
x
x
i
n
Bl
1
n
Bl
-------- x
i
i 1 =
n
Bl

= x
x
i
n
Bl

x

x q –

x q +
 
x
x
q t
f 1 0 025

– ;
s
n
Bl
------------ =
s
1
n
Bl
1 –
----------------- x x
i
–
 
2
i 1 =
n
Bl

= x
n
Bl
x
x
i
x
s
1
n
Bl
-------- s
i
i 1 =
n
Bl

=
s
i
n
Bl
V
s
x
-- 100 =
x
s
x