FISCHER FISCHERSCOPE X-RAY 5000 Series, Operator'S Manual

Page: 135 / 188

FISCHERSCOPE
®
X-RAY 135
Description of the Characteristic Statistical Parameters Addendum
18.1.2 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
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