Metrohm 746 VA Trace Analyzer - Manual (Page 485)

6 Data processing and evaluation
746 VA Trace Analyzer / 747 VA Stand
6-22
6.9.3 Result calculation from calibration curves and error
calculation
With all three possible calibration methods, the mass concentration ρ
eff eff
in the
measuring vessel must be determined with the aid of a calibration curve. This cali-
bration curve itself must be determined by the measurement of solutions of known
mass concentration. The measured value pairs EV: / ρ
eff eff
are then used to
calculate the parameters for a given linear or nonlinear curve function. As the cal-
culation of the calibration curves, the results based on them and the associated
error calculation are basically the same in all calibration techniques, in what follows
the calculation procedure used by the 746 VA Trace Analyzer will be described in
general terms.
A search is made for the relation between the variables x and y using the measured
values x
i
, y
i
with the following assumptions:
– The variable x is error free.
– The variable y depends on x and
can be described by the function
y = y ( x ).
– The error in the measurement of y
has a normal distribution and is
sufficiently small to allow use of a
linear error calculation.
y
x
For the calculation of the calibration curve y = y ( x ), the 746 has the following 4
model functions available, depending on the calibration technique selected:
y = a + bx Straight line
y = bx Straight line through zero
y = a + bx + cx 4 Nonlinear curve of 4 th degree
y = bx + cx 4 Nonlinear curve of 4 th degree through zero
To calculate the parameters a, b and c, the method of least squares is used in
which the sum of the squared deviations of the measured values y
ii
from the esti-
mated values ^ ^ y
ii
is minimized. As the scatters σ
y,i y,i
of the measured values depend
on the measured value y, these deviations are weighted with the factor g
ii
:
The dependence of the scatters σ
yy
of the
measured value y has been determined by
the 746 VA Trace Analyzer experimentally.
Here, it was apparent that the scatter
remained constant up to a measured value
of 15 nA, but above this value then in-
creased in direct proportion to the measured
value. The factor p takes into account the
influence of the changing disturbance
variables (capillary, temp., etc.).
y
=
( σ
y,i y,i
) 2
1
with g
ii
= g
ii
( y
ii
– ^ ^ y
ii
) 2 = minimum
nn
Σ
i = 1 i = 1
( p σ
0,i 0,i
) 2
1
y
ii
^ ^ y
ii
x
ii
Estimated value
Measured value
Function y = y ( x )
σ
y y
( y ) = p ⋅ σ
0 0
( y )
y < 15 nA: σ
00
= 15 nA
y ≥ 15 nA: σ
00
= y
σ
00
15 nA