Optical emission analysis of low alloy steels (routine method) - Method for determination of C, Si, S, P, Mn, Cr, Ni and Cu

This document specifies an optical emission spectrometry spark source routine standard method for multi-element analysis of unalloyed steel and iron.

Optische Emissionsanalyse von niedriglegierten Stählen (Reihenanalyse) - Verfahren zur Bestimmung von C, Si, S, P, Mn, Cr, Ni und Cu

Analyse des aciers faiblement alliés par spectrométrié d´émission optique (méthode de routine) - Méthode de détermination de C, Si, S, P, Mn, Cr, Ni et Cu

Optična emisijska analiza malolegiranih jekel (rutinska metoda) – Metoda za določevanje C, Si, S, P, Mn, Cr, Ni in Cu

General Information

Status
Published
Publication Date
30-Nov-2004
Technical Committee
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
01-Dec-2004
Due Date
01-Dec-2004
Completion Date
01-Dec-2004

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Standards Content (Sample)

SLOVENSKI STANDARD
SIST-TP CEN/CR 10320:2004
01-december-2004
2SWLþQDHPLVLMVNDDQDOL]DPDOROHJLUDQLKMHNHO UXWLQVNDPHWRGD ±0HWRGD]D
GRORþHYDQMH&6L630Q&U1LLQ&X
Optical emission analysis of low alloy steels (routine method) - Method for determination
of C, Si, S, P, Mn, Cr, Ni and Cu
Optische Emissionsanalyse von niedriglegierten Stählen (Reihenanalyse) - Verfahren zur
Bestimmung von C, Si, S, P, Mn, Cr, Ni und Cu
Analyse des aciers faiblement alliés par spectrométrié d´émission optique (méthode de
routine) - Méthode de détermination de C, Si, S, P, Mn, Cr, Ni et Cu
Ta slovenski standard je istoveten z: CR 10320:2004
ICS:
77.040.30 Kemijska analiza kovin Chemical analysis of metals
77.080.20 Jekla Steels
SIST-TP CEN/CR 10320:2004 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST-TP CEN/CR 10320:2004

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SIST-TP CEN/CR 10320:2004
CEN REPORT
CR 10320
RAPPORT CEN
CEN BERICHT
September 2004
ICS 77.040.20; 77.140.20

English version
Optical emission analysis of low alloy steels (routine method) -
Method for determination of C, Si, S, P, Mn, Cr, Ni and Cu
Analyse des aciers faiblement alliés par spectrométrié Optische Emissionsanalyse von niedriglegierten Stählen
d´émission optique (méthode de routine) - Méthode de (Reihenanalyse) - Verfahren zur Bestimmung von C, Si, S,
détermination de C, Si, S, P, Mn, Cr, Ni et Cu P, Mn, Cr, Ni und Cu
This CEN Report was approved by CEN on 3 June 2001. It has been drawn up by the Technical Committee ECISS/TC 20.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia,
Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2004 CEN All rights of exploitation in any form and by any means reserved Ref. No. CR 10320:2004: E
worldwide for CEN national Members.

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SIST-TP CEN/CR 10320:2004
CR 10320:2004 (E)
Contents          page
Foreword.3
1 Scope .4
2 Test sample preparation .4
3 Calibration of the instrument.4
3.1 Determination of calibration curve .4
3.2 Linear correlation.5
3.3 Quadratic correlation .6
3.4 Confidence limit (Syc) and standard error (Syx) in a linear correlation .7
3.5 Confidence limit (Syc) and standard error (Syx) in a quadratic correlation.7
3.6 Correlation accuracy .8
4 Calculation of interferences .8
4.1 Spectral interferences .8
4.2 Matrix interferences.10
4.3 Calculation of an interfered element due to either matrix effect or spectral interference.10
5 Determination of performance criteria .11
5.1 Determination of background equivalent concentration BEC .11
5.2 Determination of detection limit DL.11
5.3 Determination of repeatability as relative standard deviation RSD .13
5.4 Determination of accuracy SEA .13
6 Performing analysis .13
7 Ordinary maintenance.14
8 Quality control.14
8.1 Control chart .14
8.2 Calibration curve control .15
9 Examples .15
9.1 Determination of calibration curve .15
9.2 Calculation of interferences .20
9.3 Determination of background equivalent concentration.25
9.4 Determination of detection limit.26
9.5 Determination of repeatability.27
9.6 Determination of accuracy.29
9.7 Ordinary maintenance.31
9.8 Control CHART.31
9.9 Calibration curve control .34
10 Statistical results .35
Annex A Optical emission spectrometry.37
Bibliography .60


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Foreword
This document (CR 10320:2004) has been prepared by ECISS /TC 20, "Methods of chemical analysis of ferrous
products".
3

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CR 10320:2004 (E)
1 Scope
This document specifies an optical emission spectrometry spark source routine standard method for multi-
element analysis of unalloyed steel and iron.
2 Test sample preparation
Prepare reference materials, test samples and setting up samples, by grinding to provide a uniform flat surface.
It is recommended a surface grinder with aluminium oxide, or zirconium oxide, abrasive to be employed with a
coarse grit of 60 - 100.
3 Calibration of the instrument
3.1 Determination of calibration curve
Analyse a series of reference materials (min. 5) for the element intensity/matrix intensity ratio according to the
pattern shown in Figure 1.
Calculate the average intensity for each reference material.
NOTE In (Figure 1) the first group values into parentheses refers to odd ns.
Correlate the average intensity ratio with the concentration of test element.
n
i
         (1)
cA%= I

i
i=0
where:
A means correlation constants;
i
i
I means unknown values (intensity ratio).
4

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Figure 1
3.2 Linear correlation
For linear correlations, constants are calculated in the following way:
Ay=−Ax
         (2)
01mm
5

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CR 10320:2004 (E)
()xy

A =          (3)
1
2
()x

where:
x and y are average values (Σi /n);
m m m
n number of points;
x and y are intensity ratio readouts and concentrations, respectively, of test samples.
Besides correlation parameters, calculate the following:
2
[]n xy− x y
∑∑∑
2
r =
      (4)
2 2
2 2
[]n ()x −()x ×[]n ()y −()y
∑∑ ∑∑
where r is the correlation coefficient.
A and A may also be calculated by single values according to the following equations:
0 1
2
yx − xy x
() ( )
∑∑ ∑ ∑
A =       (5)
0
2
2
nx − x
()
()
∑ ∑
yA− ()x
∑∑1
A =         (6)
0
n
nxy − x y
()
∑ ∑∑
A =
        (7)
1
2
2
nx − x
()
()
∑ ∑
3.3 Quadratic correlation
Calculate constants in the following way, by resolving the system:
2 3 42
Ax++A x A x= xy      (8)
() () () ()( )
∑ ∑ ∑ ∑
0 1 2
2 3
Ax++A ()x A (x)= (xy)      (9)
∑ ∑ ∑ ∑
01 2
2
An++A x A ()x= y       (10)
∑ ∑ ∑
01 2
where:
n is the number of tests.
2
cc−
()
∑ it ic
2
r =−1        (11)
2
()cc−

it a
6

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CR 10320:2004 (E)
where:
c is the true value of the reference material i;
it
c is the value of the reference material i read on the calibration curve;
ic
c is the average concentration of all the c
a ic

3.4 Confidence limit (Syc) and standard error (Syx) in a linear correlation
Confidence limit indicates the area where the true value of y for a given x lies at 95 % of probability. In other
words, it indicates the area including the regression range. The slope error is an evidence of the method
sensitivity, in fact the wider x range the lower the slope error. The standard error in a correlation is the extent of
the deviation around the regression line. Calculate the standard error in a linear correlation by the following
formula:
2
yA−−yA xy
() ( )
∑ ∑∑
01
Syx =       (12)
n− 2
and the confidence limit:
2
()x −x
1
i m
Syc=Syx× +
2
       (13)
n
()x

Calculate the slope error (Sb) as follows:
Syx
Sb=         (14)
2
()x

3.5 Confidence limit (Syc) and standard error (Syx) in a quadratic correlation
Calculate the standard error in a quadratic correlation by the following formula:
2
2
yA−−yA xy−A ()xy
() ( )
∑ 01∑∑∑ 2
Syx=      (15)
n−2
and the confidence limit:
2
1()x −x
i m
Syc Syx
= × +
2
      (16)
n
()x

Calculate the slope error (Sb) as follows:
7

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CR 10320:2004 (E)
Syx
Sb=         (17)
2
x
()

3.6 Correlation accuracy
Among reference standards, either secondary or tertiary, select a low, a medium and a high standard and
determine their repeatability both in concentration and intensity ratio. The resulting values indicate the method
accuracy index at the specific concentration (intensity ratio).
If RSD is correlated with concentration, a change in repeatability is obtained with respect to concentration.

4 Calculation of interferences
4.1 Spectral interferences
In the line intensity/matrix ratio, analyse at least 5 reference materials on the interference line with a variable
concentration of the interfering element but possibly free from the interfered element. Analyses should be
repeated at least four times after performing the drift correction, according to the Figure 2 scheme. Calculate the
average intensity ratio for each reference material and compute the corresponding concentration of interfered
element.

Figure 2
Correlate the resulting concentrations to the concentration of the interfering element by the method of least
squares. The following equation is obtained:
n
i
cA% = c         (18)
∑ ii
i=0
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where:
c% is the concentration of the interfered element;
c is the concentration of the interfering element;
i
A is the correlation constants (it is advisable to calculate a straight line).
i
The angle coefficient of the straight line (A ) is the factor of spectral interference of the element interfering over
1
the analyte.
This factor is nonlinear only rarely and for wide concentration ranges of the interfering and/or interfered
elements. In this case it is advisable to work with analyte families and limit concentration ranges.
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The following equation calculates the analyte concentration:
n k
i
cA%=+I fc        (19)
∑∑i jj
i==00j
where:
f means the factor of spectral interference of element j over the analyte;
j
c means its concentration.
j
It is possible to calculate interference factors in intensity. In this case correlations must be made with intensities.
The following formula is used to calculate f easier and when only one interfering element has been detected:
j
n
i
cA%=+Ifc        (20)
∑ i 11
i=0
n
i
cA%− I
∑ i
i=0
f =        (21)
1
c
1
Suitable reference materials must be selected that have a variable concentration of the interfering element and
that have already been analysed during the calibration curve construction.
4.2 Matrix interferences
Having established that matrix interferences are minimized by subdividing test samples into spectral families, it
is however possible to calculate them by selecting at least 5 reference materials with a composition as close as
possible to the matrix, the interfering and the interfered element in variable concentration. Analyse materials
according to the previous scheme and calculate interference factors by the following equation:
n k
 
i
cA%=+I 1 fc       (22)
 
∑∑i tt
 
i==00t
where:
f is the interference factor of element t over the analyte;
t
c is its concentration.
t
4.3 Calculation of an interfered element due to either matrix effect or spectral interference
The concentration of an interfered element, due to either matrix effect or line overlap, is calculated by the
following formula:
n k s
 
i
cA%=+I 1 fc +fc for t ≠ j      (23)
 
∑∑ ∑
i tt jj
 
i==00t j=0


10

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5 Determination of performance criteria
5.1 Determination of background equivalent concentration BEC
The background equivalent concentration corresponds to a net intensity whose value is equal to background
intensity. It is calculated as follows:
a) Calculate calibration curve;
b) Determine background intensity, i.e. the intensity corresponding to the intercept between curve and axis of
abscissas (I );
0
c) Multiply I by 2 (I x 2 = I );
0 0 B
d) With correlation parameters, calculate the concentration equivalent to I . The resulting value corresponds
B
to the BEC of the test element.
In a linear concentration, BEC is equal to the known term multiplied by -1.
5.2 Determination of detection limit DL
The detection limit may be assessed in two different ways according to whether the instrument DL for a given
analyte line or the method DL. is to be calculated
5.2.1 Detection limit of the method
5.2.1.1  Base straight line curve
a) Record the element intensity/matrix ratio for a series of reference materials (min. 4) in a matrix pattern as in
the following example:
RefMat 1 2 3 4
Conc. C C C C
1 2 3 4
Int. I I I I
11 21 31 41

I I I I
12 22 32 42

..........................................................................
I I I I
16 26 36 46

b)  Calculate:
RefMat 1 2 3 4
Conc. C C C C
1 2 3 4
Int. I I I I
11 21 31 41

I I I I
12 22 32 42

..........................................................................
I I I I
16 26 36  46


Σ ΣI ΣI ΣI ΣI
1i 2i 3i 4i
mean I I I I
1m 2m 3m 4m


2 2 2 2 2
Σ (I ) Σ (I ) Σ (I ) Σ (I ) Σ (I )
ni 1i 2i 3i 4i
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CR 10320:2004 (E)
2
c) Calculate Sp (pooled estimate of standard deviation) according to the following formula:
2 2 2
 
I I I
() () ()
∑∑ ∑
2 1 2 k
 
I−+ +⋅⋅+
()
∑ i
 n n n 
1 2 k
2  
Sp =      (24)
N−k
where:
I represents all readings;
i
n is the number of readings for each reference material;
i

N  is the total number of readings;
k is the number of test samples.

d) From the equation of the calibration curve
cA%=+IA         (25)
10
calculate the DL for a discharge:
DL= A ×t×Sp
        (26)
1
where:
t is the t of Student at 95 % for N - k degrees of freedom.
If r discharges are striken during an analysis:
DL
DLr =         (27)
r
where DLr is the limit of determination.
5.2.1.2 Quadratic base curve
Calculate a straight line with the lowest 5 points in the curve and compute as per point 5.2.1.1.
5.2.2 Instrument detection limit DLi
Perform 10 analyses on a reference material with an analyte concentration equal to the background. Calculate
the standard deviation of the resulting concentrations. DL is obtained from:
DLi = 3× 2×s
         (28)
0
where:
s is standard deviation of concentrations
0
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5.3 Determination of repeatability as relative standard deviation RSD
Over a short time period, perform 10 analyses on a reference material without making any drift correction
between an analysis and the other. The instrument repeatability RSD, with a 95 % confidence limit, is expressed
by:
2
d
()
∑ i
RSD= 2        (29)
21n−
()
where:
d is the difference between a given value (intensity or concentration) and the average value of it;
i
n is the number of analyses.
Calculate repeatability for at least 3 reference materials with low, medium and high concentration within the
calibration curve validity range.
5.4 Determination of accuracy SEA
Perform at least 10 analyses, each time making a drift correction, with a reference material belonging to a
specific analyte family that has not been used in the calibration curve construction. The spectrometer accuracy,
with a 95 % confidence limit, is expressed by:
2
()d

i
SEA= 2        (30)
21nI−−
()
where:
d is the difference between calculated and true concentration;
i
n is the number of analyses;
l is the degree of the calibration curve polynomial.
Calculate the instrument accuracy for at least 3 reference materials with low, medium and high concentration
within the calibration curve validity range.
6 Performing analysis
Place the sample on the sample table and position the ground surface over the counter electrode.
Excite the sample. At the end of the instrument analysis cycle, record the reading (if the intensity ratio is read),
or the concentration % m/m.
Reanalyze the sample, average the duplicate readings for each element.
Excite the samples in two opposite sides of the surface, half way between the center and the end of the grinded
surface.

13

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CR 10320:2004 (E)
7 Ordinary maintenance
It is suggested to carry out ordinary maintenance as per following schedule:
Table 1 — Maintenance schedule
Action Frequency
1.1
Check gas At least once a day
1.2
Check fluid At least once a day
1.3
Check parameters At least once a day
1.4
Clean stand Every 200 analysis, however once a day
1.5
Clean filter Every 200 analysis, however once a day
1.6
Sharpen point Every 15000 analysis
1.7
Clean lenses Every 15000 analysis
1.8
Check profile
1.8.1
Startup After 2 hours and every 8 hours during first week
1.8.2
Steady state Once a week during first month, then at least once a month.

Switching off and opening the spectrometer must be avoided, particularly in dusty environments and by
personnel other than maintenance staff.
During startup, profile must be checked at least against three wavelengths, low, medium and high respectively,
one of which should come from the matrix element, so that the whole spectrometer´s range is covered.
Subsequently, it will be sufficient to check profile against the analyte line of the matrix element.
Startup occurs when the spectrometer has been switched off for any reason and it is restarted after more than 8
hours. The experience suggests that for each hour off, one hour on is required to reach steady-state operation.
After 8 hours off, at least 24 hours on are required for steady state.
Frequencies as provided in the above table can be changed according to the manufacturer's instructions.
8 Quality control
8.1 Control chart
Soon after an instrumental drift correction is performed and then no later than every 4 hours, analyse reference
materials that have not been used in calibration curve construction. Record the test value of each certified
element on control charts as in the examples 9.8.
Acceptance limits are calculated from the correlation RDS vz. % of each element and concentration level.
Higher acceptance limit derives from nominal value + RSD, lower acceptance limit derives from nominal value -
RSD. The range +/- RSD is subdivided into 4 parts: the first quarter above nominal value is the higher control
limit, the first quarter below nominal value is the lower control limit.
The selected reference element is used for 2 analysis. The following cases may occur:
a) the average value lies within the HCL-LCL range;
b) the average value lies outside the above range, but within the HAL-LAL range;
c) the average value lies outside acceptance limits.
In case a) the instrument is calibrated and can be used for the following analysis.
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CR 10320:2004 (E)
In case b) it is advisable to carry out 2 analysis and record where the new average value lies. If the average
value lies as in point a), the instrument is calibrated. If it lies as in point b), two situations may occur:
b.1) the average value lies in the same area as formerly measured: the result is acceptable, but the risk exists
of one, though tolerable, systematic difference;
b.2) the average value lies in the opposite area: it is advisable to check the parameters affecting the
instrument repeatability, namely:
- point position and status;
- gas pressure;
- test surface;
- spectrometer temperature;
- profile;
- phototube stability;
- source stability.
Case c) means that the instrumental drift has probably not been corrected adequately. However, it is advisable
to repeat the analysis before correcting the instrumental drift.
8.2 Calibration curve control
Calibration curves in optical emission spectrometers tend to change over time. As an average, their validity as
established by experience is approx. 2 years. It is therefore advisable to check them every year. To this purpose,
a minimum 3 reference materials should be used, with low, medium and high analyte concentrations
respectively, that have undergone repeatability tests during calibration curve construction. After correcting the
instrumental drift, their intensity ratio should be measured. If the average value of 2 analysis per reference
material lies in the range Ia +/- 2s, where Ia is the average intensity ratio as obtained during the calibration
curve construction and s is the standard deviation from repeatability, the curve is still valid. If the average value
of 2 analysis with one refererence material lies outside the range Ia +/- 2s, the calibration curve is no longer
valid. It is therefore necessary to establish a new curve. The calculated values of I should be recorded on
calibration card, as in the example 9.9.
9 Examples
9.1 Determination of calibration curve
Table 2
Drift control Drift control Drift control
RefMat I RefMat I RefMat I
ii ii ii
1 13,23 5 30,031 13,56
2 18,83 4 26,865 30,48
3 16,07 3 16,012 19,60
4 27,09 2 18,824 26,22
5 30,13 1 13,383 16,06

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Table 3
Drift control Drift control Drift control
RefMat I RefMat I RefMat I
ii ii ii
1 13,48 5 30,603 16,22
2 18,87 4 27,614 26,68
3 16,13 3 16,122 18,58
4 26,12 2 18,815 29,73
5 30,00 1 13,321 13,40

Table 4
(1) (2) (3) (4) (5)

RefMat NBS 1265 BCS 405/1 BCS 431 NBS 1270 BCS 456/1

C % 0,0067 0,0340 0,0190 0,0770 0,1010

I 13,23 18,83 16,07 27,09 30,13
ii
13,38 18,82 16,01 26,86 30,03
13,56 19,60 16,06 26,22 30,48
13,48 18,87 16,13 26,12 30,00
13,32 18,81 16,12 27,61 30,60
13,40 18,58 16,22 26,68 29,73

average 13,40 18,92 16,10 26,76 30,16
80,37 113,51 96,61 160,58 180,97
Σm I
ii
2 1076,62 2148,03 1555,61 4299,21 5458,88
Σm I
ii

average C % =  0,0475
average I =  21,07
ii
Table 5
x 2 3 4
x x x
13,40 179,562406,10 32241,79
18,92 357,976772,72128139,94
16,10 259,214173,28 67189,82
26,76 716,1019162,77512795,77
30,16 909,6327434,31827418,73
105,34 2422,46 59949,19 1567786,07
Σ


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Table 6
y xy 2 2
xy y
0,0067 0,08978 1,2030520,000045
0,0340 0,64328 12,1708580,001156
0,0190 0,30590 4,9249900,000361
0,0770 2,06052 55,1395150,005929
0,1010 3,04616 91,8721860,010201
Σ 0,2377 6,14564 165,3106 0,017692

9.1.1 Calculation of a straight line correlation and its standard error
yA=+Ax         (31)
01
2
yx − xy x
() ( )
∑∑ ∑ ∑
A =       (32)
0 2
2
nx − x
()
()
∑ ∑
nxy − x y
()
∑∑∑
A =        (33)
1
2
2
nx − x
()
()
∑ ∑
A = 0,0056005
1
A = 0,0704511
0
2
[]n xy− x y
∑∑∑
2
r =
     (34)
2 2
2 2
[]() ()[]() ()
n x − x × n y − y
∑∑ ∑∑
2
r = 0,9969434
2
yA−−yA xy
() ( )
∑ 01∑∑
Syx =      (35)
n− 2
2
(Syx) = {[0,017692 + 0,0704511 × 0,2377 - 0,0056005 × 6,1456]/(5-2)}
= 0,00000659789
Sxy = 0,002569
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9.1.2 Calculation of a quadratic correlation and its standard error
2
yA=+Ax+Ax        (36)
01 2
Resolve the following system:

2 3 42
Ax++A x Ax= x y      (37)
() ( ) () ( )( )
0∑ 1∑ 2∑ ∑
2 3
Ax++A x A x= xy      (38)
() ( ) ( )
∑ ∑ ∑ ∑
01 2
2
An++A x A x= y       (39)
()
∑ ∑ ∑
01 2
where:
n is the number of data pairs
2
cc−
()
∑ it ic
2
r =−1        (40)
2
cc−
()
∑ it a
A = -0,0378397
0
A = 0,00234735
1
A = 0,0000741513
2
C 0,00693
ic:
 0,03312
 0,01917
 0,07808
 0,10041
C 0,047542
a:

2
r= [1 - (0,0000023707/0,00639163)]      (41)
2
r = 0,99963
2
2
()yA−−yA (xy)−A xy
∑ ∑ ∑ ∑
01 2
Syx=      (42)
n−2
2
(Syx) = {[0,017692 + 0,0378397 × 0,2377 – 0,00234735 × 6,14564 -   (43)
- 0,0000741513 × 165,3106]/(5-2)}
Syx = 0,00094
18

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SIST-TP CEN/CR 10320:2004

CR 10320:2004 (E)
9.1.3 Confidence limit and slope error in a straight line correlation
2
1()x −x
i m
Syc = Syx× +
2
      (44)
n
()x


Syx
Sb=         (45)
2
x
()

Table 7
x = x - x 2
i m (x -x )
i m
-7,67 58,8289
-2,15 4,6225
-4,97 24,7009
5,69 32,3761
9,09 82,6281
2
Σx = 203,1600

2 2
(Syc) = 0,00000659789 × [(1/5) + (-7,67) /203,16] = 0,00000323
Syc = 0,0018
Calculate Syc for all x .
i
2
(Sb) = 0,00000659789/203,16 = 0,0000000325
Sb = 0,00018
9.1.4 Confidence limit and slope error in a quadratic correlation
2
1()x −x
i m
Syc =Syx× +
2
      (46)
n ()
x

Syx
Sb=         (47)
2
x
()

2
2
(Syc) = 0,00000088855 ×{1/5,+,[-7,67 /203,16]}
2
(Syc) = 0,000000435
Syc = 0,0006596
19

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SIST-TP CEN/CR 10320:2004

CR 10320:2004 (E)
Calculate Syc for all x .
i
2
(Sb) = 0,0000000043736
Sb = 0,00006613

9.1.5 Correlation accuracy
The data stemming from the following example 9.5 can be used. The standard deviation from repeatabili
...

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