Apresentacao_NIST_youden-analysis-2_elipsys

Apresentacao_NIST_youden-analysis-2_elipsys

1. E
A
B
C
D
F
G
H
-15
-10
-5
0
5
10
15
-15 -10 -5 0 5 10 15
10 kg #1
10 kg #2 Youden Analysis

2. Youden Analysis
•Introduction to W. J. Youden
•Components of the Youden Graph
•Calculations
•Getting the “Circle”
•What to do with the results.

3. W. J. Youden 1900-1971
•Born in Australia
•1921 –B.S. in Chemical Engineering
•1924 –Ph.D. Analytical Chemistry
•1924-1948 –Plant Research
•1942-1945 –World War II
•1948 –NBS Statistical Consultant

4. Components of Youden Graph-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
-10
-9 -8 -7 -6 -5 -4 -3 -2 -1
0123456789
10
X Axis
Y Axis
2sd limit of
the random
components
45 degree
Origin (0,0)
Median(x,y)
Known(x,y)

5. Line Graphs to Youden GraphsE
A
B
C
D
F
G
H
-15
-10
-5
0
5
10
15
-15 -10 -5 0 5 10 15
10 kg #1
10 kg #2

6. Systematic and Random Components-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
-10
-9 -8 -7 -6 -5 -4 -3 -2 -1
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10
Plot the Point (-2,-7)
X-axis = -2 Y-
axis = -7
Total magnitude of
Error = 7.28
Calculated by using the
formula for the distance
between two points (x1,y1)
and (x2,y2):28.7
53494
)07()02(
)()(
22
2
12
2
12




d
d
d
yyxxd
Draw a line from
the Point to the 45
degree line
(Perpendicular)
Intercept Point )5.4,5.4(
5.4
2/)72(
2/)(



 yx

7. -10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
-10
-9 -8 -7 -6 -5 -4 -3 -2 -1
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10 Systematic and Random Components364.6
2/]9[
2/]5.45.4[
2/)]05.4()05.4[(
2/)]()[(
1212





d
d
d
d
yyxxd
Systematic Distance
from Origin to Intercept
Calculated by using a variation
of the Pythagorean formula for
45
o
right triangles:
Origin=(x
1,y
1)
Point = (x
2,y
2)
Random Distance from
Point to Intercept
Calculated using the formula for the
distance between two points:536.3
25.625.6
2]5.2[2]5.2[
)]5.4()7[()]5.4()2[(
)()(
22
2
12
2
12





d
d
d
d
yyxxd

8. Fitting the Ratio of Systematic & Random Errors
to the Total Error
Systematic Component = -6.364 (negative or positive)
Random Component = 3.536 (always positive)
Sum Random & Systematic = 9.900
Total Error = 7.280600.2)280.7(
900.9
536.3
680.4)280.7(
900.9
364.6




Random
Systematic

9. Where do we get the Circle?-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
-10
-9 -8 -7 -6 -5 -4 -3 -2 -1
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10
Random Error
=2.60
Each Point will
have a “Random
Error”

10. Each participant’s point provides a random error (ran).
Each random error is squared.
These squares are then summed and divided by n-1.
The square root of this result is an indication of the
standard deviation based onlyon the random
components of each point.
Multiplying the standard deviation by 2.45 gives the
value for the radius of the circle. (95% of the points
should fall within this circle if all systematic errors
could be eliminated.)1
2



n
ran
s
(modified) Calculating the radius of the Circle

11. Getting the Circle on the Graph
•Formula of a Circlecircle) of radius(r
222
 yxr 22
rxy 
•Formula rewritten in terms of y

12. Rules of Youden Analysis
•Requires Two Artifacts
–Must have two values to plot a point
•Artifacts must be same Nominal Value
–“Cannot compare Apples & Oranges”
•Same procedure must be used to test both Artifacts
–SOP -Restraint -Equipment -Metrologist
•Artifacts should not be Tested at Same Time
–Random errors appear to become more systematic when tested at the same time
•Participants should be working at the same precision level
•Don’t Over-Analyze
–A point that lies outside the circle doesn’t necessarily mean that there is a
problem (although it is never a good thing)

13. Let’s take a look
at the
Spreadsheet