4. Accuracy and Precision

5. Accuracy- indicates the difference between measured value and the expected (true) value. If observed (measured) values are near the expected (true) value, the measurement has high accuracy.
Precision- indicates the differences among each measured value; if measured values are close together the measurement has high precision.

6. A Precise Score 4 Arrows from Contestant #2 14th Annual
Archery Contest
4 Arrows from
Contestant #1
The two contestants are highly precise, however, their accuracy is not very good. There is some subtle problem with their equipment or how they are using it.

7. A Precise and Accurate Score
14th Annual
Archery Contest
4 Arrows from
Contestant #3
The third contestant has a score that is precise and accurate.

8. Neither Precise nor Accurate Score
14th Annual
Archery Contest
14th Annual
Archery Contest
Neither Precise nor Accurate Score
Archery Contest
14th Annual
4 Arrows from
Contestant # 4
Archery Contest
14th Annual
The fourth contestant should not quit their other sport.
(This contestant needs to work on the concept of 4 arrows as well)

9. Accuracy of a measurement describes the difference between an observed value and the expected (true) value. If observed value is near the expected (true) value, measurement has high accuracy.
Precision of a measurement describes the differences among individual measurements themselves; if they are close together there is high precision.

10. Accuracy and Precision
How do we quantify these observations so that we can attach a number to the ideas of precision and accuracy of each event?
Accuracy and precision have no quantitative significance, and are used in a rough descriptive sense only.

11. Error and Deviation
Error expresses accuracy in the form of a number that relates the measured value to the true (expected) value.
Deviation expresses precision in the form of a number that relates the measured value to its closeness to other measured values.

12. Error
Error expresses accuracy in the form of a number that relates the measured value to the true (expected) value.
Error is the numerical difference between the observed value, xi and expected (true) value, .

13. Error
Error is the numerical difference between the observed value, xi and expected (true) value, .
For this case, the expected
position on the target for the expert is assigned the true (expected) score. This position is assigned a distance value of 0 and distance from this perfect score point on the target to an actual contestant point on the target is the error.

14. Error
Error is the numerical difference between the observed value, xi and expected (true) value, .
This is the center point that is used to measure a radius
to each of the 8 target points shown.

15. Error Contestant # 1 try # error 1 8.0 2 9.5 3 9.5 4 8.3
Error is the numerical difference between the observed value, xi and expected (true) value, . 11 9 7 4 6 10
Contestant # 1
try # error 2 6 1
8.0 2
9.5 3
9.5 4
8.3
This is the center point that is used to measure a radius
to each of the 8 target points shown.

16. Error Contestant # 2 try # error X5 ? 10.5 X6 10.5 X7 9.5 X8 9.5
In this example, the perfect score, , is equal to zero. A contestant's score, xi, is subtracted from to indicate the error. X5 ?
10.5 X6
10.5 11 X7
9.5 9 6 X8
9.5 7 5
= perfect score = 0
Error =(observed score, xi ) - 2
X = = 10.5
X = = 8.0
Error Calculation
X = = 9.5
X = = 9.5
X = = 8.3
X = =10.5
X = = 9.5
X = = 9.5 2
Contestant # 1
try # error X1
( ) = 8.0 X2
( ) = 9.5 X3 X4
( ) = 8.3 6 8 10

17. Deviation 11 9 6 7 5 2 2 6 11 6 8 10

18. Deviation Contestant # 1 1 8.0 2 9.5 3 4 8.3 try # Xi Score
One measure of precision is the numerical difference between the observed value, xi , and mean value for that group of measurements.
This is known as the deviation.
Deviation
Deviation Calculations X1
= - 0.8 = X2
= 0.7 X3 X4
= -0.5 11
Contestant # 1 1
8.0 2
9.5 3 4
8.3
try # Xi
Score X1 X2 X3 X4 9 6 7 5 2
Note: X1 = = 8.8 2 6 11 6 8 10
Mean score for contestant # 1
( ) n =
(X1 + X2 + X3 + X4)
(35.3) 4
(8.83)
X1 =

19. Deviation Contestant # 2 1 10.5 2 3 9.5 4 try # Xi Score X5 X6 X7 X811
Deviation Calculations 9 6 7 X5 = X2 = X7 = X8 = X6 5 2 2 6
Note: X2 = 10.0 8 10
Mean score for contestant # 2
( ) n =
(X5 + X6 + X7 + X8)
(40.0) 4
(10.0)
X2 =

20. Why? Who won? 14th Annual Archery Contest # 2 ?
Error and Deviation
Accuracy and Precision
Contestant # 2
Note: X2 = average score for contestant #2 = 10.0
Average Error
Average Deviation
10.0
0.1
14th Annual
Archery Contest 10 8 6 5 2 9 7 11
# 2 ?
Why is Contestant #1 average deviation = 0?
This person did not always hit the exact same spot on the target!
Why?
Who won?
Which contestant is
a better archer?
# 1 ?
Note: X1 = average score for contestant #1 = 8.8
Contestant # 1
Average Error
Average Deviation
8.8
0.0
Why are the average scores equal to the average errors?
How can we change the average deviation calculation so that a zero value only happens when all the arrows hit the same spot?
Does that always happen?

21. Precision Repeatability Hysteresis
(As the idea is used in high tech manufacturing).
Repeatability
A term often used to indicate if the measuring system, the measuring device, the computer and the person, give the same measurement value each time a measurement is made under the same set of condition.
Hysteresis
A term used to indicate that a measurement system recording values of temperature, for example, does not give the same temperature value as the temperature is going up when compared to when the temperature is going down.

22. An Example for the term Repeatability
Precision
An Example for the term Repeatability
In the process of manufacturing 300 or so chip on the surface of each silicon wafer, a set of wafers
are placed in a very hot furnace.
In fact, the wafers shown entering this furnace will be placed in and out of the furnace at lest 10 time before the chips are completely fabricated.

23. Precision (Repeatability) The process specialist must operate
the furnace computer control
system and also analyze the
temperature data as the
furnace temperature goes up
and then down.
The wafers enter the furnace
when the furnace temperature
is at 700 oC. The temperature is then raised slowly a rate of , 5-10 oC per minute, until it gets over 1000 oC.

24. Precision (Repeatability) The table below shows the performance
of two different temperature sensors. Both sensors measure temperature from 700 oC to 1200oC. Either one could be use in the furnace.
Which one would you recommend be
use as a replacement sensor?
Device #1 #2
1010 oC
1011 oC
1012 oC
1009 oC
1013oC
1008 oC
1011 oC
1010 oC
1014 oC
1008 oC
Note:
Data in table represents 5 repeated measurements for each device. All measurements taken at the same conditions

25. The table showed the performance of two new temperature sensors taking replicate measurements under the same furnace conditions. Either one could be used as a replacement for the temperature sensor now in use.
Which one would you recommend be use as a
replacement sensor?
Device #1 #2
1010 oC
1012 oC
1013oC
1011 oC
1014 oC
1009 oC
1008 oC
The correct one to select as a replacement is the one that is more repeatable.
Therefore, the only issue now is figure out how to calculate the repeatability.
Repeatability and deviation are calculated in a similar but not identical fashion.

26. Repeatability
The calculation for Repeatability is exactly like the calculation for determining a percent grade on a quiz or test. } {
Ggrade =
(the grade you got on your test)
(the range of possible scores on
the test)
100 } {
Rrepeatability =
(the measured temperature value)
(the range of possible temperatures
that could be measured)
100

27. } { } { } { ? Grade ( %) Calculation examples Ggrade =
(the grade you got on
your test)
(the range of possible scores
on the test)
100 } { } {
52 points (test #1 Student #2)
53 (test 2, student #1)
54 (test 1, student #1)
100
= 90%
88% ?
87%
Ggrade =
60 points
Scores from 0 to 60 are possible
Student #1
Student #2
Test
number 1
54 points
90%
52 points
87% 2
53 points
88%
51 points
55 points
49 points
92%
82%
85% 3
56 points
55 points
93%
92% 4 5

28. } { } { } { It does not make any difference which sensor is installed.
Repeatability (%) Calculation examples } {
Rrepeatability =
(the measured temperature
value)
(the range of possible
temperatures that could
be measured)
100
It does not make
any difference
which sensor is
installed. } { } {
1010 oC (temp 1, Device #1)
1011 oC (temp1, Device 2)
1012 oC (temp 2, Device #1)
100
= 84% ?
84%
84.3%
Rrepeatability =
1200 oC
Device #1 #2
1010 oC
1012 oC
1013oC
1011 oC
1014 oC
1009 oC
1008 oC
Temperatures from 0 to 1200 oC are possible 1 2 3 4 5
Device #1 #2
Replicate
measurement
1010 oC
84%
1011 oC
84%
1012 oC
84%
1009 oC
1008 oC
1010 oC
84%
1013 oC
1011 oC
1014 oC
84%
85%

29. Repeatability } {
Rrepeatability =
(the measured temperature
value)
(the range of possible
temperatures that could
be measured)
100
There are many types of temperature sensors that can be used to measure the temperature inside a very hot furnace.
Most of these devices will measure temperature over a shorter range than 0 oC to 1200 oC.
When this is the case, the Repeatability calculation is done using a more general rule (equation).

30. Repeatability } {
Rrepeatability =
(the measured temperature
value)
(the range of possible
temperatures that could
be measured)
100
Many temperature sensor can measure temperature over a shorter range than 0 oC to 1200 oC.
When this is the case, the Repeatability calculation is slightly different. } {
Rrepeatability =
[ (the measured temperature value) -
(lowest measurable temperature in range )]
(the range of possible temperatures that could
be measured)
100

31. What is the repeatability for the following two temperature devices if they have a temperature measurement range from 700 oC to 1200oC? } {
Rrepeatability =
100
(1010 oC oC) Temp # 1, Device # 1
(1200 oC oC)
100 } {
Rrepeatability = =
1012 oC (temp 2, Device #1)
311 oC (temp1, Device 2)
310 oC (temp 1, Device #1)
62%
500 oC
Device #1 #2
1010 oC
1012 oC
1013oC
1011 oC
1014 oC
1009 oC
1008 oC
1010 oC
Temperatures from 700 oC to 1200 oC possible 1 2 3 4 5
Device #1 #2
Replicate
measurement
62%
1011 oC
62%
1012 oC
62%
1009 oC
1008 oC
1010 oC
62%
1013 oC
1011 oC
1014 oC
63%
62%

32. Temperatures from 700 oC to 1200 oC possible3 4 5
Device #1 #2
Replicate
measurement
1012 oC
1013 oC
1011 oC
1014 oC
1010 oC
62%
63%
1011 oC
1009 oC
1008 oC
1010 oC
62%
Thus when the two sensors have a shorter range, Device # 2 has a more consistence performance.

33. Accuracy and Precision
( a quick concept review)

34. Accuracy and Precision
( a quick concept review)

35. An example for Accuracy or Precision?
Accuracy and Precision
( a quick concept review)
An example for Accuracy or Precision?
An example for Error or Deviation?

36. Accuracy and Precision
( a quick concept review)

37. An example for Accuracy or Precision?
Accuracy and Precision
( a quick concept review)
An example for Accuracy or Precision?
An example for Error or Deviation?

38. An example for Accuracy or Precision?
Accuracy and Precision
( a quick concept review)
An example for Accuracy or Precision?
An example for Error or Deviation?

39. Accuracy and Precision
( a quick concept review)