Measurement & Uncertainty - Basic concept and its application
Feb. 7. 2012
JongOh CHOI ([email protected])
Sir William Thomson, Lord Kelvin (1824-1907)
“When you can measure
what you are speaking about,
and express it in numbers,
you know something about it;
but when you cannot measure it,
when you cannot express it in numbers,
your knowledge is of a meager and unsatisfactory kind;
it may be the beginning of knowledge,
but you have scarcely in your thoughts advanced
to the state of science, whatever the matter may be.”
Knowledge and measurement
, etc
Head, Center of Standards and Quality management
Chair, Uncertainty committee of KRISS
Education
Ph. D. Analytical Chemistry, (1992) M. Eng. Chemical Engineering, (1983) B. Eng. Chemical Engineering, (1981)
Field of Interest
- Quality of Management (2005 -) - Vocabulary in Metrology (2004 -)
- Uncertainty in Measurement (2003 -) - Reliability of Chemical measurement (National Research Laboratory 1999)
- Analytical chemistry
More than 260 Lectures on
Measurement & Uncertainty, Reference Materials, PT, QMS, etc
Make it measurable !!
No argument on measurement results!!!
Contents
1. Concept - measurement, traceability, uncertainty
2. Uncertainty evaluation 3. Error vs. Uncertainty 4. Uncertainty in multiple measurements
1. Temperature of this room
2. What time is it now?
3. Concentration of caffeine of this tea
4. Hardness testing
5. IQ (Intellectual Quotient) test
6. Ordering based on children’s height.
7. Evaluate the performance of staff members.
8. Evaluate the customer satisfaction of our service.
9. Choosing your job
measurement in your mind
1. Length
2. Height
3. …..
4. …….
5. …….
measurement in your mind II
Compilation : What are you going to do ?
GUM 2008 VIM
2007, 2nd ed.
SI 2006 (8th Ed.)
Unit Uncertainty Vocabulary
Vocabulary
• Quantity property of a phenomenon, body, or substance, to which a number
can be assigned with respect to a reference
• Value
number and reference together expressing magnitude of a quantity
• Measurand : quantity intended to be measured
• Measurement
process of experimentally obtaining one or more quantity values that can reasonably be attributed to a quantity
• Measurement result information about the set of quantity values being attributed to a measurand
Measurement result
Value Value and uncertainty
Value for regulation Limit of Tolerance
uncertainty
10 ppm 0
Compliance or not
Zanzibar effect
Measurement, traceability and uncertainty
Measurement Result
(Value and uncertainty)
Known value and its uncertainty
( in Reference)
Measurement
Unknown/Known
Measurement
Standards
(include CRM) Given uncertainty
Uncertainty in comparison
Uncertainty in the value
=
+ References
Standard Procedure
(ISO Standards)
Measurement Procedure
(ISO standards, EPA methods
IAEA methods)
16
Approach 1: Standardization
“harmonized methods”
International Harmonisation
Approach 2: Metrology
“Metrological traceability”
“Measurement uncertainty”
prescribed method-performance
characteristics
prescribed methods/procedures
Who is going to win in the court?
review
New need for traceability?
Unit: cube meter (SI-System)
Primary or Reference
Measurement Standard:
granite cube gauge blocks/laser,
Interferometer
Working Measurement
Standards:
wooden cube micrometers, vernier caliper,
etc.
Application: manufacture of stone blocks
or pieces
control of dimensions
Recalibration period: each full moon according to frequency of
usage
Traceability: local International
Ancient Egypt Modern World
Traceability : after the measurement ???
Metrological traceability: VIM 3 (2007)
− property of measurement result whereby the result can be related reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty
Quantity
property of a phenomenon, body, or substance, to which a number can be
assigned with respect to a reference (VIM3)
Role of MS, CRM and MP !!!
It is the pre-requisite for your measurement !!!
CIPM-MRA
on calibration and measurement certificate
ILAC-MRA
on calibration and testing certificate NMI
Accredited
Lab.
Industrial work site
Country A
Country B
NMI
Accredited
Lab
Industrial work site Country C
Traceability
NMI
Accredited
Lab.
Industrial work site
Calibration
CRM
Worldwide compatibility
through worldwide comparability of measurement results.
One measurement, Accepted everywhere !!!
One standard, One test, Accepted everywhere !!!
KCs according to the MRA signed in 1999
KC
자동차 배기가스 중 일산화탄소 농도 분석 / 세계 최고의 측정능력 입증
- 이탈리아 표준기관(IEN)에 오존가스 표준측정기 제작 수출
한국 KRISS
미국 NIST 독일
PTB 일본 NMIJ
영국 NPL
국제비교 217개 분야 참여
* 국제비교 참여실적(217건) : 세계 6위
Gas Measurement
Key Comparison, 1 kg
Contents
1. Concept - measurement, traceability, uncertainty
2. Uncertainty evaluation 3. Error vs. Uncertainty 4. Uncertainty in multiple measurements
Uncertainty Evaluation
Sampling Analyst
extraction
stability
matrix
ability
experience
Laboratory Reagent Instrument
Temp
humidity
pressure
Reference m.
purity
impurity
resolution
automation
drift
Data treatment
Calibration
Assumption
Result
Variation of each parameter
Guide to the expression of Uncertainty in Measurement (GUM), 1993, BIPM,IEC,IFCC,ISO, IUPAC, IUPAP, OIML
Modeling the measurement
Identifying uncertainty components for each input quantity
Evaluating standard uncertainty Type A, Type B
Combining standard uncertainties of input quantities
Expanded uncertainty
Coverage factor
Sensitivity coefficient
5 steps in MU evaluation
n
su
nsu
sor
),...,,( 21 nxxxfy
ixu
iN
i i
xux
fyu 2
2
1
2
c )(
2k
)(c yukU
),...(),(),(
3,
2,
1,
i
i
i
xuxuxu
Type A evaluation of uncertainty
• Mean
• Standard Deviation
• S.D of the mean
• Degree of freedom
n
xx i
1
)( 2
n
xxs
i
n
s
1 n
3 Standard Uncertainty n
sui
Type B evaluation
• Previous measurement data
• Experience with or general knowledge of the
behavior and properties of relevant materials and
instrument
• Manufacturer’s specifications
• Data provided in calibration and other certificate
• Uncertainties assigned to reference data taken
from handbooks
Traceability of mass
The kilogram is the unit of mass; it is equal to the mass of
the international prototype of the kilogram.
NMI
BIPM
Uncertainty evaluation
Weight using a balance at home,
72.45, 72.54, 72.53, 72.44, 72.39, 72.51, 72.33 kg
1) My weight?
2) Standard uncertainty ?
3) Expanded uncertainty ?
Calibration report
2,kg05.012.7200000.72 k
Result
Observation 72.45 72.3972.54 72.5172.53 72.3372.44
Mean 72.45571Std. Dev. 0.077429Std. Unc. 0.029265 Type A evaluation
Correction 0.12Std. Unc 0.025 0.05 k =2 Type B evaluation
Result 72.336Comb. Std. Unc. 0.038Exp. Unc 0.077
cxy )()()( 2
B
2
Ac cuxuyu
Valu
e a
nd u
nce
rtain
ty
Measurement result can be different. ????
Time, method, place, person, procedure
Contents
1. Concept - measurement, traceability, uncertainty
2. Uncertainty evaluation 3. Error vs. Uncertainty 4. Uncertainty in multiple measurements
Conceptual changes of uncertainty
~ 1992 An estimate characterizing the range of values with which
the true value of a measurand lies (VIM 1)
~ 1984 A measure of the possible error in the estimated value of the
measurand as provided by the result of a measurement
~ 2007 Parameter associated with the result of a measurement, that
characterizes the dispersion of the values that could reasonably be
attributed to the measurand (VIM 2)
2008 ~ Parameter that characterizes the dispersion of the quantity
value that are being attributed to a measurand, based on the information
used. (VIM 3)
38
GUM E.5.4.
While the approach based on “true” value and
error yields the same numerical results as the approach taken in this Guide, this Guide’s concept of uncertainty eliminates the confusion between error and uncertainty. Indeed, this Guide’s operational approach, wherein the focus is on the observed (or estimated) variability of the value, makes any mention of error entirely unnecessary.
Reminder
Error
In general, a measurement has imperfections that give rise to an error in the measurement result.
Error = Measurement result – True vale
True value : value consistent with the definition of a given particular quantity
Error 1 = Measurement result – True vale True value : value consistent with the definition of a given particular quantity
Defining two errors
Error 2 = Measured value – Reference value
Reference value (Assigned value) :
The reference quantity value can be a true quantity value of the measurand,
in which case measurement error is unknowable, or an appropriate, known
quantity value such as a conventional quantity value or a specified target
quantity value to be realized in a production process.
Error 2 and uncertainty
What is your interpretation?
The objective of a measurement is to determine the value of the measurand. (GUM, 1993)
- True value (error approach)
- Measured value (uncertainty approach)
1st
2nd
Range of true value (limit of error) vs. Uncertainty
Contents
1. Concept - measurement, traceability, uncertainty
2. Uncertainty evaluation 3. Error vs. Uncertainty 4. Uncertainty in multiple measurements
(Beyond repeatability conditions and GUM)
- Different locations - Different methods - Different instruments
Results from different instruments or laboratories
Something to remember
Diazinon (Day-to-Day Results)
0
1
2
3
4
5
6
7
Lab. Code
Re
su
lts
(m
g/k
g)
A-4 A-7 A-14 A-9 A-3 A-12 A-6 A-10 A-5 A-2 A-13 A-8 A-11 A-1
Day 1
Day 2Day 3
Overall
2
21 xxxy
)()( 2
c Buxuyu
Uncertainty for multiple measurements by GUM
JongOh CHOI et al.
1. Uncertainty evaluation for multiple measurements by GUM,
Accred. Qual. Assur 8 : 13 (2003)
2. Uncertainty evaluation for multiple measurements by GUM, II
Accred. Qual. Assur 8 : 205 (2003)
3. Uncertainty evaluation for multiple measurements by GUM, III
Accred. Qual. Assur (2008)
kysyuyu /)()()( wAPA,
?
Contents
1. Concept - measurement, traceability, uncertainty
2. Uncertainty evaluation 3. Error vs. Uncertainty 4. Uncertainty in multiple measurements
0.8
0.85
0.9
0.95
1
1.05
1 2 3 4 5
This is what you are about to do.
JongOh CHOI
choijongoh @ kriss.re.kr
Make it measurable !!
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