Measurement & Uncertainty - Basic concept and its application

Feb. 7. 2012

JongOh CHOI (choijongoh@kriss.re.kr)

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 !!