Measurement & Uncertainty - Concept and its application

June. 20 2012

JongOh Choi (choijongoh@kriss.re.kr)

I don’t know what I don’t know.

If we don’t express what we know

in the form of numbers,

we really don’t know much about it.

If we don’t know much about it,

we can’t control it.

If we can’t control it,

we are at the mercy of chance.

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 -) - Uncertainty in Measurement (2003 -) - Reliability of Chemical measurement (National Research Laboratory 1999)

- Analytical chemistry

More than 270 Lectures on

Measurement & Uncertainty, Reference Materials, PT, QMS, Standards etc

Make it measurable !!!

To be your Choice

in Measurement

Very Practical Philosopher on Measurement

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

What are you going to do ?

Contents

1. Error vs. Uncertainty 2. Concept

- measurement, traceability, uncertainty

3. Uncertainty evaluation 4. Uncertainty in multiple measurements

GUM 2008, 1993

VIM

2007, 2nd ed.

SI 2006 (8th Ed.)

Unit Uncertainty Vocabulary

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 or partner

Measurement in your mind

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

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)

12

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.

GUM E.5.4.

Obtained from a training course on uncertainty

?

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

Value Value and uncertainty (k=2, 95 %, level of confidence)

Value for regulation Limit of Tolerance

uncertainty

Driver Under Influence with uncertainty

0.05 % 0

DUI I : Proper accusation?

the uncertainty is 0.003 %.

0.05 % 0

DUI II :

0.053 %

No more false

accusation ?

0.05 % 0

DUI III

0.053 %

U = 2 u ?

U = 3 u

0.05 % 0

DUI IV ?

0.055 %

U = 3 u ?

the uncertainty is 0.003 %.

Contents

1. Error vs. Uncertainty 2. Concept

- measurement, traceability, uncertainty

3. Uncertainty evaluation 4. Uncertainty in multiple measurements

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

Review

Error 2 and uncertainty

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.

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)

29

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?

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

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

Review

1. Measurement

process of experimentally obtaining one or more quantity values

that can reasonably be attributed to a quantity

2. Traceability

property of a measurement result whereby the result can be

related to a stated metrological reference through a documented

unbroken chain of calibrations of measuring systems, each

contributing to the measurement uncertainty

3. Measurement uncertainty

Parameter that characterizes the dispersion of the quantity values

that are being attributed to a measurand, based on the information

used. (VIM 3, 2007)

~ 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)

Conceptual changes of uncertainty

Classical approach

Uncertainty approach

1st

2nd

Range of true value (limit of error) vs. Uncertainty

Contents

1. Error vs. Uncertainty 2. Concept

- measurement, traceability, uncertainty

3. Uncertainty evaluation 4. Uncertainty in multiple measurements

Results from different instruments or laboratories

2

21 xxxy

)()( 2

c Buxuyu

Valu

e a

nd u

nce

rtain

ty

Measurement result can be different. ????

Time, method, place, person, procedure

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,

?

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 or partner

Measurement vs. Evaluation

JongOh CHOI

choijongoh @ kriss.re.kr

Please do not torture the data until it confess !!

© P De Bièvre BIPM NMU Symposium TSUKUBA 2005-05-16

PD

B05014

Metrologists set up a measurement model, then improve it, if necessary.

On the contrary, statisticians use the measured values to set up a statistical model, then explain the measurement results. We should take a KCRV as a result of collaborative measurement (to achieve compatible results), rather than of statistical treatments (for the explanation of errors). Source: JongOh Choi, BIPM-NMIJ-KCRV Workshop TOKYO 2005-05-16

Please don’t torture the data !!!!

No argument on measurement results!!!

0.8

0.85

0.9

0.95

1

1.05

1 2 3 4 5

This is what you are about to do.

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)

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

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

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

Argon concentration measurements in dry air.

Year Author Method of

measurements Argon concentration in

dry air (mmol/mol)

1895 Rayleigh and

Ramsey chemical 7.8-8.8

1895 Schloesing chemical 9.35 (0.02)

1895 Kellas chemical 9.37

1903 Moissan chemical 9.34 (0.02)

1911 Moureu and

Lepape chemical 9.32

1945 Cady and Cady chemical 9.35 (0.1)

1949 Chackett et al. chemical 9.17 (0.04)

1957 Oana chemical 9.17 (0.07)

1969

2004

Hughes

Park and Kim

Mass spectrometry

Mass spectrometry

9.16 (0.10)

9.331 (0.003)

10 ppm 0

Compliance or not