practical approach to measurement uncertainty in a civil

A Practical approach to

measurement uncertainty in

a civil materials laboratory

settingSession M309

Objectives

➢ Background;

➢ Systematic Approach to Measurement Uncertainty;

➢ Uncertainty of Measurement (UoM) example focussing

on compacted voids determination;

➢ Summary.

❖ With support of: G. Mturi & K. Mogonedi, CSIR

B. Pearce, Learning Matters etc

H. Badenhorst, NLA

2

Background

“A measurement without a clear

understanding

of uncertainty lacks merit” ¹

¹ O’Connell et al., 2011

3

Background

² Cambridge University Press, 2019

4

What is measurement uncertainty:

Measurement:

“a value, discovered by measuring, that corresponds to the size, shape, quality, etc. of

something”²

Uncertainty:

“a situation in which something is not known, or something that is not known or certain” ²

Measurement ≠ True Value

𝑴𝒆𝒂𝒔𝒖𝒓𝒆𝒎𝒆𝒏𝒕 = 𝑩𝒆𝒔𝒕 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 ± 𝑼𝒏𝒄𝒆𝒓𝒕𝒂𝒊𝒏𝒕𝒚

Why is measurement uncertainty determination and use important and what

effect does it have:

It provides the range of error within which the true value of a measurement will

fall;

Requirement for testing and calibration facilities endeavouring to obtain or

maintain SANAS 17025 status under clause 7.6 of SANS 17025 standard;

Results coming from civil materials laboratories are used for pass/fail decision

making in engineering and construction projects;

Results are used to determine whether materials are suitable for use in specific

applications:

What is the cost of erroneous results or results provided without a known

degree of uncertainty to our clients/stakeholders?

Background

5

Background

6

How is measurement uncertainty determined in a civil materials setting:

Measurement uncertainty can be daunting to grasp, calculate and use effectively,

but…

The trick is not to panic and realise that civil materials can be

inherently variable and can cause significant error in results by

itself and we just have to take it one step at a time.

Measurement Uncertainty Approach

7

How do your results become traceable back to international standard?

𝑈𝐼𝑆𝑂

𝑈𝑁𝑆𝑂 = 𝑈𝑁𝑅𝑆 + 𝑈𝐼𝑆𝑂

𝑈17025 𝐶𝑎𝑙 = 𝑈𝑁𝑅𝑂 + 𝑈𝐿𝑎𝑏 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑠 𝑢𝑐 =

𝑖=1

𝑛

𝑢𝑖2


8

ISOGUM – ISO Guide to the Expression of Uncertainty

Develop a model of the uncertainty measurement process;

Determine the uncertainty components based on the model;

Calculate the sensitivity coefficients;

Calculate the component uncertainties;

Calculate the associated degrees of freedom as required;

Convert all uncertainties into uncertainties expressed in the same

units as the measurand;

Combine all the uncertainties. ¹



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Develop a model of the uncertainty measurement process;

The model must be realistic and must categorise variation inducing

factors into their respective variation types including their analysis regimes.


Type A Analysis

Statistical calculation

Type B Analysis

Non-statistical, ex. Calibration certificate

uncertainties, reference tables or books,etc.

Random Error

- Always present

- Unpredictable

- Caused by instrumentation, changes in

environmental conditions, etc.

- Can use statistical analysis to analyse data

Systematic Error

- Predictable and typically constant

- Causes can be accounted for or eliminated

- Often caused by imperfect observation

methods or calibrations


10


Determine the uncertainty components based on the model:

Isolate each component in the model that is anticipated to cause

variation in the measured results.

Calculate the sensitivity coefficients:

Sensitivity coefficients are multipliers that are used to convert uncertainty

components into the correct units of measure and magnitude required. ³

Not needed if the component is already in the unit and magnitude required. ³

Calculate the component uncertainties:

Determine component uncertainty 𝑼𝒊 as laid out in model.


³ ISOBUDGETS, 2019


11


Calculate the associated degrees of freedom as required:

“The number of values in the final calculation which are free to vary” ³

Convert all uncertainties into uncertainties expressed in the

same units as the measurand:

Use sensitivity coefficients determined to convert uncertainties into same

measurement unit.

Combine all the uncertainties:

𝑢𝑐 =

𝑖=1

𝑛

𝑢𝑖2

³ ISOBUDGETS, 2019

Measurement Uncertainty Example

12

To illustrate an approach toward measurement uncertainty determination,

let us utilise the process to determine the uncertainty involved with the

determination of voids in compacted asphalt specimens.

To start, one must first isolate the variables of the voids calculation:

𝑉𝑜𝑖𝑑𝑠 =𝑀𝑉𝐷 − 𝐵𝐷

𝑀𝑉𝐷𝑥 100

Where:

BD – Bulk density of compacted density determined from SANS 3001 AS10

MVD – Maximum voidless density determined from SANS 3001 AS11

Overall uncertainty of measurement for compacted voids is thus

compounded from the UoM of the MVD and the BD test procedures.


13

Something to keep at the back of your mind as we go through the process….

Sources of Error

Samples

Procedure

PeopleEnvironment

Equipment


BD uncertainty analysis model:

14


BD uncertainty analysis:

Possible error inducing factors

Equipment People Procedure Environment Sample

Thermometer Competency Specimen

temperature

Ambient

temperature

Incoming sample

representativeness

Waterbath Multiple operators

performing tests

Soaking time Humidity In-lab sample

handling to obtain

test specimens

Digital Balance Time constraints Handling time

before SSD

Multiple test

influence

UoM stemming from

compaction process

Cloth Attention to detail Cloth dampness Space limitations

Stopwatch/Timer



1. Standard Uncertainty (𝑈𝑠) for inherent variability of the material _ Type A

… Experimental Standard deviation of the mean (EDSM):

𝑬𝑫𝑺𝑴 =𝝈

𝒏=𝟖. 𝟏𝟑

𝟏𝟔= 𝟐. 𝟎𝟑 𝒌𝒈/𝒎𝟑

2. Temperature effect uncertainty (𝑈𝑇) _ Type B

Thermometer uncertainty -> ± 0.2°C

thus

0.4307 𝒌𝒈/𝒎𝟑/ °C x 0.2 °C = ± 0.09 𝒌𝒈/𝒎𝟑

𝑼𝑻 =𝟎. 𝟎𝟗

𝟑= 𝟏. 𝟕𝟑𝒌𝒈/𝒎𝟑

y = -0.4307x + 2588.1R² = 0.94942576

2576

2577

2577

2578

2578

2579

2579

20 22 24 26 28 30

BD

Temperature

Change in BD with Variation in temperature

Note: This is

only an exerpt

from the full

analysis for

illustration

purposes



3. Soaking Time effect (𝑈𝑠𝑡) _ Type A

Taking variation within the 3 – 5 minutes soaking time limits from the

method into account:

𝑈𝑠𝑡 =𝝈

𝒏=

𝟑.𝟑𝟗

𝟖= 𝟏. 𝟐𝟎 𝒌𝒈/𝒎𝟑

4. Handling time effect (𝑈ℎ𝑡) _ Type A

As method does not specify handling time, standard procedure for lab of <20 seconds was

checked in conjunction with 10 seconds handling time variance.

𝑼𝒉𝒕 =𝟕. 𝟐𝟖

𝟑𝟐= 𝟏. 𝟐𝟗𝒌𝒈/𝒎𝟑

Note: This is

only an exerpt

from the full

analysis for

illustration

purposes



BD combined uncertainty (𝑈𝐵𝐷𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑)

The BD of the specimens tested for this particular sample is therefore:

2572 ± 3 𝒌𝒈/𝒎𝟑

𝑢𝑐 =

𝑖=1

𝑛

𝑢𝑖2

𝑢𝑐 = 𝑢𝑠2 + 𝑢𝑇

2 + 𝑢ℎ𝑡2 + 𝑢𝑠𝑡

2

𝑢𝑐 = 2.032 + 1.732 + 1.292 + 1.202

𝒖𝒄 = 𝟑. 𝟐𝟎 𝒌𝒈/𝒎𝟑 ≅3 𝒌𝒈/𝒎𝟑Note: This is

only an exerpt

from the full

analysis for

illustration

purposes

MVD uncertainty analysis model:


19

Measurement Uncertainty Example MVD uncertainty analysis:

Possible error inducing factors

Equipment People Procedure Environment Sample

Thermometer Competency Sample

temperature

Ambient

temperature

Incoming sample

representativeness

Waterbath Multiple operators

performing tests

Time under vacuum Humidity In-lab sample

handling to obtain

test specimens

Digital Balance Time constraints Vacuum pressure Multiple test

influence

Pressure gauge/

manometer

Attention to detail Flask handling Space limitations

Stopwatch/Timer Shaking intervals

Soap solution effect


MVD uncertainty analysis:

1. Standard Uncertainty (𝑈𝑠) for inherent variability of the material _ Type A

… Experimental Standard deviation of the mean (EDSM):

𝑬𝑫𝑺𝑴 =𝝈

𝒏=𝟐. 𝟎𝟖

𝟏𝟐= 𝟎. 𝟔 𝒌𝒈/𝒎𝟑

2. Temperature effect uncertainty (𝑈𝑇) _ Type B

Thermometer uncertainty -> ± 0.2°C

thus

0.5806 𝒌𝒈/𝒎𝟑/ °C x 0.2 °C = ± 0.12 𝒌𝒈/𝒎𝟑

𝑼𝑻 =𝟎. 𝟏𝟐

𝟑= 𝟏. 𝟕𝟑𝒌𝒈/𝒎𝟑

Note: This is

only an exerpt

from the full

analysis for

illustration

purposes

y = -0.5806x + 2686.4R² = 0.998

2669

2670

2671

2672

2673

2674

20 22 24 26 28 30

MVD

Temperature

Change in MVD with Variation in temperature



3. Pressure effect (𝑈𝑃𝑟) _ Type A

(Note: can also have a type B component depending on equipment setup)

Method specifies 30mm Hg vacuum pressure, variation checked at 20, 25 a& 30mm Hg:

𝑈𝑃𝑟 =𝝈

𝒏=

𝟑.𝟐𝟐𝟏

𝟐𝟏= 𝟎. 𝟕𝟎 𝒌𝒈/𝒎𝟑

Note: This is

only an exerpt

from the full

analysis for

illustration

purposes



MVD combined uncertainty (𝑈𝑀𝑉𝐷𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑)

The MVD of the specimens tested for this particular sample is therefore:

2672 ± 2 𝒌𝒈/𝒎𝟑

𝑢𝑐 =

𝑖=1

𝑛

𝑢𝑖2

𝑢𝑐 = 𝑢𝑠2 + 𝑢𝑇

2 + 𝑢ℎ𝑡2

𝑢𝑐 = 0.62 + 1.732 + 0.702

𝒖𝒄 = 𝟏. 𝟗𝟔 𝒌𝒈/𝒎𝟑 ≅ 𝟐 𝒌𝒈/𝒎𝟑Note: This is

only an exerpt

from the full

analysis for

illustration

purposes

Combined uncertainty of both MVD and BD testing results in:

Measurement Uncertainty Example BD

Error

MVD

Error

Voids

Error

24

𝑉𝑜𝑖𝑑𝑠 =𝑀𝑉𝐷 −𝐵𝐷

𝑀𝑉𝐷𝑥 100 =

2672 −2572

2672𝑥 100 = 3.7%

𝑈𝐵𝐷 = 3 𝑘𝑔/𝑚3 𝑈𝑀𝑉𝐷 = 2 𝑘𝑔/𝑚3

𝑅𝑒𝑠𝑢𝑙𝑡𝐵𝐷 = 2572 𝑘𝑔/𝑚3 𝑅𝑒𝑠𝑢𝑙𝑡𝑀𝑉𝐷 = 2672 𝑘𝑔/𝑚3

Resultant voids:

But …

What about the uncertainty?????????????

Combined uncertainty of both MVD and BD testing results in:


25

𝑽𝒐𝒊𝒅𝒔 =𝑀𝑉𝐷 −𝐵𝐷

𝑀𝑉𝐷𝑥 100 =

2672 −2572

2672𝑥 100 = 𝟑. 𝟕%± 𝟎. 𝟐%

𝑈𝐵𝐷 = 3 𝑘𝑔/𝑚3 𝑈𝑀𝑉𝐷 = 2 𝑘𝑔/𝑚3

𝑅𝑒𝑠𝑢𝑙𝑡𝐵𝐷 = 2572 𝑘𝑔/𝑚3 𝑅𝑒𝑠𝑢𝑙𝑡𝑀𝑉𝐷 = 2672 𝑘𝑔/𝑚3

Due to the uncertainty of both MVD and BD:

BD

Error

MVD

Error

Voids

Error

Summary

Determining and communicating the degree of uncertainty of

measurement that your results have, give validity to your results no

matter how insignificant it might seem;

Going through the process of determining your uncertainty, gives you the

tools to narrow down on sources of error in your testing environment and

assists in addressing/eliminating them;

Always check the validity of your results within the context of your UoM

range. Repeat results that fall outside of UoM range, are invalid;

It is not necessary to determine uncertainty of measurement of every

single aspect, if there is suitable evidence as to how the factor is

addressed and maintained constant.

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Q A

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practical approach to measurement uncertainty in a civil

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