A Practical Approach To Measurement Uncertainty In A Civil Materials .

A Practical approach tomeasurement uncertainty ina civil materials laboratorysettingSession M309

ObjectivesBackground; Systematic Approach to Measurement Uncertainty; Uncertainty of Measurement (UoM) example focussing on compacted voids determination; Summary. With support of:G. Mturi & K. Mogonedi, CSIRB. Pearce, Learning Matters etcH. Badenhorst, NLA2

Background“A measurement without a clearunderstandingof uncertainty lacks merit” ¹3¹ O’Connell et al., 2011

Background What is measurement uncertainty:Measurement:“a value, discovered by measuring, that corresponds to the size, shape, quality, etc. ofsomething”²Uncertainty:“a situation in which something is not known, or something that is not known or certain” ²Measurement True Value𝑴𝒆𝒂𝒔𝒖𝒓𝒆𝒎𝒆𝒏𝒕 𝑩𝒆𝒔𝒕 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 𝑼𝒏𝒄𝒆𝒓𝒕𝒂𝒊𝒏𝒕𝒚4² Cambridge University Press, 2019

Background Why is measurement uncertainty determination and use important and whateffect does it have: It provides the range of error within which the true value of a measurement willfall; Requirement for testing and calibration facilities endeavouring to obtain ormaintain SANAS 17025 status under clause 7.6 of SANS 17025 standard; Results coming from civil materials laboratories are used for pass/fail decisionmaking in engineering and construction projects; Results are used to determine whether materials are suitable for use in specificapplications: What is the cost of erroneous results or results provided without a knowndegree of uncertainty to our clients/stakeholders?5

Background 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 beinherently variable and can cause significant error in results byitself and we just have to take it one step at a time.6

Measurement Uncertainty Approach How do your results become traceable back to international standard?𝑈𝐼𝑆𝑂𝑈𝑁𝑆𝑂 𝑈𝑁𝑅𝑆 𝑈𝐼𝑆𝑂𝑛𝑈17025 𝐶𝑎𝑙 𝑈𝑁𝑅𝑂 𝑈𝐿𝑎𝑏 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑠𝑢𝑐 𝑢𝑖 2𝑖 17

Measurement Uncertainty Approach 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 sameunits as the measurand; Combine all the uncertainties. ¹8¹ O’Connell et al., 2011

Measurement Uncertainty Approach ISOGUM – ISO Guide to the Expression of Uncertainty Develop a model of the uncertainty measurement process; The model must be realistic and must categorise variation inducingfactors into their respective variation types including their analysis regimes.Random Error- Always present- Unpredictable- Caused by instrumentation, changes inenvironmental conditions, etc.- Can use statistical analysis to analyse dataSystematic Error- Predictable and typically constant- Causes can be accounted for or eliminated- Often caused by imperfect observationmethods or calibrationsType A AnalysisStatistical calculationType B AnalysisNon-statistical, ex. Calibration certificateuncertainties, reference tables or books,etc.9¹ O’Connell et al., 2011

Measurement Uncertainty Approach ISOGUM – ISO Guide to the Expression of Uncertainty Determine the uncertainty components based on the model: Isolate each component in the model that is anticipated to causevariation in the measured results. Calculate the sensitivity coefficients: Sensitivity coefficients are multipliers that are used to convert uncertaintycomponents into the correct units of measure and magnitude required. ³ Not needed if the component is already in the unit and magnitude required. ³Calculate the component uncertainties: Determine component uncertainty 𝑼𝒊 as laid out in model.10¹ O’Connell et al., 2011³ ISOBUDGETS, 2019

Measurement Uncertainty Approach ISOGUM – ISO Guide to the Expression of Uncertainty Calculate the associated degrees of freedom as required: “The number of values in the final calculation which are free to vary” ³Convert all uncertainties into uncertainties expressed in thesame units as the measurand: Use sensitivity coefficients determined to convert uncertainties into samemeasurement unit.Combine all the uncertainties: 𝑛𝑢𝑐 𝑢𝑖 2𝑖 111³ ISOBUDGETS, 2019

Measurement Uncertainty Example To illustrate an approach toward measurement uncertainty determination,let us utilise the process to determine the uncertainty involved with thedetermination of voids in compacted asphalt specimens. To start, one must first isolate the variables of the voids calculation:𝑀𝑉𝐷 𝐵𝐷𝑉𝑜𝑖𝑑𝑠 𝑥 100𝑀𝑉𝐷Where:BD – Bulk density of compacted density determined from SANS 3001 AS10MVD – Maximum voidless density determined from SANS 3001 AS11 Overall uncertainty of measurement for compacted voids is thuscompounded from the UoM of the MVD and the BD test procedures.12

Measurement Uncertainty ExampleSomething to keep at the back of your mind as we go through the process .SamplesEquipmentProcedureSourcesof ErrorEnvironmentPeople13

Measurement Uncertainty Example BD uncertainty analysis model:14

Measurement Uncertainty Example BD uncertainty analysis:Possible error inducing ratureIncoming samplerepresentativenessWaterbathMultiple operatorsperforming testsSoaking timeHumidityIn-lab samplehandling to obtaintest specimensDigital BalanceTime constraintsHandling timebefore SSDMultiple testinfluenceUoM stemming fromcompaction processClothAttention to detailCloth dampnessSpace limitationsStopwatch/Timer

Note: This isonly an exerptfrom the fullanalysis forillustrationpurposesMeasurement Uncertainty Example BD uncertainty analysis:1. Standard Uncertainty (𝑈𝑠 ) for inherent variability of the material Type A Experimental Standard deviation of the mean (EDSM):𝝈𝟖. 𝟏𝟑𝑬𝑫𝑺𝑴 𝟐. 𝟎𝟑 𝒌𝒈/𝒎𝟑𝒏𝟏𝟔2. Temperature effect uncertainty (𝑈𝑇 ) Type BThermometer uncertainty - 0.2 CChange in BD with Variation intemperaturethus𝑼𝑻 𝟎. 𝟎𝟗𝟑 𝟏. 𝟕𝟑𝒌𝒈/𝒎𝟑BD0.4307 𝒌𝒈/𝒎𝟑 / C x 0.2 C 0.09 𝒌𝒈/𝒎𝟑25792579257825782577257725762576y -0.4307x 2588.1R² 0.949420222426Temperature2830

Measurement Uncertainty Example BD uncertainty analysis:Note: This isonly an exerptfrom the fullanalysis forillustrationpurposes3. Soaking Time effect (𝑈𝑠𝑡 ) Type ATaking variation within the 3 – 5 minutes soaking time limits from themethod into account:𝑈𝑠𝑡 𝝈𝒏 𝟑.𝟑𝟗𝟖 𝟏. 𝟐𝟎 𝒌𝒈/𝒎𝟑4. Handling time effect (𝑈ℎ𝑡 ) Type AAs method does not specify handling time, standard procedure for lab of 20 seconds waschecked in conjunction with 10 seconds handling time variance.𝑼𝒉𝒕 𝟕. 𝟐𝟖𝟑𝟐 𝟏. 𝟐𝟗𝒌𝒈/𝒎𝟑

Measurement Uncertainty Example BD uncertainty analysis:BD combined uncertainty (𝑈𝐵𝐷𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑 )𝑛𝑢𝑐 𝑢𝑖 2𝑖 1𝑢𝑐 𝑢𝑐 𝑢𝑠 2 𝑢 𝑇 2 𝑢ℎ𝑡 2 𝑢𝑠𝑡 22.032 1.732 1.292 1.202𝒖𝒄 𝟑. 𝟐𝟎 𝒌𝒈/𝒎𝟑 3 𝒌𝒈/𝒎𝟑The BD of the specimens tested for this particular sample is therefore:2572 3 𝒌𝒈/𝒎𝟑Note: This isonly an exerptfrom the fullanalysis forillustrationpurposes

Measurement Uncertainty Example MVD uncertainty analysis model:19

Measurement Uncertainty Example MVD uncertainty analysis:Possible error inducing tureIncoming samplerepresentativenessWaterbathMultiple operatorsperforming testsTime under vacuum HumidityDigital BalanceTime constraintsVacuum pressureMultiple testinfluencePressure gauge/manometerAttention to detailFlask handlingSpace limitationsStopwatch/TimerShaking intervalsSoap solution effectIn-lab samplehandling to obtaintest specimens

Note: This isonly an exerptfrom the fullanalysis forillustrationpurposesMeasurement Uncertainty Example MVD uncertainty analysis:1. Standard Uncertainty (𝑈𝑠 ) for inherent variability of the material Type A Experimental Standard deviation of the mean (EDSM):𝝈𝟐. 𝟎𝟖𝑬𝑫𝑺𝑴 𝟎. 𝟔 𝒌𝒈/𝒎𝟑𝒏𝟏𝟐2. Temperature effect uncertainty (𝑈𝑇 ) Type BThermometer uncertainty - 0.2 CChange in MVD with Variation intemperaturethus C x 0.2 C �𝟑 /𝑼𝑻 𝟎. 𝟏𝟐𝟑 𝟏. 𝟕𝟑𝒌𝒈/𝒎𝟑26722671y -0.5806x 2686.4R² 0.9982670266920222426Temperature2830

Measurement Uncertainty Example MVD uncertainty analysis: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 𝝈𝒏 𝟑.𝟐𝟐𝟏𝟐𝟏 𝟎. 𝟕𝟎 𝒌𝒈/𝒎𝟑Note: This isonly an exerptfrom the fullanalysis forillustrationpurposes

Measurement Uncertainty Example MVD uncertainty analysis:MVD combined uncertainty (𝑈𝑀𝑉𝐷𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑 )𝑛𝑢𝑐 𝑢𝑖 2𝑖 1𝑢𝑐 𝑢𝑐 𝑢𝑠 2 𝑢 𝑇 2 𝑢ℎ𝑡 20.62 1.732 0.702𝒖𝒄 𝟏. 𝟗𝟔 𝒌𝒈/𝒎𝟑 𝟐 𝒌𝒈/𝒎𝟑The MVD of the specimens tested for this particular sample is therefore:2672 2 𝒌𝒈/𝒎𝟑Note: This isonly an exerptfrom the fullanalysis forillustrationpurposes

Measurement Uncertainty Example BDErrorCombined uncertainty of both MVD and BD testing results in:𝑅𝑒𝑠𝑢𝑙𝑡𝐵𝐷 𝐷 2672 𝑘𝑔/𝑚𝑈𝐵𝐷 3 𝑘𝑔/𝑚3MVDError3𝑈𝑀𝑉𝐷 2 𝑘𝑔/𝑚3Resultant voids:𝑉𝑜𝑖𝑑𝑠 𝑀𝑉𝐷 𝐵𝐷𝑥𝑀𝑉𝐷100 2672 2572𝑥2672100 3.7%But What about the uncertainty?24VoidsError

Measurement Uncertainty Example BDErrorCombined uncertainty of both MVD and BD testing results in:𝑅𝑒𝑠𝑢𝑙𝑡𝐵𝐷 2572𝑘𝑔/𝑚3𝑈𝐵𝐷 3 𝑘𝑔/𝑚3𝑅𝑒𝑠𝑢𝑙𝑡𝑀𝑉𝐷 2672 𝑘𝑔/𝑚MVDError3𝑈𝑀𝑉𝐷 2 𝑘𝑔/𝑚3Due to the uncertainty of both MVD and BD:𝑽𝒐𝒊𝒅𝒔 𝑀𝑉𝐷 𝐵𝐷𝑥𝑀𝑉𝐷100 2672 2572𝑥2672100 𝟑. 𝟕% 𝟎. 𝟐%25VoidsError

Summary Determining and communicating the degree of uncertainty ofmeasurement that your results have, give validity to your results nomatter how insignificant it might seem; Going through the process of determining your uncertainty, gives you thetools to narrow down on sources of error in your testing environment andassists in addressing/eliminating them; Always check the validity of your results within the context of your UoMrange. Repeat results that fall outside of UoM range, are invalid; It is not necessary to determine uncertainty of measurement of everysingle aspect, if there is suitable evidence as to how the factor isaddressed and maintained constant.26

QA27

Measurement Uncertainty Approach 10 ISOGUM -ISO Guide to the Expression of Uncertainty 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