ASTM-uncertainty-calculation-example_2.pdf

Uncertainty

• a measurement is not very meaningful unless there is some way of estimating the associated uncertainty

• good analyses should include uncertainty estimates

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Uncertainty

•Per section 2.2.1 of the GUM

• The word “uncertainty” means doubt, and thus in the broadest sense “Uncertainty of measurement” means doubt the validity of the result of a measurement.

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Uncertainty

• Uncertainty is a measure of how close a particular test result, the product of one laboratory, is to the true value.

• There is no assurance that any laboratory using the same test method will have the same accuracy; some will be better and some worse. Specifications of apparatus and materials in test methods attempt to control uncertainty but cannot guarantee a value.

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Uncertainty

• In Metrology, two common types of uncertainty evaluations are Type A and Type B.

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Uncertainty

Type A Uncertainty -

• The method of evaluation of uncertainty by the statistical analysis of a series of observations.

• Repeatability condition of measurement, Intermediate precision condition of measurement, Reproducibility condition of measurement

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Uncertainty

• ASTM E2428 (TORQUE) and ASTME74 (FORCE) calibration test for the reproducibility and repeatability condition of measurement and is an example of Type A Uncertainties.

• The term used in these standards is Lower Limit Factor which applies a coverage factor of 2.4

• If the equipment used to perform the test has a relatively low overall uncertainty then a large percentage of the TTU (Total Test Uncertainty) will be quantified with reproducibility and repeatability

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Uncertainty

• Type A Example

• A series of measurements are taken to determine the Type A uncertainty of the measurement.

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Uncertainty

• Type B Uncertainty - method of evaluation of uncertainty by means other than the statistical analysis of a series of observations.

• Type B uncertainty - Evaluation based on information associated with a quantity value of a certified reference material, - obtained from a calibration certificate or manufacture’s specifications, obtained from the accuracy class of a verified measuring instrument, obtained from limits deduced from a test or experiment.

• Examples include torque or load cell temperature effect, drift, resolution, etc.

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Uncertainty

• Type B evaluation method:

The method of evaluation of uncertainty of measurement by means other than statistical analysis of a series of observations.

Examples:

Based on specification

History of parameter

Other knowledge or test of the process parameter

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Uncertainty

• So if we are dealing with A component of Uncertainty it is either Type A or Type B, If we have both Type A and Type B uncertainties and RSS (root sum square) then this becomes a Combined Standard Uncertainty and if we apply a coverage factor to the Combined Uncertainty this becomes our Overall Uncertainty also known as Expanded Uncertainty.

• We will go over an expanded uncertainty analysis in the next section.

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Uncertainty

• Determining the Uncertainty of a Measurement (UOM) is different from the practice of Determining the Expected Performance of a Device.

• Determining the Expected Performance of a Device (which includes the De-Rating Specifications associated with its performance and which are NOT part of the Measurement Uncertainty Analysis performed/calculated to determine the UOM any more than the Base EP (Expected Performance) of the device is included in the UOM). In other words the manufacturer’s specification is not to be used in place of the uncertainty.

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Uncertainty Example

• The next example will deal with an example derived from an uncertainty analysis that is in the ASTM E74-13a standard as an appendix.

• Repeatability, Reproducibility, and Resolution are all accounted for in the ASTM E74 uncertainty or LLF (Lower Limit Factor).

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Uncertainty Example

• We will gather some necessary information and run through a sample expanded uncertainty calibration.

• We will need the following:

1. Calibration Report for the Device

2. The uncertainty of the instrument(s) that were used to perform the calibration

3. Calibration History (if available)

4. Manufacturer’s Specification Sheet

5. Error Sources, if known

6. Dissemination Error, if known

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Performance & Uncertainty for Calibration performed by Morehouse

• Type A Uncertainty • To do a type A uncertainty

analysis, information will be needed from the calibration report.

• The ASTM E74 LLF or Uncertainty from the report should be entered into the spreadsheet.

• In ASTM E74-13a, Uncertainty has been changed to LLF (Lower Limit Factor).

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Uncertainty Example

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• Using the Excel sheet available at http://www.mhforce.com/wp-content/uploads/2012/05/Type-A-and-B-uncertainty-analysis-ASTM-E74-1.xls

• We will enter the load cell S/N, Capacity, ASTM Uncertainty which was .237 LBF, Lowest force the standard will be used, and the Uncertainty of the standard used to perform the calibration at k=1.

COMPANYLOAD CELL MANUFACTURER ENTER

LOAD CELL S/N YOUR

CAPACITY 10000 LBF CALIBRATION

ASTM E74 Uncertainty for K=2.4 0.237 LBF INFORMATION

THE LOWEST FORCE AT WHICH THE SECONDARY STANDARD WILL BE USED 1000 LBF IN

PRIMARY FORCE CALIBRATION STANDARD UNCERTAINTY K=1 HIGHLIGHTED

PRIMARY ELECTRICAL CALIBRATION STANDARD UNCERTAINTY K=1 (IF APPLICABLE) COLUMNS

CAL DATE

P-7768

0.001%

10/27/2010

MOREHOUSE

Type A and B uncertainty analysis SAMPLE

Uncertainty Example

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• The uncertainty of the standard or standards that were used to perform the calibration should be found somewhere on the certificate of calibration with a coverage factor.

• This coverage factor is typically 2, so you will need to reduce this to k=1.

COMPANYLOAD CELL MANUFACTURER ENTER

LOAD CELL S/N YOUR

CAPACITY 10000 LBF CALIBRATION

ASTM E74 Uncertainty for K=2.4 0.237 LBF INFORMATION

THE LOWEST FORCE AT WHICH THE SECONDARY STANDARD WILL BE USED 1000 LBF IN

PRIMARY FORCE CALIBRATION STANDARD UNCERTAINTY K=1 HIGHLIGHTED

PRIMARY ELECTRICAL CALIBRATION STANDARD UNCERTAINTY K=1 (IF APPLICABLE) COLUMNS

CAL DATE

P-7768

0.001%

10/27/2010

MOREHOUSE

Type A and B uncertainty analysis SAMPLE

Uncertainty Example

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• The information from the ASTM E74 report is your Type A uncertainty. To get this, we are dividing the uncertainty or LLF by the lowest force this instrument is going to be used at. Then we divide by 2.4 the ASTM E74 coverage factor to reduce this to the uncertainty or LLF at k=1 (above).

Uncertainty Description Uncertainty Distribution Divisor Standard Uncertainty Squared

ASTM E74 Uncertainty % at the lowest calibration force to be used 0.00988% normal 1 9.88E-05 9.75E-09

9.88E-05 9.75E-09

Type A Uncertainty %

Combined Type A Uncertainty

Uncertainty Example

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• Next, we will be looking at the type B uncertainty.

• If the system was calibrated in accordance with ASTM E74 and consisted of a meter and load cell, then we will treat the ASTM E74 uncertainty or LLF as a system uncertainty, and there would not be a need to look at the Electrical Calibration Standard Uncertainty.

Uncertainty Description Uncertainty Distribution Divisor Standard Uncertainty Squared

PRIMARY FORCE CALIBRATION STANDARD UNCERTAINTY 0.001% rectangular 1 5.77E-06 3.33E-11PRIMARY ELECTRICAL CALIBRATION STANDARD UNCERTAINTY (IF APPLICABLE) 0.000% rectangular 1 0.00E+00 0.00E+00STABILITY OF THE SECONDARY FORCE STANDARD OVER TIME 0.005% rectangular 1.732 2.89E-05 8.33E-10CREEP ERROR FOUND ON LOAD CELL SPEC SHEET 0.002% rectangular 1.732 8.66E-06 7.50E-11MISALIGNMENT ERROR (SEE ASTM E1012) AND/OR SIDE LOAD SENSITIVITY FROM LOAD CELL SPEC SHEET 0.005% rectangular 1.732 2.89E-05 8.33E-10DISSEMINATION ERROR (FOR CALIBRATION LABORATORIES) 0.005% rectangular 1.732 2.89E-05 8.33E-10TEMPERATURE ERROR +/- FROM LOAD CELL SPEC SHEET 0.0015% rectangular 1.732 8.66E-06 7.50E-11

5.18E-05 2.68E-09

Type B Uncertainty %

Combined Type B Uncertainty

Uncertainty Example

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• The first type B uncertainty component to examine is the uncertainty of the standards used to perform the calibration.

• The can usually be found on the calibration laboratory’s scope of accreditation.

• In this example, the load cell was sent in with an indicator, so we will only consider the Primary Force Standard Uncertainty, which was dead weight with an uncertainty of 0.001% for K=1.

PRIMARY FORCE CALIBRATION STANDARD UNCERTAINTY 0.001% rectangular 1 5.77E-06 3.33E-11PRIMARY ELECTRICAL CALIBRATION STANDARD UNCERTAINTY (IF APPLICABLE) 0.000% rectangular 1 0.00E+00 0.00E+00

Uncertainty Example

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• This can be determined by comparing the previous calibration with the current calibration.

• The # to be used should be the number of the lowest calibration force that will be used for calibration.

• If you do not have any previous calibration data, then the suggestion would be to contact the manufacturer or use a conservative number based on similar systems.

STABILITY OF THE SECONDARY FORCE STANDARD OVER TIME 0.005% rectangular 1.732 2.89E-05 8.33E-10

Uncertainty Example

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• Calibration History can be found from taking the difference from one calibration to the next, or looking at several calibrations, if available. In this example, I would opt to use the % change of 0.005 %. This is the highest % change throughout the loading range.

Uncertainty Example

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• A less conservative way to approach change from previous would be to take the Standard Deviation of all of the change from previous numbers.

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• Creep error – This can usually be found on the manufacturer’s spec sheet, and is usually % reading for 20 minutes. Since we typically hold the force for around 30 seconds when performing the calibration, the creep error is much lower.

• If the end user replicates holding the force for 30 seconds, then the creep error of the system should be better than 0.002 %.

• A creep test can be performed and is included in the new ASTM revision for those using method A.

CREEP ERROR FOUND ON LOAD CELL SPEC SHEET 0.002% rectangular 1.732 8.66E-06 7.50E-11

UNCERTAINTY EXAMPLE

Uncertainty Example

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• A well aligned calibration machine may demonstrate bending less than 2 %.

• The % can usually be found on the load cell spec sheet under Side Load Sensitivity.

• Note: If using a Morehouse UCM and Morehouse Ultra Precision Load Cell the Morehouse press will transfer the force applied to the load cell at an angle of no more than 1/16th inch measured off centerline of the load cell.

(This number is usually 0.05 % * .0625 = .003%)

MISALIGNMENT ERROR (SEE ASTM E1012) AND/OR SIDE LOAD SENSITIVITY FROM LOAD CELL SPEC SHEET 0.005% rectangular 1.732 2.89E-05 8.33E-10

Uncertainty Example

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DISSEMINATION ERROR (FOR CALIBRATION LABORATORIES) 0.005% rectangular 1.732 2.89E-05 8.33E-10

• Dissemination Error – Assuming we have compared results with primary standards accurate to 0.002 % of applied force, and we achieved actual measurement results comparing 2 standards, each calibrated with primary standards against one another that suggested our measurements to be within 0.005 %, we will use this number for Dissemination Error.

Uncertainty Example

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• Temperature Error - This is found from the load cell spec sheet. It is usually in terms of % of reading/100 per degree F or C.

• This number should then be multiplied by the maximum temperature difference from the temperature at which the calibration was performed.

• If the manufacturer’s spec sheet suggests .0015 % per degree C and you are operating within +/- 1 degree, then use this number. If you are +/- 2 Degrees C, then use .003 %.

TEMPERATURE ERROR +/- FROM LOAD CELL SPEC SHEET 0.0015% rectangular 1.732 8.66E-06 7.50E-11

Review of everything we entered

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COMPANYLOAD CELL MANUFACTURER ENTER

LOAD CELL S/N YOUR

CAPACITY 10000 LBF CALIBRATION

ASTM E74 Uncertainty for K=2.4 0.237 LBF INFORMATION

THE LOWEST FORCE AT WHICH THE SECONDARY STANDARD WILL BE USED 1000 LBF IN

PRIMARY FORCE CALIBRATION STANDARD UNCERTAINTY K=1 HIGHLIGHTED

PRIMARY ELECTRICAL CALIBRATION STANDARD UNCERTAINTY K=1 (IF APPLICABLE) COLUMNS

CAL DATE

CALCULATED VALUESLOAD CELL UNCERTAINTY IN % FOR FULL SCALE K=2.4 0.00237%LOAD CELL UNCERTAINTY IN % FOR FULL SCALE K=1 0.00099%

LOAD CELL UNCERTAINTY IN % FOR LOWEST FORCE APPLIED K =2.4 0.02370%LOAD CELL UNCERTAINTY IN % FOR LOWEST FORCE APPLIED K =1 0.00988%

Uncertainty Description Uncertainty Distribution Divisor Standard Uncertainty Squared

ASTM E74 Uncertainty % at the lowest calibration force to be used 0.00988% normal 1 9.88E-05 9.75E-09

9.88E-05 9.75E-09

Uncertainty Description Uncertainty Distribution Divisor Standard Uncertainty Squared

PRIMARY FORCE CALIBRATION STANDARD UNCERTAINTY 0.001% rectangular 1 5.77E-06 3.33E-11PRIMARY ELECTRICAL CALIBRATION STANDARD UNCERTAINTY (IF APPLICABLE) 0.000% rectangular 1 0.00E+00 0.00E+00STABILITY OF THE SECONDARY FORCE STANDARD OVER TIME 0.005% rectangular 1.732 2.89E-05 8.33E-10CREEP ERROR FOUND ON LOAD CELL SPEC SHEET 0.002% rectangular 1.732 8.66E-06 7.50E-11MISALIGNMENT ERROR (SEE ASTM E1012) AND/OR SIDE LOAD SENSITIVITY FROM LOAD CELL SPEC SHEET 0.005% rectangular 1.732 2.89E-05 8.33E-10DISSEMINATION ERROR (FOR CALIBRATION LABORATORIES) 0.005% rectangular 1.732 2.89E-05 8.33E-10TEMPERATURE ERROR +/- FROM LOAD CELL SPEC SHEET 0.0015% rectangular 1.732 8.66E-06 7.50E-11

5.18E-05 2.68E-09

Type A Uncertainty %

Combined Type A Uncertainty

Type B Uncertainty %

Combined Type B Uncertainty

P-7768

0.001%

10/27/2010

MOREHOUSE

Type A and B uncertainty analysis SAMPLE

Uncertainty Example

Summary

• After all the data has been entered, the Big U or Expanded Uncertainty for this 10K load cell that had an ASTM E74 uncertainty or LLF of .237 LBF (K=2.4) is now 1.055 LBF for K=2 at full scale capacity.

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FOR K= 1

UC= SQUARE ROOT OF TOTAL COMBINED TYPE A AND B 0.01115%

FOR K=2

U = K * UC (UNCERTAINTY % AT THE LOWEST FORCE TO BE APPLIED) 0.022%0.223 LBF

UC AT CAPACITY * 2 ( (UNCERTAINTY % AT INSTRUMENT CAPACITY) 0.011%1.055 LBF

Uncertainty Example

• This example is just a guideline for calculating expanded uncertainty. The actual uncertainty components in your system may vary.

• In addition to this example, there is also an Uncertainty example for torque in the next section.

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