Where One Term Ends and the Next Begins, Part 3 of 7: Bias vs Uncertainty - Why Compensation Is Not Padding
Picture two bathroom scales. The first reads 2 lb heavy every single time, dead consistent. The second is perfectly centered on average but jumps around by a pound either way. The first scale has a large error and small scatter. The second has near-zero error and large scatter. They are not the same problem, and you do not fix them the same way.
That picture is the whole of this part. Everything else is the standards agreeing with it.
Figure 6. Large error with small scatter on the left; small error with large scatter on the right. Different problems, different fixes.
Error Is a Known Number. Uncertainty Is a Quantified Doubt.
The VIM (2.16) defines measurement error as the measured value minus a reference value. Measured against a calibrated standard, that difference is a bias you can find and correct. Uncertainty, by contrast, characterizes the dispersion of values that could reasonably be attributed to the measurand. One is a direction and a size. The other is a width.
The GUM makes the point in a line worth taping to the wall (Clause 3.3.1, note): a corrected result can sit very close to the true value, and so carry a negligible error, and still have a large uncertainty. Small error, big uncertainty. The two move independently.
What Bias Compensation Actually Means
The GUM's instruction (Clause 3.2.3) has three steps. Identify the systematic effect. Correct for it. Carry the uncertainty of the correction in the budget.
In force work, the correction usually arrives as the calibration itself. An ASTM E74 calibration fits a curve to the instrument's response; using that curve instead of the nominal sensitivity is bias compensation. The doubt that remains in that fit, the lower limit factor, a statistical estimate of the error in forces computed from the calibration equation, goes into the budget as a Type A term once it is divided by its coverage factor of 2.4. That is the sequence: fix the value, then account for the doubt in the fix.
What the GUM forbids is the shortcut (Clause 6.3.1, note): skipping the correction and padding the uncertainty to cover it. If you leave a known bias in place, the honest alternative is the one the Decision Rule Guidance states plainly: add it to the expanded uncertainty, U + bias. Linear addition is the price of not correcting.
Where Bias Sits Relative to TUR
The ANSI/NCSL Z540.3 Handbook settles a question people argue about. The TUR denominator is the 95 % expanded uncertainty of the calibration process, including all the influences of the item being calibrated, except for the bias of the item being calibrated. The unit's bias is what the calibration is there to find. It is the thing being measured, not a source of doubt about the measurement. So, it stays out of the denominator and shows up instead as the measured deviation that the decision rule will judge.
That is the boundary. Bias lives in the value column. Uncertainty lives in the doubt column. The decision rule compares the value column against the tolerance, using the doubt column to decide how much margin to keep.
What This Costs When It Goes Wrong
Load a 50 000 lbf tension link with the wrong pin, a 1.75 in pin where the design calls for a 50 mm (1.97 in) pin, and it reads 49 140 lbf. That is an 860 lbf miss, 1.72 % of applied, and no amount of uncertainty accounting repairs it. It is a bias you remove by using the right adapter. A lab that instead widens its uncertainty to cover a known adapter effect does two things wrong at once: it leaves the error in the value and inflates the doubt, so every downstream guardband grows and every acceptance zone shrinks, with no gain in truth.
The reverse mistake also happens. A lab corrects a bias and then forgets to carry the uncertainty of the correction. Its budget is too small, its TUR too flattering, and its PFA understated.
The Two Questions to Ask
Is this effect something I can determine and remove? Then it is a bias: correct it, and budget the uncertainty of the correction. Is it something that could reasonably push the result either way, by an amount I can only bound? Then it is uncertainty: size it, assign a distribution, combine it.
Ask those two questions of every line in your budget. The ones that answer yes to the first do not belong there.
-Henry Zumbrun, Morehouse Instrument Company
References
Sources cited across Parts 1 through 7, listed alphabetically. JCGM documents follow the citation form the BIPM recommends, with the member-organization author line and the JCGM DOI. Clause numbers given in the text refer to these editions.
A2LA. R205 — Specific Requirements: Calibration Laboratory Accreditation Program. American Association for Laboratory Accreditation, Frederick, MD.
ANSI/NCSL Z540.3-2006 (R2013). Requirements for the Calibration of Measuring and Test Equipment. NCSL International, Boulder, CO, 2006.
ASME B89.7.4.1-2005. Measurement Uncertainty Conformance Testing: Risk Analysis. The American Society of Mechanical Engineers, New York, 2005.
ASTM E74-18. Standard Practices for Calibration and Verification for Force-Measuring Instruments. ASTM International, West Conshohocken, PA, 2018. https://doi.org/10.1520/E0074-18
BIPM. The BIPM key comparison database (KCDB). Bureau International des Poids et Mesures, Sèvres. https://www.bipm.org/kcdb/
BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML. Evaluation of measurement data — Guide to the expression of uncertainty in measurement. Joint Committee for Guides in Metrology, JCGM 100:2008. https://doi.org/10.59161/JCGM100-2008E
BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML. Evaluation of measurement data — The role of measurement uncertainty in conformity assessment. Joint Committee for Guides in Metrology, JCGM 106:2012. https://doi.org/10.59161/JCGM106-2012
BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML. International vocabulary of metrology — Basic and general concepts and associated terms (VIM), 3rd edition. Joint Committee for Guides in Metrology, JCGM 200:2012. https://doi.org/10.59161/JCGM200-2012
BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML. Guide to the expression of uncertainty in measurement — Part 5: Examples. Joint Committee for Guides in Metrology, JCGM GUM-5:2026. https://doi.org/10.59161/JCGMGUM-5-2026
Carroll, L. Alice's Adventures in Wonderland. Macmillan, London, 1865.
Cenker, G., Zumbrun, H. and Shah, D. Decision Rule Guidance. Morehouse Instrument Company, York, PA. https://mhforce.com/documentation-tools/
Dobbert, M. "A Guard-Band Strategy for Managing False-Accept Risk." Proceedings of the NCSL International Workshop & Symposium, Orlando, FL, 2008.
Eagle, A. R. "A Method for Handling Errors in Testing and Measuring." Industrial Quality Control, Vol. 10, pp. 10–15, March 1954.
Grubbs, F. E. and Coon, H. J. "On Setting Test Limits Relative to Specification Limits." Industrial Quality Control, Vol. 10, pp. 15–20, March 1954.
Harris, G. L. "GMP 13 — Good Measurement Practice for Ensuring Traceability." In: Selected Laboratory and Measurement Practices and Procedures to Support Basic Mass Calibrations, NIST IR 6969, National Institute of Standards and Technology, Gaithersburg, MD, 2019.
Hayes, J. L. Factors Affecting Measuring Reliability. U.S. Naval Ordnance Laboratory, Technical Memorandum No. 63-106, Corona, CA, 1955.
ILAC-G8:09/2019. Guidelines on Decision Rules and Statements of Conformity. International Laboratory Accreditation Cooperation, 2019.
ILAC-P14:09/2020. ILAC Policy for Measurement Uncertainty in Calibration. International Laboratory Accreditation Cooperation, 2020.
ISO/IEC 17025:2017. General requirements for the competence of testing and calibration laboratories. International Organization for Standardization, Geneva, 2017.
ISO/IEC 17043:2023. Conformity assessment — General requirements for the competence of proficiency testing providers. International Organization for Standardization, Geneva, 2023.
Mimbs, S. M. "Using Reliability to Meet Z540.3’s 2 % Rule." NCSL International Workshop & Symposium, National Harbor, MD, 2011. NASA KSC-2011-151.
Morehouse Instrument Company. Decision Rules Interactive Calculator. https://decisionrules.mhforce.com
Morehouse Instrument Company. Guidance on Uncertainty Budgets for Force Measuring Devices. York, PA. https://mhforce.com/documentation-tools/
Morehouse Instrument Company. GUM in Plain English (series). York, PA. https://mhforce.com/documentation-tools/
Morehouse Instrument Company. Morehouse CMC Workbook. York, PA. https://mhforce.com/documentation-tools/
Morehouse Instrument Company. Morehouse True Cost Calculator and The True Cost of Measurement Decisions. York, PA. https://mhforce.com/documentation-tools/
Morehouse Instrument Company. Start With the End in Mind. York, PA, 2026. https://mhforce.com/wp-content/uploads/2026/05/Start_With_The_End_in_Mind.pdf
Morehouse Instrument Company. Probability of False Reject (PFR) (webinar). York, PA.
NASA-HDBK-8739.19-4. Estimation and Evaluation of Measurement Decision Risk. NASA Measurement Quality Assurance Handbook, Annex 4. National Aeronautics and Space Administration, Washington, DC, 2010.
NCSL International. Handbook for the Application of ANSI/NCSL Z540.3-2006 — Requirements for the Calibration of Measuring and Test Equipment. NCSL International, Boulder, CO, 2009.
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UKAS. LAB 48: Decision Rules and Statements of Conformity, Edition 5. United Kingdom Accreditation Service, Staines-upon-Thames, 2024.
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