Where One Term Ends and the Next Begins, Part 2 of 7: CMC vs Measurement Uncertainty: The Number on Your Certificate
Pull up any accredited lab's scope of accreditation, and you will find a line for force: perhaps 0.002 % of applied, or 0.025 % of applied, or 0.05 % of applied. Many people read that line and assume it is the uncertainty they will get. Then the certificate arrives with a larger number, and the phone rings.
Three different numbers get called "uncertainty" in that conversation. They are related; however, they are not the same.
Measurement Uncertainty Is a Property of One Result
The GUM builds uncertainty one measurement at a time. Write the model. Size every input by data (Type A) or by what you already know (Type B). Combine by root-sum-of-squares. Carry the degrees of freedom. Expand by a coverage factor you can defend. For the force-measuring instrument we walked through in the GUM in Plain English series, the result at 5000 lbf was U = 1.71 lbf, k = 2.57, approximately 95 % confidence.
That number belongs to that instrument, on that machine, at that point. It includes the instrument's own repeatability (0.58 lbf, three-quarters of the variance), the reference standard's stability (0.29 lbf), and the reference standard's calibration uncertainty (0.05 lbf), which barely registered once squared. Change the instrument and the number changes.
Figure 3. Where the doubt comes from in the 5000 lbf budget. Repeatability sets three-quarters of the variance; the reference standard's own calibration uncertainty barely registers.
In this situation, the issue is likely an operator problem or poor repeatability in what is being tested. The solution is to buy a better load cell for comparison, or have the operator learn to use the equipment properly. What is interesting is that the MU budgets quickly tell you where to focus your efforts to improve your measurement capability.
CMC Is a Property of the Laboratory
The Calibration and Measurement Capability is defined in ILAC-P14 as the capability available to customers under normal conditions, as described in the lab's scope of accreditation. It is evaluated for the best existing device: the most stable, highest-resolution force transducer and indicator the lab is realistically going to see. It is the lab's best case.
Two rules follow from that definition. ILAC-P14 states the first in its CMC policy (Section 4) and the second in its policy on uncertainty in calibration (Section 5).
First, the CMC must include the contributions of the reference standards used. A lab cannot claim a CMC equal to or lower than the uncertainty of the lab that calibrated its references, because that reference uncertainty enters the budget as one positive term among several. The reference you choose sets the floor. ISO/IEC 17025:2017 Clause 7.6 says the same thing from the other side: the lab must evaluate uncertainty for all calibrations, and math does not run uphill.
Second, the uncertainty stated on a customer's certificate must cover the same contributions as the CMC, with the best-existing-device components replaced by the customer's device. The reported uncertainty is therefore normally larger than the CMC. If a certificate shows an uncertainty smaller than the lab's CMC, something is wrong with the certificate or with the scope.
Figure 4. The two ILAC-P14 rules drawn as a staircase. The reference laboratory's CMC is the floor under your CMC, and your CMC is the floor under every certificate you issue. Each step adds contributions to the one it inherits, and nothing on the way down the chain can make the number smaller.
The Certificate Number Is Where the Two Meet
So the chain reads: the reference lab's CMC becomes one Type B term in your budget. Your budget, evaluated with the best existing device, becomes your CMC. Your CMC becomes the floor under every certificate you issue. Each certificate carries your CMC contributions plus the customer's instrument's repeatability, resolution, and the rest.
Watch what that does at the top of the chain. Calibrate the same instrument against deadweight primary standards known to 0.0016 % and the expanded uncertainty at 100 000 lbf comes out near 3.78 lbf. Calibrate it against a secondary machine known to 0.025 %, and the same point jumps to about 25.23 lbf. Same instrument, same care, roughly 6.7 times the uncertainty, purely from the standard above you.
Figure 5. The reference laboratory's CMC is the floor. The certificate uncertainty sits above it in both cases; the only difference is how high the floor was to begin with.
The Boundary
Measurement uncertainty is the doubt in one result. CMC is the lab's best-case doubt for the best device it is likely to see. The certificate uncertainty is the lab's CMC contributions plus your instrument's own. Three numbers, one chain, and the only direction any of them can move as you go down the chain is up. Figure 4 is the whole part in one picture; if you remember nothing else, remember that the staircase only goes up.
Two mistakes cross this boundary. The first is quoting the CMC as if it were the certificate uncertainty, which overstates capability and, as the Decision Rule Guidance notes, understates every PFA and guardband derived from it. The second is treating the certificate uncertainty as if it were a spec-sheet accuracy. UKAS LAB 48 spends a full page on the word "accuracy" and concludes that the VIM treats it as a qualitative concept with no established methodology for assigning a number. Uncertainty has one. Use it.
The Number Is Not Done Until Another Laboratory Agrees
Everything above is arithmetic the lab performs on itself. ISO/IEC 17025:2017 does not let it stop there. Clause 7.7.1 requires a procedure for monitoring the validity of results, with the data recorded in such a way that trends are detectable and, where practicable, analyzed with statistical techniques. The clause's own list of monitoring tools includes check or working standards with control charts, intermediate checks on measuring equipment, replicate calibrations, and intralaboratory comparisons. A control chart that starts walking is the earliest sign that the budget no longer describes the process.
Clause 7.7.2 pushes the check outside the building: the laboratory shall monitor its performance by comparison with the results of other laboratories, through participation in proficiency testing, in interlaboratory comparisons other than proficiency testing, or both. ISO/IEC 17043 supplies the definitions the standard leans on. An interlaboratory comparison is the organization, performance, and evaluation of measurements on the same or similar items by two or more laboratories under predetermined conditions. Proficiency testing is the evaluation of participant performance against pre-established criteria by means of those comparisons.
The pass criterion for a calibration comparison is the En ratio: the difference between your result and the reference laboratory's value, divided by the root-sum-of-squares of the two expanded uncertainties. |En| ≤ 1 means the two results agree within the uncertainties both parties claimed. |En| > 1 means at least one of the claimed uncertainties is wrong, and Clause 7.7.3 says what happens next: the monitoring data shall be analyzed, and when results fall outside pre-defined criteria, action shall be taken to prevent incorrect results from being reported.
This is the part the budget alone cannot do. A measurement uncertainty claim is not finished when the root-sum-of-squares is computed and the coverage factor is applied. It is finished when the lab demonstrates an En ratio below one against an independent reference, through an ILC or PT, and keeps demonstrating it period after period with trend data showing the process is stable. Until then, the CMC on the scope and the uncertainty on the certificate are claims waiting on evidence.
If you want to see how a CMC is built for force, the Guidance on Uncertainty Budgets for Force Measuring Devices lists every contributor A2LA R205 expects, and the free Morehouse CMC workbook does the arithmetic, degrees of freedom and coverage factor included.
-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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Reese, P. and Harben, J. "Risk Mitigation Strategies for Compliance Testing." NCSLI Measure, Vol. 7, No. 1, 2012.
UKAS. LAB 48: Decision Rules and Statements of Conformity, Edition 5. United Kingdom Accreditation Service, Staines-upon-Thames, 2024.
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