JCGM GUM-5:2026 Has a Force Example in It!

The Scatter Was Never the Story: The JCGM’s Breaking-Force Example and What Really Drives Force Uncertainty

Steel wire rope used for hoisting in vertical mine shafts. Source: JCGM GUM-5:2026, Example 15, clauses 15.1–15.6.

Thousands of workers ride steel wire rope down mine shafts every day, which is why the law in mining countries requires hoisting rope to be tested to destruction. You cannot break the same rope twice, so the laboratory in this story cut six pieces from one coil and pulled each one until it failed.

The six breaking forces landed between 10 003 kN and 10 008 kN. Six pulls on a ten-thousand-kilonewton rope, spread across just 5 kN. The standard uncertainty of the mean worked out to 0.7 kN, a beautifully tight result.

The reported expanded uncertainty? 19.4 kN (k = 1.96, 95 % coverage probability).

Stay with that for a second. If the rope itself only scattered 0.7 kN, where did the other nineteen kilonewtons of doubt come from? Not from the rope. From the measuring system. That is the entire thesis of my book’s subtitle, Top Conditions, Methods, and Systems that Impact Force Calibration Results, and now the JCGM has published a worked force example that proves it line by line. It is Example 15 of JCGM GUM-5:2026, built on real data from the CSIR Rope Testing Laboratory in South Africa, and every force laboratory should read it.

Where the doubt actually lives

Table 15.1: Rectangular PDFs assigned to correction effects for the rope breaking-force model. Source: JCGM GUM-5:2026, Table 15.1, clause 15.3.2.

Because the test is destructive, repeatability in the usual sense is impossible, so the six specimens carry the rope’s variability, and everything else enters as measurement corrections, exactly as JCGM GUM-6:2020 says to build an observation equation. Here is the budget; every value is a standard uncertainty:

Combine those in quadrature and multiply by k = 1.96 and you get the 19.4 kN. Now look at the ranking. The rope, the thing being tested, the reason the whole laboratory exists, is the smallest number in the budget. Its contribution to the combined variance is 0.2 %. Temperature beat it by a factor of eight. Resolution beat it by a factor of seven. The reference load cell beat it by nearly a factor of seven.

The scatter was never the story. The system was the story.

Three lessons for every force laboratory

Force Calibration for Technicians and Quality Managers, 4th Edition (2026), by Henry Zumbrun, Morehouse Instrument Company.

First: your budget lines are the same ones. Machine cell error, reference cell error, resolution, environment. Those are the exact lines the e-book walks through in How to Calculate Measurement Uncertainty for Force and the CMC guidance chapters, and this example shows why none of them is a formality. Resolution alone contributed 5.0 kN here. Resolution is a floor you cannot budget away, only buy your way past with a better indicator, which is why the book spends a whole chapter asking how many decimal places are enough. (Note: I do wish the force example would have used an example with much lower resolution, as 5 kN is so dominant, and the breaking force observations seem to count by 1 kN; this is still much larger than devices we typically see).

Second: your reference standard and your environment set your ceiling. The reference load cell added 4.7 kN of doubt, and temperature added 5.9 kN, the single largest line in the budget. Choose a better reference (the book’s chapter How to Choose the Best Reference Standard Load Cell exists for exactly this decision) and control the environment, and the expanded uncertainty on this test could fall by half without touching the rope, the machine, or the procedure. What if a laboratory did the opposite and poured all its effort into more specimens? Ten more pulls would shave the 0.7 kN term and change the answer by almost nothing. Effort spent where the doubt is not.

Third: the Monte Carlo method is your validator, not your enemy. The JCGM ran one million Monte Carlo trials in 0.2 seconds to check the GUM framework result: 9.9 kN by the law of propagation of uncertainty against 10.1 kN by simulation, with a 95 % interval of 9 986.0 kN to 10 025.3 kN. When the two methods agree that closely, the classical framework is validated for that budget, which is exactly the role JCGM 101 assigns to Monte Carlo. When they disagree, believe in the simulation. Also, the simulation is very easy to check; you can run your favorite AI tool and ask it to take your data and run a simulation. When I do this, the numbers are usually pretty close.

The Weibull footnote that is really a warning

There is one more move in the example worth flagging. Destructive-test researchers typically model breaking force with a Weibull distribution rather than a normal one, so the JCGM fit both. Same mean, same standard deviation, so the GUM framework literally cannot tell them apart; its answer depends only on those two numbers. Monte Carlo can tell them apart, because it draws from the full shape of the distribution.

Here it made no difference, because the specimen scatter was 0.2 % of the budget. But run the what-if. What if your test machine had fine resolution, a deadweight-calibrated reference, and tight temperature control, so the specimen variability dominated? Then the distribution shape would drive the answer, the GUM framework’s conditions would no longer hold, and Monte Carlo with the Weibull would be the defensible result. The better your measuring system gets, the more the statistics of the thing you are testing come out of hiding. That is not a problem. That is the goal. Apollo 13's flight director had the right idea: failure is not an option, and neither is guessing at your distribution shape.

The Morehouse CMC calculator, and how it builds the reference standard line

The Morehouse CMC Calculations for Force Measurements worksheet, Section 1: Data Entry, v3.34. Available free at mhforce.com.

Morehouse publishes the spreadsheet we use for this work. It is called CMC Calculations for Force Measurements, it is free at mhforce.com, and it is currently at version 3 +. You enter reference standard data and a repeatability study, and it returns an uncertainty budget for up to 12 test points, a fitted curve across the range, and an expanded uncertainty you can defend on a scope of accreditation.

The line the JCGM example calls reference load cell error is not a number you look up. In the worksheet, it is assembled from five inputs, each traceable to a document you already have. The ASTM E74 lower limit factor comes off the reference standard's calibration report and is reduced to one standard deviation, because ASTM reports it at k = 2.4. The resolution of the reference standard comes off the same report. The stability of the reference standard comes from two calibrations performed at different times, which is the only honest way to characterize drift. The reference laboratory's reported uncertainty or CMC is entered either as a percentage of applied force or in force units per point. Temperature effect on sensitivity comes off the load cell specification sheet and is applied against the measured temperature variation of your environment. If you calibrate to ISO 376 rather than ASTM E74, the worksheet takes the ISO 376 uncertainty coefficients in place of the lower limit factor.

Section 2 of the worksheet is the budget itself:

Each line carries a magnitude, a divisor, degrees of freedom, a standard uncertainty, a variance and a percentage contribution to the combined variance. The percentage column is the one that answers the question the JCGM example raises, which is where the doubt actually lives.

How the worksheet lines up with the JCGM method

Nothing in the spreadsheet is a Morehouse invention. Every step is the GUM procedure, and the mapping is close to one-to-one:

The worksheet defaults to k = 2 at 95.45 %(this can be changed), which is what ILAC P-14 expects on a scope of accreditation, and it lets you switch to Student's t when the effective degrees of freedom are low enough to matter. It then fits the per-point results with a first- or second-order curve, corrected so that no point ends up underreported, so you can state a CMC anywhere in the range instead of only at the points you happened to test.

Which is why the new force example is welcome without being a substitute. Worked force examples in the guides have been rare, so Example 15 is genuinely good to have. But read what it is. It evaluates the uncertainty of a breaking force measured six times on a system whose measurement corrections are already characterized. It does not tell you how to characterize them. Nothing in clause 15 explains how you arrive at 4.7 kN for the reference load cell or 3.9 kN for the machine load cell. That work happens before the example starts, and it is the work the calculator does.

How to Develop an Uncertainty Budget for a Morehouse Calibrating Machine using ASTM E74 as the Calibration Standard, by Henry Zumbrun, Morehouse Instrument Company.

The long form is written up in How to Develop an Uncertainty Budget for a Morehouse Calibrating Machine using ASTM E74 as the Calibration Standard. It discusses all contributors with real data, gives our guidance on which contributions belong in Type A and which belong in Type B, and shows what the numbers look like at the 100 000 lbf point of a Universal Calibrating Machine. Figure 1 is a smaller and more typical case, straight out of the worksheet: a 10 000 lbf load cell, U-7643, calibrated on 28 August 2026 against reference standard M-9500, 36 data points on the ASTM E74 certificate, three repeatability runs in mV/V converted to force, budget evaluated at the 10 000 lbf point.

Go deeper

Example 15 runs from clause 15.1 to 15.6 of JCGM GUM-5:2026, free to download from the BIPM. For the working version of every line in that budget, resolution, reference standards, environment, repeatability and reproducibility, and the uncertainty math that ties them together, the e-book Force Calibration for Technicians: Top Conditions, Methods, and Systems that Impact Force Calibration Results (4th edition, 2026) is available at mhforce.com. Then pull your own most recent uncertainty budget and rank the lines. If you have never checked whether your biggest contributor is the environment or the resolution rather than the repeatability, the JCGM just handed you a worked example proving it probably is. If you want help with that ranking, or with references that shrink it, contact us. Or, as Yoda would put it: do or do not calibrate, there is no guess.

-Henry Zumbrun, Morehouse Instrument Company

References

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, clauses 15.1 to 15.6. doi:10.59161/YNLY8209. Available at https://www.bipm.org/en/doi/10.59161/YNLY8209.

BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Evaluation of measurement data — Supplement 1 to the “Guide to the expression of uncertainty in measurement” — Propagation of distributions using a Monte Carlo method. Joint Committee for Guides in Metrology, JCGM 101:2008. doi:10.59161/JCGM101-2008. Available at https://www.bipm.org/en/doi/10.59161/JCGM101-2008.

BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Guide to the expression of uncertainty in measurement — Part 6: Developing and using measurement models. Joint Committee for Guides in Metrology, JCGM GUM-6:2020. doi:10.59161/JCGMGUM-6-2020. Available at https://www.bipm.org/en/doi/10.59161/JCGMGUM-6-2020.

Zumbrun, H. Force Calibration for Technicians: Top Conditions, Methods, and Systems that Impact Force Calibration Results, 4th edition, Morehouse Instrument Company, 2026. Available at mhforce.com.

Zumbrun, H. How to Develop an Uncertainty Budget for a Morehouse Calibrating Machine using ASTM E74 as the Calibration Standard, Morehouse Instrument Company. Available at https://mhforce.com/wp-content/uploads/2021/05/How-to-Develop-an-Uncertainty-Budget-for-a-Morehouse-Calibrating-Machine-5-2024.pdf 

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