Estimating Uncertainty

Metrological traceability to non-SI units

by Dilip Shah

In the March and May 2015 Measure for Measure columns,1, 2 there was a discussion on measurement challenges and how to report measurements with a degree of confidence by reporting measurement uncertainty to support metrological traceability.

Estimating measurement uncertainty for calibration laboratories can still be a significant effort to support metrological traceability. However, most of the calibration laboratory parameters are common and traceable to the International System of Units measurements, commonly referred to as SI units, after the concepts for estimation are grasped.

For certain test and calibration disciplines, the documented unbroken chain may not be directly traceable to SI units. This may be because there is more than one input to the test method, and the output is a different unit from that of the inputs, which are expressed in units not traceable to SI units. Figure 1 illustrates this measurement process.

Figure 1

There are more combinations for test laboratories for estimating uncertainty than for calibration laboratories. Therefore, the test laboratories face other challenges because they may not have all the output test parameters that are directly traceable to an SI unit.

Take, for example, a pharmaceutical organization that mixes the recipe for a medication. It may mix the ingredients for the recipe by weight or volume. While weight and volume are metrologically traceable, the end result may not be. The end result may be a qualitative or quantitative measure in a different unit. If the end result can be quantified by traditional uncertainty estimation means (traceable to SI Units), the problem may not be as difficult.

If the traditional estimation methods cannot be deployed, the lab may need to participate in a proficiency test or an interlaboratory comparison program to claim the metrological traceability (for measurement not directly traceable to SI units). This requirement is identified in ISO/IEC 17025 Section

When there are many different units of measurement, the uncertainty contributors may be expressed in a unit-less quantity, such a percentage or parts per million. The output result is expressed in the same unit-less quantity.

If a relationship to the uncertainty contributors can be expressed mathematically to the output result, the repeatability of several simulations with the resultant output quantity can be used to estimate uncertainty. The uncertainty estimation of torque is a good example.

Torque is defined as distance x force. If the distance is defined in meters and the force is defined in Newtons, the resultant torque is in Newton.meters (N.m). Therefore, the uncertainty of torque can be quantified by repeatability of several random simulations of

distance (+/- distanceuncertainty) x force (+/- forceuncertainty).

In this case, all quantities, including the output, are traceable to SI units. However, the technique can be used for non-SI unit output quantities.

In chemical metrology, there is another technique called the Kragten spreadsheet approach, which can be used to estimate the uncertainty. The Kragten spreadsheet can be used to simplify the calculations of partial differentials. The procedure takes advantage of an approximate numerical method of differentiation and only requires knowledge of the calculation used to derive the final result (including any necessary correction factors or influences) and of the numerical values of the parameters and their uncertainties. A future Measure for Measure column will describe and provide an example of using the Kragten spreadsheet method.

Making and reporting a measurement with its associated measurement uncertainty becomes more important as you face the new measurement challenges. Nanotechnology is here, and measurements on a small scale require better tools with more precision and accuracy.


  1. Dilip Shah, "Measuring Device Revolution," Quality Progress, March 2015, pp. 46-47.
  2. Dilip Shah, "Measuring Confidence," Quality Progress, May 2015, pp. 46-48.
  3. International Organization for Standardization and International Electrotechnical Commission, ISO/IEC 17025—General requirements for the competence of testing and calibration laboratories, Section

Dilip Shah is president of E = mc3 Solutions in Medina, OH. He is the past chair of ASQ’s Measurement Quality Division and past chair of Akron-Canton Section. Shah, an ASQ fellow, is also co-author of The Metrology Handbook (ASQ Quality Press, 2012), and an ASQ-certified quality engineer, auditor and calibration technician.

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