Give Us Your Best
by Philip Stein

hile working in the field of laboratory accreditation, I became aware of an issue that seems to confuse almost everyone: deciding what to include in an uncertainty statement.

When a lab calibrates an instrument for one of its customers, it will report the result and, if requested, provide a statement of the uncertainty of the result. How that uncertainty statement should be calculated is what causes confusion. Perhaps I can shine some light on it rather than add to the chaos.

When Is Uncertainty
Not Uncertainty?

There are two opposing points of view on what to include:

• View one: After applying test signals to the customer’s instrument and recording the actual readings that resulted, I report only the uncertainty of my test signals, omitting errors due to the customer’s equipment. Using this information, the customer calculates how much of the total error of the measurement system could be attributed to calibration.

• View two: After applying test signals to the customer’s instrument and recording the actual readings that resulted, I calculate and report an estimate of the total uncertainty the customer’s measurement system will experience due to that particular instrument and its calibration.

Another way of expressing this issue is to ask, “Should the uncertainty due to the instrument (or gage) being tested be included in the value reported to the customer?” The answer is “no” according to view one and “yes” according to view two.

There’s Another Way

There is a third view, and it has been expressed in the European standard EA–4/02. (For more information, visit www.european-accreditation. org.) But before I get into that, I need to give you a little background.

International standard ISO/IEC 17025 requires each laboratory to calculate the measurement uncertainty of each calibration result and report it to the client if requested (reporting it is not required).

ISO Guide 58, the standard for accreditation bodies, requires each accredited lab to publish a document called the scope of accreditation, which lists each parameter the lab can measure or calibrate, along with the range of values that can be dealt with and a specialized statement of uncertainty called the best measurement capability (BMC). This is calculated the same way as other statements of measurement uncertainty according to Guide 58.

EA–4/02 defines BMC as “the smallest uncertainty of measurement that a laboratory can achieve within its scope of accreditation when performing more or less routine calibrations of nearly ideal measuring instruments designed for the measurement of that quantity.”

View three says uncertainty due to the instrument or gage should be included in the BMC only to the extent that a “nearly ideal” instrument is uncertain. According to the standard, this view is required only for BMC calculations, but it does offer a solution to the problem of whether to choose view one or two.

An Example

Exactly what is meant by “nearly ideal” here? Using a handheld micrometer as an example, I will list some influences that can contribute to the uncertainty of a measurement made with this tool. Everything on this list is caused by the tool itself, not the calibration, the operator or the environment:

• Resolution: The best micrometer has a minimum resolution of 50 microinches.

• Thread pitch: The nominal thread pitch is 40 turns per inch, but it might be in error.

• Thread drunkenness: Although the overall pitch may be correct, the pitch within a single turn, or within a small range of turns, might be distorted.

• End play: The spindle of the tool might be able to move back and forth, thus allowing various measurements of the same quantity.

• Contact face wear: The faces of the spindle and anvil might be worn in any one of several typical patterns rather than being flat.

• Contact geometry: The object being measured by the micrometer might not have flat, parallel surfaces that can be accurately contacted by the measuring faces.

Of these, an ideal micrometer will have perfect thread pitch and no drunkenness, end play or face wear. All those parameters are sample defects—things that are wrong with a particular micrometer.

An ideal micrometer will, however, still have limited resolution and may have trouble with contact geometry because these parameters are functions of the design of the tool and will be true of all tools, even ideal ones.

This aspect of view three gives useful guidance to the practitioner attempting to create an uncertainty budget for the measurement. When deciding whether a particular influence quantity should be included, asking whether it would still be an influence from a nearly ideal instrument is definitive.

How To Choose
The Correct View

At this point, it’s easy to decide which view should be used when reporting uncertainty on a calibration certificate to a customer.

View one can’t be used because there’s a universal rule that says no laboratory may report accredited results in which the uncertainty is smaller than that lab’s BMC for that parameter and range. Since view one does not include any influence quantities attributable to the item being calibrated, this uncertainty will be smaller than or equal to the result from view three. And since view three is required to be used for BMC, smaller results reported according to view one cannot be cited.

View two, however, can be used. The uncertainty reported here will surely be equal to or greater than the BMC and will therefore obey the rules. View two includes influence components that arise from the use of the instrument at the customer’s application. Such influences can include environmental properties (temperature), operator error, details of the measuring fixture or setup, or the quality of the reagents or other disposable supplies used during calibration.

While the uncertainty from these influences might be important when the customer uses the instrument, the calibration laboratory has no control over how, when or in what environment the instrument is applied. It’s a fantasy to think the calibration lab can calculate the uncertainty in use since it doesn’t know the conditions of use.

Ultimately, these contradictory requirements lead us to conclude the method detailed in view three and in the European standard is the correct one to use for all uncertainty reports.

PHILIP STEIN is a metrology and quality consultant in private practice in Pennington, NJ. He holds a master’s degree in measurement science from George Washington University in Washington, DC, and is an ASQ Fellow.-

78 I MAY 2004 I www.asq.org

Choose from three
different views on what to include in an uncertainty statement.


If you would like to comment on this article, please post your remarks on the Quality Progress Discussion Board at www.asq.org, or e-mail them to editor@asq.org.



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