More Certainty About Uncertainty(?)

One thing is certain—uncertainty is certainly complicated.

Published: Wednesday, August 13, 2008 - 22:00

There’s an amazing amount of information available about what uncertainty is and how to specify it. If I understood it completely, I would become a consultant and stop writing this column. In spite of that, this column may shed some light on this increasingly popular, and misunderstood, topic.

Standards on uncertainty
In the June 2008 edition of this column, I wrote about measurement uncertainty and its relationship to measurement-accuracy specifications. I discussed, in general, what uncertainty means and its implications when interpreting measurements. Basically, any measurement must include a quantitative statement of its uncertainty. For example, a length measurement can be 22" ± 1/4". This means that the measured value is 22" but the actual value may be anywhere between 21-3/4" and 22-1/4". As a percentage of the measured value, there’s an uncertainty of ± 1.1 percent. In this simple example, confidence intervals aren’t even considered. As you might imagine, absolutes are rare. If variables come into play, a measured value is that value only for an instant in time. Take temperature. As discussed in earlier “Measurement Matters,” it’s difficult to control the temperature of an environment. In the most stringently controlled environments, even the body heat of a single person can cause a temperature change that can influence a measurement. Because objects expand when heated and contract when cooled, changing temperature can change the measuring device as well as the part itself. Consider your home thermostat. It attempts to maintain a constant temperature by turning on the air conditioner when the temperature rises to a certain point, cooling the room below the set temperature so an average temperature is achieved.

Thinking about uncertainty in the context of your home thermostat, the manufacturer should say that it maintains the set temperature to ± 2 degrees, for example. In other words, you can be certain that the actual temperature is within ±2 degrees of the setting. (The fact that temperature is measured at the thermostat means that the temperature in other parts of the room can be very different. That discrepancy is important to remember when considering a measuring system and a part.)

Standards for uncertainty
Just as there are numerous parameters that can be measured, there are correspondingly numerous standards for stating the uncertainty of those measured parameters. A Google search for “measurement uncertainty” yields 4,320,000 results. Narrowing the search to “ISO uncertainty standards” yields 1,360,000 results. It’s apparent that there are two subjects here—one is uncertainty itself, regardless of the measured parameter. The other is the subject of uncertainty of specific measurements. For example, there are standards for specific items, such as air quality (ISO 11222) and for micrometers (ISO 3611). There are also American National Standards Institute (ANSI), American Association of Mechanical Engineers (ASME), and National Institute of Standards and Technology (NIST) standards, among others, which may address uncertainty in similar or different ways, or avoid it altogether. This lack of harmony in expressing uncertainty is one limitation to having universal understanding and agreement.

Expressing uncertainty
As I mentioned earlier, not only is the description of uncertainty contentious, there are standards about how to express uncertainty. ISO/TAG 4/WG 3 is the 100-page Guide to the Expression of Uncertainty in Measurement (or GUM as it is now often called). NIST also explains how to express uncertainty through several pages on its web site. It’s easier to discuss measurement uncertainty in a context. For example, ISO 17025 discusses sources of measurement uncertainty and how to specify it.

ISO 17025
Formerly known as ISO Guide 25, ISO 17025 is the standard followed by many calibration labs. This standard provides a good explanation of factors that contribute to measurement uncertainty. It includes taking into account the uncertainty budget, which includes all the variables that may potentially influence a measurement. Whether you account for them or not, there are certain factors that always make up an uncertainty budget. There’s the overall environment of the calibration lab where the measurement will be performed (including temperature, barometric pressure, humidity, vibration, air currents, etc.). There are variables related to the measurement artifact (the calibration standard)—its temperature and the validity of its own measurement certification (the uncertainty of the measuring device that certified the artifact)—as well as how the artifact has been handled and stored. A precision length standard that is carelessly tossed into a toolbox will contribute greatly to the uncertainty budget no matter what it says on its calibration certificate. Finally, there’s the test process itself. Operator training and experience can contribute to the uncertainty budget. Each factor in the uncertainty budget contributes a percentage of the total measurement uncertainty. Ultimately, 100 percent of the uncertainty value is the sum of all the contributors in the uncertainty budget.

Visualizing uncertainty
Because there are so many kinds of measurement, I will return to the subjects I’m most familiar with—length and dimension measurements. Uncertainty of a device being calibrated leads to nonspecific claims that can be made about that device. For example, calibration is done relative to an artifact. Any artifact has uncertainty. A measuring device has uncertainty. That means that there’s a +/– range within which the measurement of any specific linear dimension will fall. For example, a perfect artifact exactly 1-inch long may measure as 1" ± .002" when its uncertainty is taken into account. What happens when measurement of an artifact is at the edge of the device’s measurement uncertainty? The following illustrations explain the problem.

Here is an ideal value and its upper and lower specification limits.

The blue lines represent the true value of a calibrated artifact with its uncertainty (+/–). The ^ symbol represents a measurement of that artifact by the measurement system. In this case even though that measurement does not match the ideal, there’s high confidence that the measured value of the artifact is within the system specification. This is because the entire uncertainty of the artifact is within the system’s specification range.

This case presents a problem with confidence. As you can see, the measured value of the artifact at the ^ symbol is within the measuring device’s + spec limit, but its positive uncertainty value is outside the limit. One interpretation of ISO 17025 is that for a measurement to be within tolerance, the measured value and its entire uncertainty must be within the upper and lower specification limits of the ideal value. By that definition this measurement is out of tolerance. However, because the measured value is within the upper and lower tolerances of the measuring device, without taking uncertainty into account, you might conclude that the measurement is within specification.

You can be certain.
You might think after all this that you cannot be certain of any measurement. Of course, that isn’t true. Uncertainty is important. Taking good control of the variables that can influence your measurements and understanding contributors to the uncertainty budget can actually increase your confidence in measurements you make.

About The Author

Fred Mason

Frederick Mason has more than 20 years of experience in metrology in engineering and in domestic and international marketing roles. He has a broad range of experience, including holography, laser and white-light interferometry, microscopy, and video and multisensor metrology. He’s the vice president, marketing communications, for Quality Vision International, parent company of Optical Gaging Products, RAM Optical Instrumentation, VIEW Micro-Metrology, and Quality Vision Services.