MEASURE FOR MEASURE
Are You Sure?
Understand measurement uncertainty to gauge performance
by Christopher L. Grachanen
According to the International Vocabulary of Metrology—Basic and general concepts and associated terms (VIM), measurement results are defined as a "set of quantity values being attributed to a measurand together with any other available relevant information."1 The VIM defines measurand as "quantity intended to be measured."2
Measurement results are normally associated with an interval (range) characteristically referred to as a tolerance, limits of error and specification (relative information). This interval can be symmetrical, such as in the case of reporting the measurement results for a thermocouple-based device as 100°C +/- 2.0°C. Or, it can be one-sided, such as when reporting oscilloscope bandwidth as greater than or equal to one gigahertz. Measurement results given within an interval provides evaluators with limits to gauge results to their specific application requirements to determine satisfactoriness of performance.
From a metrological purist perspective, measurement results reported with just an interval do not give sufficient information as to the uncertainty (unlikelihood) that the obtained results are within their stated interval. Stated another way, measurement results stated with only an interval do not give any suggestion as to what level of confidence you can assume about the results. An example of a measurement result with interval and confidence is:
10V +/- 1mV @ 95 confidence level.
In this example, V represents voltage and mV represents millivolts.
The industry standard for computing measurement uncertainty is the International Organization for Standardization and International Electrotechnical Commission publication Guide to the Expression of Uncertainty in Measurement (GUM). The GUM provides recommended methods for computing an expanded measurement uncertainty from an ensemble of individual measurement uncertainty contributors coupled with their associated confidence levels.
One of the challenges associated with computing an expanded uncertainty per the GUM is determining what measurement uncertainty contributors should be included in the measurement ensemble, and what measurement uncertainty contributors are deemed insignificant, and therefore, need not be included but should, as a best practice, be documented.
The American Association for Laboratory Accreditation, a nonprofit, non-governmental, membership society offering programs for the accreditation of testing and calibration laboratories, makes the following recommendation in its publication, R205: Specific Requirements: Calibration Laboratory Accreditation Program, clause 4.2.1: "Every measurement uncertainty shall take into consideration the following standard contributors, even in cases where they are determined to be insignificant, and documentation of the consideration shall be made:
- Reference standard uncertainty.
- Reference standard stability.
To elaborate on these standard contributors, you can use the VIM for guidance:
- Repeatability4 is the measurement precision under a set of repeatability conditions of measurement.
- Resolution is the smallest change in a quantity being measured that causes a perceptible change in the corresponding indication. For a measurement device with display, resolution is defined as the smallest difference between displayed indications that can be meaningfully distinguished.
- Reproducibility5 is measurement precision under reproducibility conditions.
- Reference standard uncertainty is the uncertainty associated with the measurement standard designated for the calibration of other measurement standards and devices. Instrumental measurement uncertainty is obtained through calibration of a measuring instrument or measuring system—not to be confused with the uncertainty of a primary measurement standard.
- Reference standard stability is the stability associated with the measurement standard designated for the calibration of other measurement standards and devices. Stability of a measuring instrument is the property of a measuring device whereby its metrological properties remain constant in time.
- Environmental factors are the ambient conditions, such as temperature, humidity and barometric pressure, that can influence measurement results. The amount of influence depends on the type of measurements being made, the duration of the measurements, and the offset or variability of influential environmental conditions from recommended operating levels.
Depending on the measurements being performed, there may be other uncertainty contributors, such as linearity, hysteresis and jitter. Some of the measurement contributors mentioned in this column may be deemed insignificant and not included in the measurement uncertainty ensemble. But as a best practice, they should documented as insignificant.
Understanding the principles and idiosyncrasies of a measurement is essential to accurately determining its expanded uncertainty. Without adequate knowledge of a measurement, you risk excluding significant uncertainty contributors as well as overestimating or underestimating contributors. It cannot be overly emphasized that any assumptions associated with uncertainty contributors should be defendable, documented and reflective of the influences and conditions relative during a measurement.
When evaluating any measurement results, it is a good practice to ask two questions:
- What is the interval the measurement results are estimated to fall within (tolerance or specification)?
- What is the confidence level associated with the measurements?
Asking these questions will help ensure you know not only your measurement results, but also the level of confidence of the results so that you can use the measurements to accurately gauge performance.
References and notes
- Joint Committee for Guides in Metrology, International Vocabulary of Metrology—Basic and general concepts and associated terms, 2008.
- American Association for Laboratory Accreditation, R205: Specific Requirements: Calibration Laboratory Accreditation Program, clause 4.2.1, 2012.
- Gage repeatability and reproducibility (R&R) is a popular method for determining standard contributors of repeatability for measurements.
- Gage R&R is also a popular method for determining standard contributors of reproducibility for measurements.
Christopher L. Grachanen is a master engineer and operations manager at Hewlett-Packard Co. in Houston. He earned an MBA from Regis University in Denver. Grachanen is a co-author of The Metrology Handbook (ASQ Quality Press), a senior member of ASQ, an ASQ-certified calibration technician and the treasurer of the Measurement Quality Division.