Uncertainty of Measurement

If measurements cannot be perfectly exact, we need to know the size of the imperfection; this is Uncertainty of Measurement.

To best try to explain what Uncertainty of Measurement is, let us consider a simple task. Imagine measuring the length of a piece of string. If we gave our piece of string to a group of 10 people and asked them to measure it we would most likely receive 10 different answers. The reason for this would be due to Sources of Uncertainty. This could include:
  • Straightness of the string
  • End flatness of string (raggedness of the end fibers)
  • Tension of the string
  • Humidity affecting the string
  • Temperature affecting the string
  • Resolution of the ruler (the smallest division on the ruler)
  • Correctness of the ruler (how perfect was the ruler when it was calibrated)
  • Correctness of measurement of the master device used to calibrate the ruler
  • How many readings taken to determine the measurement length
  • Repeatability of the measurements

As you can now see the environment, method, and equipment all contribute opportunities for variations and doubt. And we have to conclude that:

  • Nothing is CERTAIN in measurement
  • The only certainty is that any measurement will not be perfectly exact

Quantifying the Uncertainty of a Measurement can be a complicated, but methodical task. The International Standards Organisation (ISO) has produced a document called The Guide to the Uncertainty of Measurement (GUM), which provides internationally recognized methods for determination of Uncertainty Budgets and associated calculations. More recently, many ISO and ASTM standards also include appendices detailing how to work out uncertainty of measurement. Because measurement variation is a major contribution in any Uncertainty Budget, probability as well as size of variation has to be defined when expressing Uncertainty of Measurement.