What is Measurement Uncertainty and Why is it Important?

Measurement uncertainty refers to the doubt or degree of imprecision associated with the result of a measurement.  It is a term used to describe the range of values within which the true value of a measurement is likely to lie.  If I measure a gage block multiple times with a CMM, I can expect to get a different result for each measurement.  Measuring that same gage block with a tape measure or laser micrometer will give yet another set of different results with varying degrees of uncertainty.  Each piece of measuring equipment has its own associated measurement uncertainty. These values can usually be found on the manufacturer’s spec sheets and are usually represented as a formula.  For example, a CMM might state its measurement uncertainty with the following formula:

U(µm) = 1.7+L/333
(where L is the measured length)

This formula is defining a range that says for every measurement obtained that the actual True value will fall somewhere within this defined range.

Formula depicting measurement uncertainty

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Accuracy You Can Trust

True value refers to the actual length of an object which can never be absolutely determined since it is impossible to make a perfect measurement.  So, in practice, a NIST or ISO traceable reference standard is used when calculating measurement uncertainty.  Error is the difference between the Measured value and the True value, while Accuracy is the closeness of agreement between the Measured value and True value. Accuracy and Uncertainty are often confused with one another, with Accuracy incorrectly being used when Uncertainty should be.  Accuracy is qualitative with no numerical value associated with it and is often expressed as being low or high.  Uncertainty on the other hand is quantitative and expressed as a range of values like the formula given above.  One could say that a piece of measuring equipment with a small Uncertainty range is more accurate than the measuring equipment with a larger Uncertainty range.

Error, accuracy, precision, and uncertainty are usually pictorially shown with a scatter shot diagram as shown below.

Systematic and random error in a diagram

The error in any measurement is made up of 2 components, systematic error and random error and does not include mistakes. Systematic error shifts all measurements in a repeatable way so that the average value varies by a predictable amount, making the result either too small or too big.  This is represented as Bias in the diagram.  Systematic error can usually be minimized or corrected through calibration or equipment adjustment (zeroing a caliper or micrometer). Random error on the other hand varies the results by an unpredictable amount and cannot be corrected.

Some contributing factors to random error are:

Tape measure and 2 rulers where the scales don't line up

Quality of the Measuring Scale

A tape measure and 2 rulers where the scales all don’t line up.  
Which one is right?

Rulers showing fractional estimates and precision of the measuring scale

Precision of the Measuring Scale

Ruler C has higher precision and will give more accurate results.
Some error can be attributed to fractional estimates between the scale markings.

Thermal expansion of railroad tracks

Environmental Conditions

Temperature, humidity, and vibrations can contribute to random error.  Parts with a high CTE can expand or shrink with temperature fluctuations.  This picture shows how thermal expansion caused the railroad tracks to bend because they grew too long.

Random error can’t be corrected
but it can be minimized.

Random error can’t be corrected but it can be minimized. Purchasing a higher quality machine will have higher grade measuring scales with better resolution. Performing measurements in a controlled laboratory where the temperature and humidity are held steady can reduce the environmental effects on measurements.  

Measurement uncertainty is calculated by taking into account all of the sources of error that can contribute to the measurement. The process of calculating measurement uncertainty is called uncertainty analysis. Uncertainty analysis involves identifying the sources of uncertainty, estimating the size of the uncertainty, and combining these estimates to determine the overall uncertainty associated with the measurement.  The detailed process can be found in the ISO Guide to the Expression of Uncertainty in Measurement (GUM).  Measurement uncertainty can also be estimated using statistical methods on measured data that was collected with all sources of error present during the measurement.

Measurement uncertainty is important because it provides a measure of the quality of the measurement. Without an understanding of measurement uncertainty, it is impossible to know how reliable a measurement is, or how much trust we can place in the data that is generated from that measurement. If the uncertainty associated with a measurement is too high, it may be impossible to draw any meaningful conclusions from the data.

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