For decades, I've advocated the adoption of an international standard to define a uniform basis for stating measurement accuracy on sales literature. This sounds like an obvious need, yet during the past half century—while repeating the need in five editions of my handbook—it hasn't materialized.

In this column, I'll first define the terms used in our everyday "accuracy-related" language. Then I'll explain the need for including calibration and rangeability in all accuracy statements, and conclude by suggesting a more meaningful format for accuracy statements.

Accuracy terminology

Let’s use archery to explain some of the terms used to describe measurement accuracy. In Figure 1, we see an example with most of the arrows are in a tight pattern, but away from the center of the target. What does this tell us? It tells us the shooter was a good one, but had some interference, such as wind, affecting his performance. Now assume the arrow penetrations represent measurement results of reading the same value by different sensors. How should we state the accuracy of this group of sensors? Well, we would measure the percentages represented by dimensions A, B, C and D, where:

A is the diameter of the spread and is referred to as Standard Error, Precision or Dispersion of that group of sensors. The larger the number of devices being tested, the larger this diameter, and the higher the percentage of test results that would fall inside it. Therefore, we usually state the standard error on the basis of the percentage of the measurements falling inside the circle (50%, 68.3% or 95%). Naturally, the higher this percentage, the lower he average accuracy. Therefore, stating the value of A without stating that only 50% of the devices meet the corresponding accuracy is misleading. The percentage value is Probability, and the lower its value, the less reliable the average sensor in the group is likely to be. In process control, we expect that the publisher’s standard error is 95% or better, but without it being stated, we do not know.

B: This radius is called Random Error, Repeatability or Reference Accuracy. This being the smallest number, some sales literature only state this one. If the purpose of the measurement is only to maintain the process at the same conditions as it was previously, then such a repeatable (but inaccurate) measurement is sufficient, but only then.

C: This distance is called Systematic Error or Bias, often caused by zero shift. Systematic error can often be eliminated by re-calibration or re-zeroing.

D: This distance in called Total Error, Total Accuracy or Total Uncertainty. If the goal of the measurement is to determine the true value of a variable because the information serves accounting or quality control purposes, a repeatable measurement (minimizing B) is insufficient, and this total accuracy must be minimized. This can be done by first calibrating the sensor under actual operating conditions, then making sure that the detector is properly installed and maintained.

Sensor E is not considered in evaluating the average accuracy of the group of sensors, but is reflected by the Probability Percentage, which states if 50%, 68.3% or 95% of the tested sensors met the stated average accuracy.

Calibration must be quantified

The specifications of all sensors should state if the device is calibrated or not, and if it is, how is it calibrated? The levels of calibration include:

C1: Full calibration, meaning that the sensor is individually calibrated under actual operating pressure and temperature conditions, and at normal load. In this case, the actual process fluid (not only water or air) is used for the test. One might note that in case of large flowmeters, this is seldom done, because of the limited availability of testing facilities for large flows.