Measurement Uncertainty: The Dark Arts

When talking about uncertainty it is fair to say that the devil is in the details. But first, let’s start with the definition of Measurement Uncertainty; “non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand, base on the information used” (JCGM 200:2012 -VIM). In other words, it can be said that the uncertainty of a measured value is how much we doubt its trueness.

In the context of performance test results there are two main components of the total uncertainty (ASME PTC 19.1); these are the uncertainty due to random error and the uncertainty due to systematic error.  Uncertainty due to random error is the one that varies randomly in measurements; so, one of its key contributors is the standard deviation of measurements during the period of a test. Uncertainty due to systematic error is the one that remains constant during the test; this is the one that its main contributors are the precision of equipment used in the test measurement and the redundancy of measurements (in other words, how many instruments are there measuring the same variable during the test). Results of a performance test should never be presented without an uncertainty level. This value dictates whether the goal of the test has been met.

The smallest value of uncertainty is always desirable to minimize doubts in test result. Reducing uncertainty does come with an increase in cost. It is quite helpful to have a notion of how some elements contribute to the uncertainty calculation result, so one can take certain actions in advance to assure a satisfactory uncertainty that will not have an unfavorable effect on the validity of some tests.   Some of the most important parameters to pay close attention to are the following,

1. On random uncertainty

• Standard deviation of measurement data: to reach the smallest possible standard deviation value in a set of data measurement during a test, it is crucial that the system under test has reached stable operating conditions before the start of data collection and remains so during the entire period.
• Number of data points per instrument: the data collection system should be setup to have the maximum number of data points possible per instrument.

2. On systematic uncertainty

• Test instrumentation precision: this is a fix contribution and is one that should be look at thoroughly before a test to ensure using instrumentation with adequate precision. If that is achieved during preparation, a big step towards the smallest uncertainty is taken in advance.

• Number of instruments per variable: for parameters yielding high influence on the final results is important to have redundancy; at least two instruments per measurement point or even more. When the point of measurement consists of an area of substantial size; it is necessary to implement the most number of instruments distributed in the area in such a way that a representative measurement is obtained from all of them.

Results of a performance test take several parameters to complete the calculations. Each variable contributes to the total uncertainty in a certain proportion; to know what the proportion contribution of each variable is a sensitivity analysis is performed that tells you what change in percentage each measurement will generate on the final result, 1% or 1ºC variation. For example, in a test meant to measure maximum power of a plant corrected for ambient conditions, the plant electrical output measurement has a sensitivity of 1:1 on the final result. That is: a variation of 1% of the measured output will move the final result by 1%.

Sometimes the number of parameters is so extensive that it is very difficult to give them all close attention. What should be done in these cases, is to single out the variables with the greatest impact on the result and concentrate resources decreasing uncertainty of these measurement. For instance, instruments of better precision can be used, multiple instruments can be installed. This is typically done to measure ambient temperature during testing for example.

During the test, the person in charge of conducting should take good engineering judgement to make the call when the system under test is stable; and special attention should be paid to the variables with the greatest impact on the result.

The cost associated to a test system is key. It is most important to consider the goal of testing and ensure an adequate level of uncertainty. If conducting testing to measure results that are worth millions for plant, such as maximum capacity testing, the uncertainty should be considered accordingly.  An investment to achieve low uncertainty is justifiable and even required. If one is measuring a result that is for information only, not for actionable goals, then a high level of accuracy may not be needed.

Finally, it is important to note that the level of confidence of a result must be coherent. A result with an uncertainty of ±3% is not very useful if one is attempting to measure an improvement of 1%: the inherent doubt of 3% is already larger than the expected improvement. This is where sound engineering judgement comes into play.