Confidence Limits in (Infrared )Temperature Measurements

Characterizing the performance sensitivity of an imager is a matter for experts, especially the equipment manufacturers. If suppliers expect you to believe that instruments have a certain measurement capability, they should be following the same basic measurement principles that you need to follow in reporting results.

They know, or should know, and be able to explain to you, the measurement capability details of their equipment in numerical terms. You may have to request the information because it is usually not included as part of the equipment specifications.

In fact, the specifications produced by most imager makers are often vague and incomplete, leaving much to the imagination of the user. Part of the problem with imager measurement specifications is that the devices were developed as imaging devices and not quantitative measurement devices.

The only measurement specifications that are of value for understanding measurement capabilities are those that come complete with uncertainty values at stated confidence levels under stated conditions of measurement. For example, temperature calibration is often expressed as accuracy.

The preferred technical term is uncertainty, not accuracy, and it should be expressed in the same terms as NIST uses in expressing measurement uncertainty. NIST’s booklet, NIST Technical Note 1297: Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results includes an explanation of how they use the term.

The booklet can be downloaded from the Web and is free by mail also.

Basic Measurement Statistics

Measurements of objects having temperature variations made with devices that are slightly imperfect require that an average measurement be determined. Individual measurement results are, in reality, samples from the range of possible values that the instrument reports. There is a true average value and some variability about that average.

If we take only one measurement, we could be anywhere within the range of possible values.

However, if the factors causing the fluctuations are random, then the effect of making additional measurement is well known and explained in simple statistics. An excellent reference to both measurement statistics and temperature measurement and calibration is the book Traceable Temperature by J.V. Nicholas and D.R. White, (John Wiley & Sons). Some of the important definitions used in statistics are defined in Table 2 below. Please note that a major shift has occurred in US industry over the last 10 years or so.

Measurement practices are being tightened up in all industries as ways to help improve global competitiveness. The techniques and resources are well established since they have been practiced without interruption by the military, power-generation and aerospace industries since the 1950’s.

Table 2-Measurement Terms & Statistics

Confidence Limits and Levels

The resulting confidence limits, the real object of this paper, and level of confidence are directly related as shown in Table 3. They are based on the variability in measurement results. The confidence limits are related to the size of the standard variance and uncertainty. The confidence level results from the statistics of random errors and describes the percentage of readings that will be within the desired confidence limits.

Table 3- Confidence Factors

So, how does one achieve the confidence levels in temperature and temperature gradient measurements with a quantitative thermal imager?

It is a big question and one that cannot be answered quickly or easily because of the many factors involved. However, the steps to obtain the limits are rather straightforward and can be easily outlined.

There are two big steps with lots of little details to be acquired in the first.

Step 1: Determine the confidence level that you can achieve in measurements in the field. That involves knowing your equipment’s calibration uncertainty and its likely measurement uncertainty under less than ideal conditions. We’ve touched on that, but there is also a series of tests called R&R tests to measure the influence of the equipment operator(s) on the measurement results. If properly done, the field variability sensitivity and the operator influences can be grouped together in one set of tests.

Step 2: Determine the confidence level that your customer requires. If the two levels do not match at the outset, you could be in trouble or in roses, depending on which is larger.

If you are in “trouble” there are two options, they are:

Option 1: If the customer requests smaller measurement uncertainty or better capabilities than you can deliver, one could explain that your measurement capabilities are as you have measured and documented and represent a realistic appraisal of the capability of state-of-the-art equipment and trained operators.

This option, of course, assumes two things: first, that your conclusions are true, backed by documentation and second, hat the customer may be seeking unrealistic measurement performance. You should be able to convince the customer that you are competent and request that similar documentation be provided from any competitor. It doesn’t always work, partly because some customers refuse to become better educated, and also when the requirements are really better than your capability.

Option 2: If the customer really needs measurements better than your best capabilities, you could undertake improving them. Having assessed your present capability carefully, you would have a very good idea of where to begin such improvements and what the cost tradeoffs would be.

But there is one more step to be considered before you have a complete understanding of your measurement capabilities or confidence limits, i.e., the combined effects of instrument errors, operator skill and measurement condition influences.

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Tagged as: confidence limit, gage r&r, grr, irinfo, irinfo2003, nist, r&r, traceable calibration, uncertainty