# Uncertainty Versus Accuracy in Measurement

People strive for optimum accuracy as they want accurate tools and accurate measurements. Hence accuracy is considered as a positive attribute. On the other hand, uncertainty seems to have only negative connotations.

## Accuracy

Accuracy is a desirable aspect which is conceptually well defined. There are some definitions available for ‘accurate measurement’ in the ISO vocabulary of metrology terms. According to them, a ‘measurand’ is the specific quantity to be measured and the ‘accuracy of measurement’ is defined as the closeness of agreement between the outcome of a measurement and the actual value of the measurand. Since the true value is unknowable, it may be logically not possible to quantify the accuracy of a particular measurement. Hence, in the ISO vocabulary of terms in metrology, it also mentioned that ‘accuracy is a qualitative concept.’

The definition of accuracy presents a logical problem. To simplify the problem and concentrate on other issues, the terms ‘accuracy’ and ‘uncertainty’ could be considered as synonyms, at least for optical measurements. According to ‘Gage maker’s rule,’ the test instrument must be 10x more accurate when compared to the tolerance. Hence it is a challenge to establish the accuracy of a tool, especially if it is a complex tool.

The complexity increases when the accuracy of a brand X interferometer is not specified. What is the action to be taken if a component ‘passes’ when quantified on a profilometer, and ‘fails’ when quantified on an interferometer when both instruments are claimed to be capable of λ/10 metrology?

## Uncertainty

According to the definition outlined in the ISO vocabulary of terms in metrology, the ‘uncertainty of a measurement’ is a ‘parameter, related to the outcome of a measurement, characterizes the dispersion of the values that could logically be attributed to the measurand.’ Uncertainty is related to a specific measurement of a particular component. Although the instrument plays a part in the uncertainty of a measurement, the uncertainty is not attributed to the instrument utilized.

Uncertainty is not just the measurand’s standard deviation, but also takes into account estimates of all contributions to the dispersion of values that might logically be attributed to the measurand.

The ‘Guide to the Expression of Uncertainty in Measurement’ defines Type A uncertainties are those which the metrologist selects to treat by statistical techniques, and Type B uncertainties are those treated by other aspects such as the judgment of the metrologist, analysis, handbook values, and much more.

None of these techniques is neither wrong nor superior to the others. A typical problem in optical measurement is defined by different phrases including ‘uncertainty in the realization of the measurand,’ ‘uncertainty in the definition of the measurand,’ and ‘measurement divergence.’ Uncertainty in the outcome of a measurement may crop up from a partial definition of the measurand, considering the characteristics of the components submitted to test.

Agreement or disagreement between measurements performed on various instruments can be assessed in the perspective of the uncertainties of the measurements.

The ‘Guide to the Expression of Uncertainty in Measurement’ presents the methodology for estimating uncertainty. The objective is to provide a good evaluation of the uncertainty on the basis of data of the measurement process. Although a comprehensive model is not needed, understanding the key contributors to the uncertainty is required.

## Conformance Testing and Decision Rules

The key conceptual advantage of ‘uncertainty’ over ‘accuracy’ comes in the field of conformance testing. If no agreement is present, it may be assumed that the default decision rule of ISO 14253 Part 1 comes to play. According to the standard, a vendor shall lower the tolerance by measuring uncertainty in the acceptance test so as to corroborate conformance to specification.

On the other hand, the user must extend the tolerance by the uncertainty of his incoming inspection in order to establish non-conformance. Enhanced metrology increases production headroom for a vendor. For instance, the vendor has to make a λ/11 component to conform a λ/10 specification if the metrology is λ/100. For the buyer, λ/100 metrology in incoming QA represents that a λ/11 specification is all that is needed to meet a λ/10 performance.

## Conclusion

Although accuracy is desirable in measurement, it is a source of confusion. On the other hand, uncertainty measurements are internationally standardized, enabling the application of various sources of information in order to provide a simple decision rule for acceptance testing.

Developments in the optical components and systems market ensure that uncertainty analyses will become the standard.

This information has been sourced, reviewed and adapted from materials provided by Zygo Corporation.

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