Measurement Uncertainty and Traceability Issues in National and International Measurements

This paper discusses some recent laboratory intercomparisions with emphasis on the success of the uncertainty statement to include the reference value. Some factors that affect this capability are discussed. Recently developed national and international standards in the area of measurement uncertainty are presented as resources for industrial metrologists. Introduction The field of metrology has always been focused on measurement accuracy, which is defined as the closeness of agreement between the result of a measurement and the true value of the measurand. A decade ago the formalism for quantitatively expressing accuracy was published by the ISO in the “Guide to the Expression of Uncertainty in Measurement” (GUM) [1]. It is now the definitive document on evaluating measurement uncertainty. It is a remarkably selfconsistent and complete document and has been adopted by National Measurement Institutes (NMIs), including NIST in the United States. In 1997 the GUM was adopted as a national (ANSI) standard in the US and is designated NCSL Z540-2-1997. In recent years, considerable interest has developed over issues concerning measurement uncertainty and traceability. The motivations for this are many. The globalization of the economy allows industry to outsource workpiece production and inspection on a worldwide scale. Hence component interchangeability (not only between components produced by one supplier but also between the same nominal component produced by several different suppliers) can be assured only if all suppliers employ metrology to a common set of units (typically the SI units). Similarly, inspection services are frequently outsourced and the magnitude of the measurement uncertainty is taken as a measure of the quality and reliability of the measurement result; so measurement uncertainty is becoming a currency of metrology. Concomitantly, various national and international quality standards and laboratory accreditation programs are being revised to include language addressing measurement uncertainty and traceability. Finally, as workpiece tolerances steadily decrease, the cost of inspection usually increases, thus the ability to easily achieve a 10:1 ratio of the tolerance interval to measurement uncertainty interval is increasingly difficult or impossible. Measurement uncertainty is also affecting the economics of production through the cost of expensive equipment and facilities to perform metrology and in the cost of incorrect decisions, e.g., rejecting conforming workpieces or accepting nonconforming ones. Hence optimizing measurement uncertainty in an economic sense is now becoming an important issue in both laboratories and industry. This paper briefly reviews the capabilities of metrologists to create reasonable uncertainty statements and provides some recently developed standards and other documents as a resource helpful in creating uncertainty statements. Measurement Uncertainty Statements An expanded uncertainty statement is meant to encompass a large fraction of the values that can be reasonably attributed to the measurand. The concept of reasonableness inherently invokes judgment, prior information, as well as classical (frequentist) statistics. Consequently, it can be argued that there is no single “right answer” or “correct value” for the expanded uncertainty. It depends not only on the measurement system but also on the totality of the experience and knowledge of the metrologist. Hence, two different metrologists can perform two nearly identical measurements on the same measurand using the same measurement system and produce two quantitatively different uncertainty statements. Each uncertainty statement would be a personal statement of belief or “state of knowledge” concerning what can be concluded about the measurand. As new information becomes available the uncertainty statements must be updated to reflect the current state of knowledge. Similarly, what constitutes a reasonable uncertainty statement must be continually updated with new information. Figure 1 displays a recent comparison of gauge block measurements and their associated expanded (k = 2) uncertainties [2]. In Figure 1(a) the lab denoted by the arrow has a measured value that is exactly equal to the reference value, yet has the largest measurement uncertainty of all the participants. Initially such an uncertainty statement might be considered to be far too conservative. However, on a second gauge block shown in Figure 1(b) the same laboratory has a measurement uncertainty statement that just includes the reference value. In consideration of these two results the uncertainty statement might now be considered quite reasonable. A third result, shown in Figure 1(c), has the reference value far from being included in the laboratory’s uncertainty statement. Consequently, given this additional information it might be reasonable to conclude that the participant is too optimistic in their uncertainty evaluation since one in three uncertainty statements do not include the reference value. This illustrates several issues concerning uncertainty statements. (1) It is possible to have (unknowingly) a small error yet a large uncertainty statement. This might occur when little information is available on some influence quantity resulting in assigning a relatively large standard uncertainty. Hence a large uncertainty relative to the observed errors could be a reasonable statement since it satisfies the criteria of “encompasses a large fraction of the values that can reasonably be attributed to the measurand.” Conversely, if small measurement errors are repeatedly observed, for example when using calibrated check standards to evaluate the measurement process, this new information should be used to reexamine and reduce the measurement uncertainty. (2) An uncertainty evaluation should include only a “single significant figure,” that is, agreement between experts at the 10 % level should be considered very good. (3) It is relatively easy to invalidate an uncertainty statement compared to validating one, by examining measurement errors. For example, if three out of five measurement errors (determined by measuring calibrated artifacts) lie outside of the uncertainty statement, this alone would be strong evidence that such an uncertainty statement is invalid, i.e., it does not encompass a large fraction of the reasonable values that can be attributed to the measurand. Figure 1 Results from a recent international gauge block comparison. All uncertainty bars are for a coverage factor of k = 2