# Selected Publications on Dimensional Metrology

**Uncertainty and Statistics**

**Uncertainty and Dimensional Calibrations**, Doiron, Theodore D. Dr., Stoup, John R., Journal of Research of the National Institute of Standards and Technology **102** (6), 30 p. (November-December 1997).

**Abstract:** The calculation of uncertainty for a measurement is an effort to set reasonable bounds for the measurement result according to standardized rules. Since every measurement produces only an estimate of the answer, the primary requisite of an uncertainty statement is to inform the reader of how sure the writer is that the answer is in a certain range. This report explains how we have implemented these rules for dimensional calibrations of nine different types of gages: gage blocks, gage wires, ring gages, gage balls, roundness standards, optical flats, indexing tables, angle blocks, and sieves.

**Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results**, Taylor, Barry N., Kuyatt, Chris E., NIST Technical Note **1297** (Supersedes NIST Technical Note 1297, January 1993), 25 p. (September 1994).

**Abstract:** The previous edition, which was the first, of this National Institute of Standards and Technology (NIST) Technical Note (TN 1297) was initially published in January 1993. A second printing followed shortly thereafter, and in total some 10,000 copies were distributed to individuals at NIST and in both the United States at large and abroad—to metrologists, scientists, engineers, statisticians, and others who are concerned with measurement and the evaluation and expression of the uncertainty of the result of a measurement. On the whole, these individuals gave TN 1297 a very positive reception. We were, of course, pleased that a document intended as a guide to NIST staff was also considered to be of significant value to the international measurement community. Several of the recipients of the 1993 edition of TN 1297 asked us questions concerning some of the points it addressed and some it did not. In view of the nature of the subject of evaluating and expressing measurement uncertainty and the fact that the principles presented in TN 1297 are intended to be applicable to a broad range of measurements, such questions were not at all unexpected. It soon occurred to us that it might be helpful to the current and future users of TN 1297 if the most important of these questions were addressed in a new edition. To this end, we have added to the 1993 edition of TN 1297 a new appendix—Appendix D—which attempts to clarify and give additional guidance on a number of topics, including the use of certain terms such as accuracy and precision. We hope that this new appendix will make this 1994 edition of TN 1297 even more useful than its predecessor. We also took the opportunity provided us by the preparation of a new edition of TN 1297 to make very minor word changes in a few portions of the text. These changes were made in order to recognize the official publication in October 1993 of the ISO Guide to the Expression of Uncertainty in Measurement on which TN 1297 is based (for example, the reference to the Guide was updated); and to bring TN 1297 into full harmony with the Guide (for example, “estimated correction” has been changed to simply “correction,” and “can be asserted to lie” has been changed to “is believed to lie”).

**Traceability of Laser Interferometric Length Measurements**, Layer, Howard P., Estler, W. Tyler Dr., NBS Technical Note **1248**, 5 p. (June 1988).

**Abstract:** The National Bureau of Standards maintains the standard of length in accordance with the definition of the meter, adopted by the General Conference of Weights and Measures (1983). This standard is used within NBS to form a consistent system of units which are used in NBS calibration services.

**Statistical Concepts in Metrology—With a Postscript on Statistical Graphics**, Ku, Harry H., NBS Special Publication **747**, 48 p. (August 1988).

**Abstract:** “Statistical Concepts in Metrology” was originally written as Chapter 2 for the Handbook of Industrial Metrology published by the American Society of Tool and Manufacturing Engineers, 1967. It was reprinted as on of 40 papers in NBS Special Publication 300, Volume I, Precision Measurement and Calibration; Statistical Concepts and Procedures, 1969. Since then this chapter has been used as basic text in statistics in Bureau-sponsored courses and seminars, including those for Electricity, Electronics, and Analytical Chemistry.

While concepts and techniques introduced in the original chapter remain valid and appropriate, some additions on recent development of graphical methods for the treatment of data would be useful. Graphical methods can be used effectively to “explore” information in data sets prior to the application of classical statistical procedures. For this reason additional sections on statistical graphics are added as a postscript.

**Industrial Measurement Series, Measurement Evaluation**, Mandel, John, Nanni, Luis F., NBS Special Publication **700-2**, Industrial Measurement Series, 65 p. (March 1986).

**Abstract:** This paper was published originally as a chapter in the book entitled “Quality Assurance Practices for Health Laboratories.” It is for that reason that the examples used as illustrations are taken from health-related fields of research. However, the statistical concepts and methods presented here are entirely general and therefore also applicable to measurements originating in physics, chemistry, engineering, and other technical disciplines. The reader should have no difficulty in applying the material of this paper to the systems of measurement in his particular field of activity.

**The Use of the Method of Least Squares in Calibration**, Cameron, J.M., NBS Internal Report **74-587**, 30 p. (September 1974).

**Abstract:** This paper presents a discussion of the techniques of statistics that arise in the analysis of data from the comparative experiments used in the calibration of objects relative to a reference group of standards. In calibration one usually measures differences between nominally equal objects and uses the values assigned to the standards as the linear restraint to bring the system up to full rank. The use of the method of least squares in this situation is discussed with examples taken from the calibration work of the National Bureau of Standards.

This summary of statistical techniques is intended for metrologists and was presented at the NBS seminar on High-Efficiency Methods for Dimensional Calibrations given 10-11 June 1974.

**Uncertainties Related to Thermal Expansion in Dimensional Metrology**, Doiron, Theodore D. Dr., NCSLI Measure Paper **011-2006**, 13 p. (2006).

**Abstract:** Thermal expansion effects are very important in dimensional metrology. In this paper a measurement model, and associated equations, are developed for the case of a one-dimensional measurement of a steel test gage using a measuring machine and master gage. After presenting the uncertainty components for this measurement, several example measurement situations with difference levels of temperature control are calculated and discussed. For each situation, the magnitude of the different sources of uncertainty are compared in order to rationally allocate resources to improve the overall measurement uncertainty.