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A Retuned Horwitz Procedure for Upgrading Certificates of Older Standard Reference Materials



John R. Sieber, Antonio M. Possolo, Michael S. Epstein


Many older certified reference materials have certificates of analysis that do not fully comply with ISO Guide 31. This applies to many NIST Standard Reference Materials (SRM) that have published uncertainty estimates not compliant with the GUM or have no uncertainty estimates at all. When older certification records are sparse and insufficient data are available for a full, modern, statistical analysis, it can be useful to apply the concept of the Horwitz formula relating measurement uncertainty to constituent mass fraction across a population of results from a variety of test methods. Because the quality inherent in results obtained during SRM development projects is likely better than the quality of at least some data used by Horwitz to derive the published relationship, it is sensible to retune the concept, using a large set of results from NIST SRM projects. This approach is described with examples provided, and its utility is discussed in comparison to and in combination with alternative approaches such as Type A evaluation using Student’s t coverage intervals and a Bayesian procedure. A six step process is defined to tackle a variety of situations encountered with older SRMs. NIST is applying this approach to upgrade numerous certificates for metals, ores and related materials.
Special Publication (NIST SP) - 260-198
Report Number


reference materials, uncertainty estimation, certificate of analysis, ISO Guide 31


Sieber, J. , Possolo, A. and Epstein, M. (2019), A Retuned Horwitz Procedure for Upgrading Certificates of Older Standard Reference Materials, Special Publication (NIST SP), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed April 23, 2024)
Created May 10, 2019, Updated March 12, 2020