The problem of determining a consensus value and its uncertainty from the results of multiple methods or laboratories is discussed. Desirable criteria of a solution are presented. A solution motivated by the ISO Guide to the Expression of Uncertainty in Measurement (ISO GUM) is introduced and applied in a detailed worked example. A Bayesian hierarchical model motivated by the proposed solution is presented and compared to the solution.

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This paper proposes a method to extend the current ISO Guide to the Expression of Uncertainty in Measurement to include the case of known, but uncorrected, measurement bias. It is strongly recommended that measurement results be corrected for bias, however in some situations this may not be practical, hence an extension of the Guide is proposed to address this special situation. The method keeps with the spirit of the Guide in maintaining the link between uncertainty and statistical confidence. Similarly, the method maintains the transferability of one uncertainty statement to be included as a component in another uncertainty analysis. The procedure involves modifying the calculation of the expanded uncertainty, allowing it to become asymmetric about the measurement value. The method is compared to other alternative procedures, and an illustration of how it affects tolerance zones is presented.

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This paper presents a detailed discussion of the technical aspects of the calibration process with emphasis on the definition of the measurand, the conditions under which the calibration results are valid, and the subsequent use of the calibration results in measurement uncertainty statements. The concepts of measurement uncertainty, error, systematic error, and reproducibility are also addressed as they pertain to the calibration process.Key words: calibration; error; influence quantities; measurand; systematic error; uncertainty. Accepted: January 16, 2001Available online: http://www.nist.gov/jres IntroductionThe concept of calibration has generally been associated with statements regarding the accuracy of a standard, gauge, or measuring instrument. Although calibration typically involves many administrative, procedural, and documentary activities [1][2][3], in this paper we will focus on technical issues associated with measurement error and uncertainty as it relates to the calibration process. Modern metrological concepts increasingly link the topics of measurement traceability, laboratory accreditation, and quality assurance programs to the topic of measurement uncertainty. An essential component of all uncertainty budgets is the employment of calibrated gauges, standards, or instruments. It is the calibration process that transfers a reference value, usually an International System (SI) unit, to the artifact or instrument under calibration and hence establishes the "unbroken chain of comparisons" required for traceability. Calibration (VIM-1993)-set of operations that establish, under specified conditions, the relationship between values of quantities indicated by a measuring instrument or measuring system, or values represented by a material measure or a reference material, and the corresponding values realized by standards.1 Even calibrations that use "self-calibration" methods, e.g., straightedge reversal using an indicator, require uncertainty statements since the uncertainty of the indicator must be assessed. 2. A calibration may also determine other metrological properties such as the effect of influence quantities.

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