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A Careful Consideration of the Calibration Concept

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A Careful Consideration of the Calibration Concept Volume 106, Number 2, March–April 2001 Journal of Research of the National Institute of Standards and Technology [J. Res. Natl. Inst. Stand. Technol. 106, 371–379 (2001)] A Careful Consideration of the Calibration Concept Volume 106 Number 2 March–April 2001 S. D. Phillips, W. T. Estler, This paper presents a detailed discussion of Key words: calibration; error; influence T. Doiron, K. R. Eberhardt, the technical aspects of the calibration quantities; measurand; systematic error; un- andM.S.Levenson process with emphasis on the definition of certainty. the measurand, the conditions under National Institute of Standards and which the calibration results are valid, and the subsequent use of the calibration Technology, results in measurement uncertainty Accepted: January 16, 2001 Gaithersburg, MD 20899-0001 statements. The concepts of measurement uncertainty, error, systematic error, and [email protected] reproducibility are also addressed as they pertain to the calibration process. Available online: http://www.nist.gov/jres [email protected] [email protected] 1. Introduction The concept of calibration has generally been associ- under calibration and hence establishes the “unbroken ated with statements regarding the accuracy of a stan- chain of comparisons” required for traceability.1 dard, gauge, or measuring instrument. Although calibra- The ISO International Vocabulary of Basic and Gen- tion typically involves many administrative, procedural, eral Terms in Metrology (VIM) [4] defines calibration as and documentary activities [1–3], in this paper we will follows: focus on technical issues associated with measurement Calibration (VIM-1993)—set of operations that estab- error and uncertainty as it relates to the calibration pro- lish, under specified conditions, the relationship be- cess. Modern metrological concepts increasingly link tween values of quantities indicated by a measuring the topics of measurement traceability, laboratory ac- instrument or measuring system, or values represented creditation, and quality assurance programs to the topic by a material measure or a reference material, and the of measurement uncertainty. An essential component of corresponding values realized by standards. all uncertainty budgets is the employment of calibrated gauges, standards, or instruments. It is the calibration 1 Even calibrations that use “self-calibration” methods, e.g., straight- process that transfers a reference value, usually an Inter- edge reversal using an indicator, require uncertainty statements since national System (SI) unit, to the artifact or instrument the uncertainty of the indicator must be assessed. 371 Volume 106, Number 2, March–April 2001 Journal of Research of the National Institute of Standards and Technology Notes: perfectly circular workpiece may be significant.2 Due to manufacturing imperfections, the diameter of a work- 1. The result of a calibration permits either the assign- piece is incompletely defined and this can lead to ment of values of measurands to the indications or “methods divergence problems” where different mea- the determination of corrections with respect to suring instruments yield significantly different results. indications. For example, when measuring a bore, a two-point 2. A calibration may also determine other metrologi- diameter as measured with a micrometer,3 a least- cal properties such as the effect of influence squares fit diameter as measured with a coordinate quantities. measuring machine,4 and a maximum inscribed dia- meter as found using a plug gauge, will each yield a 3. The result of a calibration may be recorded in a different numerical value because each measurement document, sometimes called a calibration certifi- method realizes a different quantity permitted by the cate or a calibration report. poorly defined measurand. No amount of improvement While the body of the VIM definition is sufficiently in the accuracy of these measurement methods will general to accommodate nearly all calibration situations, cause their results to converge as they are fundamentally this generality provides little guidance as to what consti- measuring different quantities (two point, least-squares, tutes a calibration. It is the purpose of this paper to and maximum inscribed diameters). Hence, the elaborate on this topic. Our discussion will be guided methods divergence problem is actually an uncertainty primarily by the Guide to the Expression of Uncertainty source associated with an incomplete definition of the in Measurement (GUM) [5]. We will focus our attention measurand. A similar example is the measurement of the on three concepts associated with the VIM definition: hardness of a material. The local hardness (micro- (1) the measurand; (2) the “specified conditions” of the hardness) is often significantly different than the calibration; and (3) the “relationship” between average hardness; consequently, unless a particular test measured or indicated values and those of reference location is specified, measurements at different values. locations can produce significantly different results. A complete definition of the measurand will, in the general case, allow corrections to be applied for differ- 2. Calibration Issues ent measurement methods. For example, the calibration 2.1 The Measurand of a chrome-carbide gauge block using a gauge block comparator and a steel master requires the correction for The measurand is the particular quantity subject to the differential mechanical penetration of the probe tips measurement (VIM 2.6). It is defined by a set of since the length of the block is defined as the un- specifications, i.e. instructions, not a numerical value. deformed length.5 While in principle the complete Indeed, the measurand is an idealized concept and it definition of the measurand requires an infinite amount may be impossible to produce an actual gauge, artifact, of information, in practice it usually contains detailed or instrument exactly to the specifications of the information appropriate for a particular (usually measurand. The measurand specifies the value(s) of the conventional) measurement method and may be signifi- relevant influence quantities and these must be specified cantly incomplete if alternative measurement methods sufficiently well that any ambiguity is negligible with are used. For example, the measurand associated with regard to the required accuracy of the calibration (GUM an artifact’s length might be well specified when using 3.3.2 and D1–D3). The more completely defined the an instrument with mechanical contact probes (such as measurand, the less uncertainty will (potentially) be specifying a correction for the mechanical contact associated with its realization. A completely specified definition of the measurand has associated with it a unique value and an incompletely specified measurand 2 may have many values, each conforming to the (incom- For this reason, some standards such as ASME Y14.5 have further defined the diameter of a bore to be the maximum inscribed diameter. pletely defined) measurand. The ambiguity associated 3 A “two-point diameter” is also an ambiguous measurand since with an incompletely defined measurand results in an different cross sections will in general yield different two-point dia- uncertainty contributor that must assessed during the meters. measurement uncertainty evaluation. 4 A least-squares diameter fit has an unambiguous value when com- As an example of defining a measurand consider the puted from an infinite number of points; the effect of finite sampling must be included as a measurement uncertainty source. “diameter” of a bore. The simple definition as a dia- 5 The calibration of gauge blocks made of the same material as the meter may be sufficient for a low accuracy application, master generally do not require a penetration correction since the but in a high accuracy situation imperfections from a deformation is the same on both blocks and hence cancels out. 372 Volume 106, Number 2, March–April 2001 Journal of Research of the National Institute of Standards and Technology deformation), but may be less well specified when using Generally the calibration validity conditions are either optical or capacitance probing technologies. The use of those specified in the definition of the measurand or are appropriate corrections will allow convergence of the “extended conditions.” Typically, master gauges, results from different measurement methods and bring artifacts, and reference standards have calibration them into accordance with the definition of the measur- validity conditions that are identical to the conditions and.6 Hence the methods divergence problem is actually specified in the definition of the measurand. For a problem with an incompletely specified measurand. example, the results of an NIST calibrated gauge block The definition of the measurand must also be suffi- are valid only at exactly 20 ЊC. Although no laboratory ciently complete to avoid improper use of the calibrated can actually realize the conditions specified in the artifact or instrument. For example, consider a hand definition of the measurand, deviations from the validity held micrometer that is calibrated for measuring work- conditions are included in the uncertainty budget of the pieces with flat and parallel surfaces by measuring calibration. Subsequent use of these standards, e.g., in several calibrated gauge blocks (with surfaces larger calibrating other artifacts, will similarly not be at the than the micrometer anvil
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