A Careful Consideration of the Calibration Concept.
This paper presents a detailed discussion of the technical aspects of the calibration calibration /cal·i·bra·tion/ (kal?i-bra´shun) determination of the accuracy of an instrument, usually by measurement of its variation from a standard, to ascertain necessary correction factors. process with emphasis on the definition of thc 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 reproducibility Lab medicine The degree of agreement among repeated measurements of a particular parameter, presented in terms of a standard deviation or coefficient of variation of the results in a set of measurements are also addressed as they pertain to pertain to
verb relate to, concern, refer to, regard, be part of, belong to, apply to, bear on, befit, be relevant to, be appropriate to, appertain to the calibration process.
Key words: calibration; error; influence quantities; measurand; systematic error; uncertainty.
Accepted: January 16, 2001
Available online: http://www.nist.gov/jres
The 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 [1-3], in this paper we will focus on technical issues associated with measurement error and uncertainty as it relates to the calibration process. Modern metrological me·trol·o·gy
n. pl. me·trol·o·gies
1. The science that deals with measurement.
2. A system of measurement. concepts increasingly link the topics of measurement traceability, laboratory accreditation accreditation,
n a process of formal recognition of a school or institution attesting to the required ability and performance in an area of education, training, or practice. , and quality assurance programs to the topic of measurement uncertainty. An essential component of all uncertainty budgets is the employment of calibrated cal·i·brate
tr.v. cal·i·brat·ed, cal·i·brat·ing, cal·i·brates
1. To check, adjust, or determine by comparison with a standard (the graduations of a quantitative measuring instrument): gauges, standards, or instruments. It is the calibration process that transfers a reference value, usually an International System (SI) unit, to the artifact A distortion in an image or sound caused by a limitation or malfunction in the hardware or software. Artifacts may or may not be easily detectable. Under intense inspection, one might find artifacts all the time, but a few pixels out of balance or a few milliseconds of abnormal sound or instrument under calibration and hence establishes the "unbroken chain of comparisons" required for traceability. 
The ISO (1) See ISO speed.
(2) (International Organization for Standardization, Geneva, Switzerland, www.iso.ch) An organization that sets international standards, founded in 1946. The U.S. member body is ANSI. International Vocabulary of Basic and General Terms in Metrology metrology
Science of measurement. Measuring a quantity means establishing its ratio to another fixed quantity of the same kind, known as the unit of that kind of quantity. (VIM (Vendor Independent Messaging Interface) A programming interface developed by Lotus, Novell, IBM and others. In order to enable an application to send and receive mail over a VIM-compliant messaging system such as cc:Mail, programmers write to the VIM interface. )  defines calibration as follows:
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.) The result of a calibration permits either the assignment of values of measurands to the indications or the determination of corrections with respect to indications.
(2.) A calibration may also determine other metrological properties such as the effect of influence quantities.
(3.) The result of a calibration may be recorded in a document, sometimes called a calibration certificate or a calibration report.
While the body of the VIM definition is sufficiently general to accommodate nearly all calibration situations, this generality gen·er·al·i·ty
n. pl. gen·er·al·i·ties
1. The state or quality of being general.
2. An observation or principle having general application; a generalization.
3. provides little guidance as to what constitutes a calibration. It is the purpose of this paper to elaborate on this topic. Our discussion will be guided primarily by the Guide to the Expression of Uncertainty in Measurement (GUM) . We will focus our attention on three concepts associated with the VIM definition: (1) the measurand; (2) the "specified conditions" of the calibration; and (3) the "relationship" between measured or indicated values and those of reference values ref·er·ence values
A set of laboratory test values obtained from an individual or from a group in a defined state of health. .
2. Calibration Issues
2.1 The Measurand
The measurand is the particular quantity subject to measurement (VIM 2.6). It is defined by a set of specifications, i.e. instructions, not a numerical value. Indeed, the measurand is an idealized i·de·al·ize
v. i·de·al·ized, i·de·al·iz·ing, i·de·al·iz·es
1. To regard as ideal.
2. To make or envision as ideal.
1. concept and it may be impossible to produce an actual gauge, artifact, or instrument exactly to the specifications of the measurand. The measurand specifies the value(s) of the relevant influence quantities and these must be specified sufficiently well that any ambiguity is negligible This article or section is written like a personal reflection or and may require .
Please [ improve this article] by rewriting this article or section in an . with regard to the required accuracy of the calibration (GUM 3.3.2 and D1-D3): The more completely defined the measurand, the less uncertainty will (potentially) be associated with its realization. A completely specified definition of the measurand has associated with it a unique value and an incompletely specified measurand may have many values, each conforming to the (incompletely defined) measurand. The ambiguity associated with an incompletely defined measurand results in an uncertainty contributor that must assessed during the mea surement uncertainty evaluation.
As an example of defining a measurand consider the "diameter" of a bore. The simple definition as a diameter may be sufficient for a low accuracy application, but in a high accuracy situation imperfections from a perfectly circular workpiece Noun 1. workpiece - work consisting of a piece of metal being machined
piece of work, work - a product produced or accomplished through the effort or activity or agency of a person or thing; "it is not regarded as one of his more memorable works"; "the symphony was may be significant.  Due to manufacturing imperfections, the diameter of a workpiece is incompletely defined and this can lead to "methods divergence divergence
In mathematics, a differential operator applied to a three-dimensional vector-valued function. The result is a function that describes a rate of change. The divergence of a vector v is given by problems" where different measuring instruments yield significantly different results. For example, when measuring a bore, a two-point diameter as measured with a micrometer micrometer (mīkrŏm`ətər, mī`krōmē'tər).
1 Instrument used for measuring extremely small distances. ,  a least-squares fit diameter as measured with a coordinate measuring machine,  and a maximum inscribed in·scribe
tr.v. in·scribed, in·scrib·ing, in·scribes
a. To write, print, carve, or engrave (words or letters) on or in a surface.
b. To mark or engrave (a surface) with words or letters. diameter as found using a plug gauge, will each yield a different numerical value because each measurement method realizes a different quantity permitted by the poorly defined measurand. No amount of improvement in the accuracy of these measurement methods will cause their results to converge con·verge
v. con·verged, con·verg·ing, con·verg·es
a. To tend toward or approach an intersecting point: lines that converge.
b. as they are fundamentally measuring different quantities (two point, least-squares, and maximum inscribed diameters). Hence, the methods divergence problem is actually an uncertainty source associated with an incomplete definition of the measurand. A similar exam ple is the measurement of the hardness of a material. The local hardness (microhardness) is often significantly different than the average hardness; consequently, unless a particular test location is specified, measurements at different locations can produce significantly different results.
A complete definition of the measurand will, in the general case, allow corrections to be applied for different measurement methods. For example, the calibration of a chrome-carbide gauge block using a gauge block comparator comparator
Instrument for comparing something with a similar thing or with a standard measure, in particular to measure small displacements in mechanical devices. In astronomy, the blink comparator is used to examine photographic plates for signs of moving bodies. and a steel master requires the correction for the differential mechanical penetration of the probe tips since the length of the block is defined as the undeformed length.  While in principle the complete definition of the measurand requires an infinite amount of information, in practice it usually contains detailed information appropriate for a particular (usually conventional) measurement method and may be significantly incomplete if alternative measurement methods are used. For example, the measurand associated with an artifact's length might be well specified when using an instrument with mechanical contact probes (such as specifying a correction for the mechanical contact deformation deformation /de·for·ma·tion/ (de?for-ma´shun)
1. in dysmorphology, a type of structural defect characterized by the abnormal form or position of a body part, caused by a nondisruptive mechanical force.
2. ), but may be less well specified when using optical or capacitance capacitance, in electricity, capability of a body, system, circuit, or device for storing electric charge. Capacitance is expressed as the ratio of stored charge in coulombs to the impressed potential difference in volts. probing technologies. The use o f appropriate corrections will allow convergence of the results from different measurement methods and bring them into accordance Accordance is Bible Study Software for Macintosh developed by OakTree Software, Inc.
As well as a standalone program, it is the base software packaged by Zondervan in their Bible Study suites for Macintosh. with the definition of the measurand.  Hence the methods divergence problem is actually a problem with an incompletely specified measurand.
The definition of the measurand must also be sufficiently complete to avoid improper
Iron block on which metal is placed for shaping, originally by hand with a hammer. The blacksmith's anvil is usually of wrought iron (sometimes of cast iron), with a smooth working surface of hardened steel. size). This procedure does not calibrate To adjust or bring into balance. Scanners, CRTs and similar peripherals may require periodic adjustment. Unlike digital devices, the electronic components within these analog devices may change from their original specification. See color calibration and tweak. the micrometer for measuring ball diameters because the flatness and parallelism An overlapping of processing, input/output (I/O) or both.
1. parallelism - parallel processing.
2. (parallel) parallelism - The maximum number of independent subtasks in a given task at a given point in its execution. E.g. of the anvils are unknown and are significant influence quantities for the (ball diameter) measurand.
Included in the definition of the measurand is a set of conditions that specify all the values of the influence quantities relevant to the measurand. Typically, the higher the accuracy requirements, the more extensive the list of specified influence quantities in order to have negligible uncertainty associated with the definition of the measurand. Note that definition of the measurand must address all significant conditions, i.e., influence quantities, not just environmental conditions.
2.2 The Specified Validity Conditions
The conditions under which the results of a calibration are valid must be stated in the calibration documentation, i.e., the calibration report. These conditions, which we will call the calibration validity conditions,  include the values (or range of values) of all significant influence quantities for which the calibration results are valid. In the case of instruments, the validity conditions also include the number of measurements used to compute To perform mathematical operations or general computer processing. For an explanation of "The 3 C's," or how the computer processes data, see computer. a result, because if repeated measurements by an instrument yield different results, then the mean (mathematical average) result will usually have a smaller uncertainty than a single result.
Generally the calibration validity conditions are either those specified in the definition of the measurand or are "extended conditions." Typically, master gauges, artifacts artifacts
see specimen artifacts. , and reference standards have calibration validity conditions that are identical to the conditions specified in the definition of the measurand. For example, the results of an NIST calibrated gauge block are valid only at exactly 20[degrees]C, Although no laboratory can actually realize the conditions specified in the definition of the measurand, deviations from the validity conditions are included in the uncertainty budget of the calibration. Subsequent use of these standards, e.g., in calibrating other artifacts, will similarly not be at the validity conditions, i.e. not exactly at the conditions in the definition of the measurand. Hence the metrologist is obligated ob·li·gate
tr.v. ob·li·gat·ed, ob·li·gat·ing, ob·li·gates
1. To bind, compel, or constrain by a social, legal, or moral tie. See Synonyms at force.
2. To cause to be grateful or indebted; oblige. to develop an uncertainty budget which includes not only the uncertainty stated in the calibration report of the reference artifact, but also any failure to exactly realize the (measurand-defining) conditions of the reference artifact during subsequent calibrations which use the reference artifact as the "master." Thus the uncertainty of each subsequent calibration in a traceability chain will be greater than the uncertainty of the previous calibration since the measurand-defining conditions generally cannot be fully achieved.
In contrast, some industrial calibrations involve "extended validity conditions" that are appropriate for their particular needs. These conditions may differ significantly from those that define the measurand; in particular it may include a range of influence quantities or specify a particular set of conditions that differ from those that define the measurand. For example, a factory floor worker using an instrument may not want to develop an uncertainty budget for every measurement performed. What may be desired is a-calibration report that states an uncertainty under validity conditions that include the conditions of actual use. A common example is a voltmeter calibration that gives an uncertainty statement over a range of ambient temperatures Outside temperature at any given altitude, preferably expressed in degrees centigrade. . The calibration of an instrument or artifact under extended validity conditions must have its errors and uncertainties assessed over this range of conditions, or alternatively, if a sufficient model describing the behavior of the artifact or instrument exists, then t he consequences of these conditions can be calculated and included in the calibration report. As with the definition of the measurand, specifying the extended validity conditions involves stating the permitted values of any influence quantity that affects the measurement. In some situations a calibration report may specify a series of uncertainty statements corresponding to a series of different validity conditions, allowing the end user to select the conditions most appropriate for the measurement.
2.3 The Relationship
The "relationship" between measured or indicated values and those of the reference values is a key issue with regards to calibration. The calibration process may include a wide variety of activities, including determining the mathematical relationships between influence quantities and the indications of instruments, the creation of the actual indications, e.g., the scribing scribe
1. A public clerk or secretary, especially in ancient times.
2. A professional copyist of manuscripts and documents.
3. A writer or journalist.
4. See scriber.
v. of graduations onto a scale, and the adjustment of parameters to correct for known systematic effects.  However, all calibrations must include a statement about the accuracy of the instrument or artifact as required by traceability. This is the relationship we will focus on in this paper. This statement may take many different forms but it describes the estimated systematic error  (or the deviation DEVIATION, insurance, contracts. A voluntary departure, without necessity, or any reasonable cause, from the regular and usual course of the voyage insured.
2. from a stated nominal value Nominal Value
The stated value of an issued security that remains fixed, as opposed to its market value, which fluctuates.
When referring to fixed-income securities, the nominal value is also the face value. ) and the associated uncertainty, for the specific measurand, under the validity conditions of the calibration. The values of the estimated systematic error (or deviation from nominal), together with their a ssociated uncertainties may be expressed in a table, calibration curve In analytical chemistry, a calibration curve is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration. , or other means of documentation.
For many instruments and artifacts, the measurement result is a continuous variable, e.g., a micrometer may measure length continuously over a zero to 50 mm interval. Since it is impossible to calibrate such an instrument or artifact for all possible values, engineering judgement must be used during the calibration process to assess the reasonable errors associated with the measurement results over the interval. What constitutes reasonable errors is best left to a standards organization A standards organization, also sometimes referred to as a standards body, a standards development organization or SDO (depending on what is being referenced), is any entity whose primary activities are developing, coordinating, promulgating, revising, amending, or other bodies that develop performance evaluation Performance evaluation
The assessment of a manager's results, which involves, first, determining whether the money manager added value by outperforming the established benchmark (performance measurement) and, second, determining how the money manager achieved the calculated return tests specific to the particular technology relevant to the instrument or artifact under consideration. The issues of uncertainty, error, systematic error, and reproducibility are important to the topic of calibration; a discussion of these issues is presented in the Appendix.
2.4 Reporting Calibration Results
There are numerous different methods used to report the accuracy of calibration results. Some of the more common methods are listed below together with comments.
1. Measurement Result and Uncertainty. The best estimate of the value associated with the measurand is typically the mean of repeated measurements that have been adjusted for all needed corrections. This format is typical of artifacts or instruments that have no previous measurement history or reference value. Uncertainty statements should conform to Verb 1. conform to - satisfy a condition or restriction; "Does this paper meet the requirements for the degree?"
coordinate - be co-ordinated; "These activities coordinate well" the GUM and are usually stated (by national and international default) using a coverage factor of two (see Appendix A).
2. Deviation from Nominal or Reference Value and Uncertainty. This format is typical of artifacts that have been assigned a nominal or reference value. For example, gauge block calibrations typically report the deviation from the stated nominal length of the block and the uncertainty in this deviation. Sometimes these deviations are erroneously er·ro·ne·ous
Containing or derived from error; mistaken: erroneous conclusions.
[Middle English, from Latin err referred to as "corrections," however VIM 3.15 clearly defines corrections as the negative of the estimated systematic error which involves the "true" (not nominal) value associated with the measurand.
3. Estimated Systematic Error and Uncertainty. This format is typical of instrument calibration where the reported estimated systematic error is later used to provide a correction value used in subsequent measurements. A variant variant /var·i·ant/ (var´e-ant)
1. something that differs in some characteristic from the class to which it belongs.
2. exhibiting such variation.
adj. of this method is to report the correction value and its uncertainty; the correction value differs in sign from the estimated systematic error and any calibration table or calibration curve should clearly indicate if the presented data is the estimated systematic error or the correction value. A special case of this method is when the estimated systematic error has been adjusted to zero. In this case it should be clearly reported that the estimated systematic error is zero and the remaining uncertainty stated.
4. Metrological Requirements. This format is typical of industrial calibrations where some requirement has been established, typically a "maximum permissible per·mis·si·ble
Permitted; allowable: permissible tax deductions; permissible behavior in school.
per·mis error" (MPE MPE
Master of Public Education ) for instruments or a maximum deviation from nominal for artifacts. For example, a calibration of a hand-held micrometer could be required to demonstrate conformance con·for·mance
Noun 1. conformance - correspondence in form or appearance
agreement, correspondence - compatibility of observations; "there was no agreement between theory and with a stated MPE value. Similarly a calibration of a gauge block could be required to demonstrate that the deviations from nominal be less than some stated value Stated Value
A value that, instead of being par value, is assigned to a corporation's stock for accounting purposes. Stated value has no relation to market price.
Notes: provided by a grade classification in order for the block to be in conformance with that grade. When demonstrating conformance to a metrological requirement, the decision rule should be stated in the calibration report." (A decision rule clearly states how measurement uncertainty will be addressed when demonstrating conformance according to according to
1. As stated or indicated by; on the authority of: according to historians.
2. In keeping with: according to instructions.
3. Subsequent Measurement Uncertainty Statements
The results of a calibration describe the value and uncertainty associated with our knowledge of a specific measurand under specified validity conditions for an artifact or instrument. Typically, the artifact or instrument is used in subsequent measurements that are not calibrations. A traceable measurement requires both an unbroken chain of comparisons back to a reference value (typically a SI unit) and also an uncertainty statement. It is the use of a calibrated instrument or artifact in a measurement that provides the unbroken chain of comparisons back to the reference value. However, frequently the uncertainty statement provided by the calibration is insufficient for the subsequent measurement under consideration since the validity conditions of the calibration do not include those of the subsequent use. In some cases involving complex instruments, the measurand of the subsequent measurement may be significantly different from the measurand of the master used to calibrate the instrument. Consequently, it is up to the end user or metrologist to create an uncertainty statement for the measurement of interest. We now consider the relationship between calibration results and subsequent measurements.
The definition of the measurand of the calibrated instrument or artifact includes a stated set of conditions for all influence quantities. Similarly, the calibration results are valid for a specified set of validity conditions which may (or may not) be the same as the conditions in the measurand definition. We now introduce the measurement conditions that specify the values of the influence quantities that prevail during the subsequent measurements using the calibrated instrument or artifact. Two cases are possible:
1. Measurement conditions are included in the calibration validity conditions. In the case of a calibration with extended validity conditions, it is possible that the measurement conditions are contained within the calibration validity conditions. In this case the measurement uncertainty statement can be obtained directly from the calibration report. Additionally the calibration report may contain sufficient information to correct the measurement result for the estimated systematic error associated with the artifact or instrument.
2. Measurement conditions different from calibration validity conditions. In this case, the measurement conditions are not contained in the calibration validity conditions. This will always be the case for an artifact or instrument with calibration validity conditions specified as the conditions in the definition of the measurand, i.e., not extended validity conditions. Alternatively, this may also occur when the calibration's extended validity conditions do not fully include the measurement conditions. In these cases the information contained in the calibration report is not sufficient and it is necessary to develop an uncertainty budget for the subsequent measurement. In some cases developing the uncertainty budget may be quite simple, e.g., an instrument that is calibrated under a set of extended validity conditions that includes measuring steel artifacts is now used to measure aluminum artifacts; this new measurement condition might be easily be taken into account since the properties of materials are gen erally well known. In other cases the uncertainty budget may be very difficult to develop, e.g., an instrument with a complex dependence on environmental conditions, is used in environmental conditions significantly different from those of the calibration validity conditions. To create a measurement uncertainty statement for this case, there must be an acceptable procedure to assess the change of the estimated systematic error and the uncertainty from the calibration validity conditions to the measurement conditions. Such an evaluation will always increase the measurement uncertainty because it will add new corrections for systematic effects, together with their uncertainties associated with the measurement conditions. Some methods to evaluate these effects include:
* Guidance, such as evaluation procedures, provided in the calibration report.
* Instrument performance specifications provided by the manufacturer.
* Mathematical/physical model of the measurement process. Such a model provides a functional relationship between the value of the measurand indicated by the instrument and the relevant condition parameters. (Typical condition parameters might be temperature, workpiece thermal expansion thermal expansion
Increase in volume of a material as its temperature is increased, usually expressed as a fractional change in dimensions per unit temperature change. coefficient coefficient /co·ef·fi·cient/ (ko?ah-fish´int)
1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities.
2. , etc.)
* Heuristic A method of problem solving using exploration and trial and error methods. Heuristic program design provides a framework for solving the problem in contrast with a fixed set of rules (algorithmic) that cannot vary.
1. plausibility model argued from an expert Type B perspective. Acceptance of such an evaluation will depend strongly on the perceived qualifications of the expert.
We have described several of the technical issues associated with the calibration process. The distinction between the measurand conditions, the calibration validity conditions (not to be confused with the conditions prevailing at the time of the calibration), and the conditions of subsequent measurements are emphasized. The use of calibrated instruments or artifacts in traceable subsequent measurements will require the development of their own uncertainty statement if the conditions of measurement are outside the calibration validity conditions.
5. Appendix A. Uncertainty, Error, Systematic Error, and Reproducibility
Uncertainty of measurement, in its broadest sense, means doubt about the validity of a measurement result (GUM 2.2.1). The ISO International Vocabulary of Basic and General Terms in Metrology (VIM) defines uncertainty as a parameter (1) Any value passed to a program by the user or by another program in order to customize the program for a particular purpose. A parameter may be anything; for example, a file name, a coordinate, a range of values, a money amount or a code of some kind. , associated with the result of a measurement, that characterizes the dispersion dispersion, in chemistry
dispersion, in chemistry, mixture in which fine particles of one substance are scattered throughout another substance. A dispersion is classed as a suspension, colloid, or solution. of the values that could be reasonably attributed to the measurand (VIM 3.9). (The "measurand" is the specific quantity being measured.) It is noteworthy to point out, firstly, that an uncertainty statement is associated with a measurement result, not with the measurement instrument (although the instrument is an uncertainty contributor), and secondly, that measurement uncertainty is associated with a specific measurand and, in general, different measurands may have different uncertainty statements even if they are measured with the same instrument. The modern method of expressing measurement uncertainty involves summarizing the combined effects of all uncertainty sources in terms of a single quantity , known as the combined standard uncertainty [u.sub.c]. In most industrial settings, measurement uncertainty is expressed as a multiple (given by the coverage factor k) of the combined standard uncertainty, yielding the expanded uncertainty U, so that U = k [u.sub.c]. The expanded uncertainty can be used to define an interval, y [+ or -] U where y is the result of a measurement, that may be expected to encompass a large fraction of the distribution of values that could be reasonably attributed to the measurand (GUM 2.3.5). Furthermore, the expanded uncertainty is often associated with a level of confidence through the coverage factor; the typical default value of the coverage factor is two ([U.sub.k=2] = 2[u.sub.c]), which is generally considered to imply a level of confidence of approximately 95 %; see Fig. 1. The specific level of confidence requires assumptions about the probability distribution Probability distribution
A function that describes all the values a random variable can take and the probability associated with each. Also called a probability function.
probability distribution that is characterized char·ac·ter·ize
tr.v. character·ized, character·iz·ing, character·iz·es
1. To describe the qualities or peculiarities of: characterized the warden as ruthless.
2. by the measurement result and its combined standard uncertainty. However, using the defaul t coverage factor of two and assuming a % confidence is usually a reasonable approximation approximation /ap·prox·i·ma·tion/ (ah-prok?si-ma´shun)
1. the act or process of bringing into proximity or apposition.
2. a numerical value of limited accuracy. provided the effective degrees of freedom is reasonably large, e.g., [greater than or equal to]20 and the uncertainty contributors have been well evaluated. A 95 % level of confidence implies that 95 % of the values that can be reasonably attributed to the measurand lie within an uncertainty interval of [+ or -] [U.sub.k=2] that is centered on the measurement result.
The error in a measurement result is defined as the measured value minus the "true value" of a measurand (VIM 3.10); see Fig. 2. Strictly speaking Adv. 1. strictly speaking - in actual fact; "properly speaking, they are not husband and wife"
properly speaking, to be precise , the error of a measurement result is never exactly known since the value of a measurand is never exactly known. However, useful estimates of an error are possible when the uncertainty in the error is small relative to the magnitude of the error. Hence errors can only be estimated when performing a measurement of (or comparison to) a standard that has a previously assigned value so that an independent estimate of the "true value" of the measurand is available.  It is worth reiterating that when estimating an error the measured value is whatever number is reported by the measurement system, and as far as determining the error of that measurement is concerned, the measured value is an exact, well-defined, value see Fig. 3. 
The uncertainty of a standard used to realize a measurand includes not only the uncertainty documented in its calibration report but also any additional uncertainty associated with the conditions the prevail at the time it is used in the calibration. For example, a gauge block with a length specified at 20 [degrees]C (the measurand) may be used to calibrate an instrument at 21 [degrees]C. After the correction for the thermal expansion of the block, there remains the uncertainty associated with the measurement temperature differing from the measurand defined conditions. This additional uncertainty must be combined with the uncertainty associated with the standard stated at 20 [degrees]C. The effect of any influence quantity present during the calibration that degrades the accuracy of the reference standard must be included in the uncertainty associated with the realization of the measurand during the calibration.
For general workpiece measurements, the measurand is an attribute of the workpiece and its "true value" is unknown (hence the point of making the measurement), and therefore the measurement error is similarly unknown. Thus, for most workpiece measurements, it is incorrect to speak of the measurement error  and the appropriate term for the workpiece measurement situation is measurement uncertainty.
Systematic Error is the (mathematical) expectation value of the error. It can be estimated as the mean error in the reported value of a measuring instrument or of an artifact. Similar to the case of error, the systematic error is never exactly known because we never know the "true value" and we cannot perform an infinite number infinite number
a number so large as to be uncountable. Represented by 8, frequently obtained by 'dividing' by zero. of measurements of a standard to produce the expectation value. The estimated systematic error may be determined from the mean of a series of repeated measurements or as a calculated value corresponding to a known systematic effect. Figure 4(a) illustrates a series of measurements that have good reproducibility but contain a large estimated systematic error in addition to a significant uncertainty associated with the realization of the measurand. As previously described, realization of the measurand includes the uncertainty associated with the reference standard under the conditions employed during the calibration.
The reproducibility of a measurement is "the closeness of agreement between results of measurements of the same measurand carried out under changed conditions of measurement" (VIM 3.7). For a calibration, the sources of the changing conditions may correspond to variations in any of the influence quantities in the definition of the measurand (some of these changes might be manifested by changing the metrologist and the measuring instrument). While each of the observed estimated errors could have a small uncertainty (because the uncertainty associated with realizing the measurand is small), the measurement uncertainty may be large due to the reproducibility; see Fig. 4(b).
In a typical calibration, the measurement uncertainty is usually a combination of the uncertainty associated with the standard (i.e., the realization of the measurand), that associated with measurement reproducibility, and other static effects ( e.g., a sensor may have an unkown fixed offset from its calibrated value and consequently this effect may not appear in the reproducibility evaluation ); see Fig. 4(c).
This work was funded in part by the US Air Force and US Navy Calibration Coordination Group (CCG CCG Chicago
CCG Collectible Card Game
CCG Canadian Coast Guard
CCG Country Commercial Guide
CCG Children's Cancer Group
CCG Commission Canadienne des Grains (Canadian Grain Commission) ) Program and the Manufacturing Engineering Manufacturing engineering
Engineering activities involved in the creation and operation of the technical and economic processes that convert raw materials, energy, and purchased items into components for sale to other manufacturers or into end products for Laboratory's Shop Floor as an NMI (NonMaskable Interrupt) A high-priority interrupt that cannot be disabled by another interrupt. It is used to report malfunctions such as parity, bus and math coprocessor errors.
NMI - Non-Maskable Interrupt project. The authors thank Mr. Thomas Carpenter (Newark AFB AFB
AFB Acid-fast bacillus, also 1. Aflatoxin B 2. Aorto-femoral bypass ) for his useful comments.
About the authors: Steve Phillips
Steve Francis Phillips (born on May 18, 1963) was the general manager of the New York Mets from 1997-2003. , Tyler Estler, and Ted Doiron are physicists Below is a list of famous physicists. Many of these from the 20th and 21st centuries are found on the list of recipients of the Nobel Prize in physics. A
(1.) Even calibrations that use "self-calibration" methods, e.g., straightedge reversal using aa indicator, require uncertainty statements since the uncertainty of the iadicator must be assessed.
(2.) For this reason, some standards such as ASME ASME - American Society of Mechanical Engineers Y14.5 have further defined the diameter of a bore to be the maximum inscribed diameter.
(3.) A "two-point diameter" is also an ambiguous measurand since different cross sections will in general yield different two-point diameters.
(4.) A least-squares diameter fit has an unambiguous value when computed from an infinite number of points; the effect of finite finite - compact sampling must be included as a measurement uncertainty source.
(5.) The calibration of gauge blocks made of the same material as the master generally do not require a penetration correction since the deformation is the same on both blocks and hence cancels out.
(6.) In some cases a metrologist will deliberately choose (for economy or convenience) to measure a related quantity that differs from the measurand, e.g., a least-squares diameter instead of a maximum inscribed diameter. In this case a estimated systematic error results, which must either be corrected or accounted for in the uncertainty statement of the measurement.
(7.) We use the term calibration validity conditions in order to avoid confusion with the conditions that happen to prevail at the time of the calibration.
(8.) Some accreditation programs require a calibration before and after adjustments are performed so that the metrological history of the instrument or artifact is maintained.
(9.) We use the term systematic error in the VIM sense, as the mean error of an infinite number of measurements.
(10.) For reference artifacts, e.g. gauge blocks, it is usually more useful to state the "deviation from the nominal value."
(11.) Some accreditation programs may require the use of a specific decision rule in order for the measurement to be considered a calibration.
(12.) The standard is intended to realize a "true value" of the measurand. Unfortunately, all standards have an associated uncertainty. This includes the uncertainty documented in its report of calibration and the uncertainty in the standard due to the conditions at the time it is used as a reference standard. We describe the combined uncertainty due to both these effects as "uncertainty in realizing the measurand" of the standard.
(13.) An extreme example of the difference between uncertainty and error is the measurement of a gauge block having a calibrated length of 10.0000 mm with a wooden rule having millimeter One thousandth of a meter, or 1/25th of an inch. See metric system. divisions. If the wooden rule yields a measurement result of 10 mm; the estimated error is zero but the uncertainty is significant.
(14.) It is still permissible to speak of the statistical properties of the error. For example, a measurement corrected for all known systematic effects has an expectation value of zero for the error, and the standard deviation In statistics, the average amount a number varies from the average number in a series of numbers.
(statistics) standard deviation - (SD) A measure of the range of values in a set of numbers. of
the probability distribution associated with the error has its value equal to that of the combined standard uncertainty.
(15.) Typically a static systematic effect is assessed by a Type B uncertainty evaluation. However, if a reproducibility study is conducted for a sufficiently long time, then it may be possible to include several different values of this static offset, e.g., due to recalibrations of a sensor, and consequently this effect may be included in the variation evaluated in the (Type A) reproducibility study.
(1.) National Conference of Standard Laboratories, NCSL NCSL National Conference of State Legislatures
NCSL National College for School Leadership
NCSL National Conference of Standards Laboratories
NCSL National Council of State Legislators
NCSL National Computer Systems Laboratory (NIST) Z540-l-1994, Calibration Laboratories and Measuring and Test Equipment--General Requirements.
(2.) International Organization for Standardization International Organization for Standardization (ISO)
Organization for determining standards in most technical and nontechnical fields. Founded in Geneva in 1947, its membership includes more than 100 countries. , ISO Guide 25, General Requirements for the Competence of Calibration and Testing Laboratories (1990).
(3.) International Organization for Standardization, ISO 10012-1, Quality Assurance Requirements for Measuring Equipment--Part 1: Metrological Confirmation System for Measuring Equipment (1992).
(4.) International Organization for Standardization, International Vocabulary of Basic and General Terms in Metrology, Geneva Geneva, canton and city, Switzerland
Geneva (jənē`və), Fr. Genève, canton (1990 pop. 373,019), 109 sq mi (282 sq km), SW Switzerland, surrounding the southwest tip of the Lake of Geneva. , Switzerland (1993).
(5.) International Organization for Standardization, Guide to the Expression of Uncertainty in Measurement, Geneva, Switzerland (1993). (Corrected and reprinted 1995.) This document is also available as a U.S. National Standard: NCSL Z540-2-1997.