Guidelines for evaluating and expressing the uncertainty of NIST measurement results

Probably not a substantial claim: may not pass S3 (load-bearing).

There is not always a simple correspondence between the classification of uncertainty components into categories A and B and the commonly used classification of uncertainty components as 'random' and 'systematic'.

“There is not always a simple correspondence between the classification of uncertainty components into categories A and B and the commonly used classification of uncertainty components as”

Probably not a substantial claim: may not pass S3 (load-bearing).

When details of NIST measurement results are provided to users by referring to published documents, the referenced documents must be kept up-to-date so that they are consistent with the measurement process in current use.

“it is imperative that the referenced documents be kept up-to-date so that they are consistent with the measurement process in current use.”

Classified as probably not a substantial claim. The quote only partly states this claim.

In cases where a valid statistical method is used or agreements require deviation, the report of uncertainty must document what was done and why.

“In both cases, the report of uncertainty must document what was done and why.”

• cites Appendix CNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Classified as probably not a substantial claim.

Estimating a coverage factor k_p requires taking into account the uncertainty of u_c(y).

“To estimate the value of such a coverage factor 1/2 (A-5) requires taking into account the uncertainty of u c ( y), that is,”

Probably not a substantial claim: may not pass S3 (load-bearing).

When a probability interpretation, such as a level of confidence, is provided for the interval defined by U or u_c, the basis for such a statement must be given.

“When this is done, the c basis for such a statement must be given.”

• cites Appendix CNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

NIST policy requires a description of how k was chosen when k is not taken equal to 2.

“A description of how k was chosen when k is not taken equal to 2.”

• cites Appendix CNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Classified as probably not a substantial claim.

The four-step coverage factor procedure is expected to find broad international acceptance because of its computational convenience, similar to k = 2 becoming the conventional coverage factor.

“The four-step procedure is included in these guidelines because it is expected to find broad acceptance internationally, due in part to its computational convenience, in much the same way that k = 2 has become the conventional coverage factor.”

May combine two claims.

NIST policy regarding reporting uncertainty is to report U together with the coverage factor k used to obtain it, or report u_c.

“Report U together with the coverage factor k used to obtain it, or report u .c”

• cites Appendix CNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

Since the early 1980s, an international consensus has been developing on a uniform approach to the expression of uncertainty in measurement.

“Since the early 1980s, an international consensus has been developing on a uniform approach to the expression of uncertainty in measurement.”

• cites [1]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [2]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

The CIPM approach does not specify how the relation between k and p is to be established.

“The CIPM approach does not specify how the relation between k and p is to be established.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Commonly, combined standard uncertainty u_c is used for reporting results of determinations of fundamental constants, fundamental metrological research, and international comparisons of realizations of SI units.

“Commonly, u is used for reporting results of c determinations of fundamental constants, fundamental metrological research, and international comparisons of realizations of SI units.”

• cites Appendix CNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

NIST policy requires a detailed description of how each component of standard uncertainty was evaluated.

“A detailed description of how each component of standard uncertainty was evaluated.”

• cites Appendix CNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

An uncertainty component arising from a systematic effect may in some cases be evaluated by method A while in other cases by method B, as may an uncertainty component arising from a random effect.

“In principle, an uncertainty component arising from a systematic effect may in some cases be evaluated by method A while in other cases by method B (see subsection 2.2), as may be an uncertainty component arising from a random effect.”

Probably not a substantial claim: may not pass S4 (based).

Only if quantitative and thoroughly documented statements of uncertainty accompany the results of NIST calibrations can the users of NIST calibration services establish their level of traceability to the U.S. standards of measurement maintained at NIST.

“For example, only if quantitative and thoroughly documented statements of uncertainty accompany the results of NIST calibrations can the users of our calibration services establish their level of traceability to the U.S. standards of measurement maintained at NIST.”

• AssumptionRests on an assumption: It is generally agreed that the usefulness of measurement results, and thus much of the information that NIST provides as an institution, is to a large extent determined by the quality of the statements of uncertainty that accompany them.

May combine two claims.

When ν_eff is comparatively small and an interval with a level of confidence close to a specified level is required, the uncertainty of u_c(y) is unlikely to be considered negligible and the small ν_eff would probably be taken into account when determining k_p.

“In this case, and in other similar cases where ν ( y) is comparatively small and an interval eff of u c having a level of confidence close to a specified level is required, it is unlikely that the uncertainty of u ( y) would be c considered negligible.Instead, the small value of ν eff , and thus the uncertainty of u ( y), would probably be taken into c account when determining k p .”

Probably not a substantial claim: may not pass S3 (load-bearing).

NIST policy recognizes that international, national, or contractual agreements to which NIST is a party may occasionally require deviation from NIST policy.

“Further, it is recognized c that international, national, or contractual agreements to which NIST is a party may occasionally require deviation from NIST policy.”

• cites Appendix CNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

The interval defined by U in the second example might be a conventional confidence interval (at least approximately) if all components of uncertainty are obtained from Type A evaluations.

“In this regard, the interval defined by U in the second example might be a conventional confidence interval (at least approximately) if all the components of uncertainty are obtained from Type A evaluations.”

Probably not a substantial claim: may not pass S3 (load-bearing).

In a 1986 recommendation, the CIPM requested that combined standard uncertainty u_c be used by all participants in giving the results of all international comparisons or other work done under the auspices of the CIPM and Comités Consultatifs.

“It should also be noted that in a 1986 recommendation [9], the CIPM requested that what is now termed combined standard uncertainty u be used”

• cites [9]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S2 (checkable), S4 (based). May combine two claims.

The use of a single approach within NIST rather than many different approaches would ensure the consistency of NIST outputs, thereby simplifying their interpretation.

“The use of a single approach within the Institute rather than many different approaches would ensure the consistency of our outputs, thereby simplifying their interpretation.”

• AssumptionRests on an assumption: Although the vast majority of NIST measurement results are accompanied by quantitative statements of uncertainty, there has never been a uniform approach at NIST to the expression of uncertainty.

May combine two claims.

The four-step coverage factor procedure is based on a proven approximation but should not be interpreted as rigorous because the approximation is extrapolated to situations where its applicability has not been fully investigated.

“However, although the procedure is based on a proven approximation, it should not be interpreted as being rigourous because the approximation is extrapolated to situations where its applicability has yet to be fully investigated.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Equation (A-3) is based on a first-order Taylor series approximation of Y = f(X_1, X_2, ..., X_N) and is referred to as the law of propagation of uncertainty.

“Equation (A-3 ) is based on a first-order Taylor series approximation of Y = f(X 1 , X 2 , . . ., X N ) and is conveniently referred to as the law of propagation of uncertainty.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

There are national as well as international standards that discuss the characterization of test methods by interlaboratory comparisons.

“There are national as well as international standards that discuss the characterization of test methods by interlaboratory comparisons.”

Probably not a substantial claim: may not pass S3 (load-bearing).

If a standard uncertainty is obtained from a source outside of the current measurement process and the nature of its individual components are unknown, it may be classified as having been obtained from a Type B evaluation.

“If a standard uncertainty is obtained from a source outside of the current measurement process and the nature of its individual components are unknown (which will often be the case), it may be classified as having been obtained from a Type B evaluation.”

Probably not a substantial claim: may not pass S3 (load-bearing).

When NIST authors participate in such characterization or measurement programs, NIST policy allows for the results to be expressed as required by the relevant standards.

“When NIST authors participate in such characterization or measurement programs, NIST policy allows for the results to be expressed as required by the relevant standards (see Appendix C, section 4).”

• cites Appendix CNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

Both u(xi) and u_i(y) can be viewed as components of uncertainty that give rise to the combined standard uncertainty u_c(y) of the measurement result y.

“In short, both u(x i ) and u i ( y) can be viewed as components of uncertainty that give rise to the combined standard uncertainty u ( y) of the measurement result y.”

Probably not a substantial claim: may not pass S3 (load-bearing).

When a measurement result is expressed in terms of a conventional reference value rather than the relevant SI unit, this is an example of a situation in which all significant components of uncertainty are not taken into account.

“(This is an example of a situation in which all significant components of uncertainty are not taken into account.)”

Probably not a substantial claim: may not pass S3 (load-bearing).

If the combined standard uncertainty u_c(y) of the measurement result y is obtained from Type A standard uncertainties (and covariances) only, it too may be considered Type A, even though no direct observations were made.

“In this same vein, if the combined standard uncertainty u ( y) of the measurement result y is obtained from Type A c standard uncertainties (and covariances) only, it too may be considered Type A, even though no direct observations were”

Probably not a substantial claim: may not pass S3 (load-bearing).

In Eq. (D-1), both u(xi) and u_i(y) can be considered components of uncertainty of the measurement result y.

“In Eq. (D-1), both u(x i ) and u i ( y) can be considered components of uncertainty of the measurement result y.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Such identification can also be given in a table which lists the components of standard uncertainty.

“However, such identification can also be given in a table which lists the components of standard uncertainty.”

Probably not a substantial claim: may not pass S3 (load-bearing).

A valid statement of reproducibility requires specification of the conditions changed.

“A valid statement of reproducibility requires specification of the conditions changed.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The t_p of this Technical Note and of the Guide and t_{1-α} are related by p = 1 - 2α.

“Thus t of this Technical Note and of the p Guide and t 1 α are related by p 1 2α.”

Probably not a substantial claim: may not pass S3 (load-bearing).

If a combined standard uncertainty is obtained from Type B standard uncertainties (and covariances) only, it too may be considered Type B.

“Similarly, if a combined standard uncertainty is obtained from Type B standard uncertainties (and covariances) only, it too may be considered Type B.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The values of t_p(ν) defined in reference [D.2] differ from the values of t_p(ν) defined as in this Technical Note and the Guide, and given in Table B.1.

“Clearly, the values of t p (ν ) defined in this way differ from the values of t p (ν ) defined as in this Technical Note and in the Guide, and given in Table B.1 (which is of the same form as that given in reference [10]).”

Probably not a substantial claim: may not pass S3 (load-bearing).

Many of NIST's sister national standards laboratories and important metrological organizations, including WECC and EUROMET, have adopted the approach recommended by the CIPM in 1981 and reaffirmed in 1986.

“Many of NIST's sister national standards laboratories as well as a number of important metrological organizations, including the Western European Calibration Cooperation (WECC) and EUROMET, have adopted the approach recommended by the International Committee for Weights and Measures (CIPM) in 1981 [1] and reaffirmed by the CIPM in 1986 [2].”

• cites [1]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [2]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

NIST SP 811 elaborates upon the NIST policy regarding the SI and explains why abbreviations such as ppm and ppb and terms such as normality and molarity should not be used.

“In particular, it elaborates upon the NIST policy regarding the SI and explains why abbreviations such as ppm and ppb and terms such as normality and molarity should not be used.”

• cites [D.3]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

A standard uncertainty known to be composed of components obtained from Type A evaluations alone should be classified as a Type A standard uncertainty, while a standard uncertainty known to be composed of components obtained from Type B evaluations alone should be classified as a Type B standard uncertainty.

“On the other hand, a standard uncertainty known to be composed of components obtained from Type A evaluations alone should be classified as a Type A standard uncertainty, while a standard uncertainty known to be composed of components obtained from Type B evaluations alone should be classified as a Type B standard uncertainty.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

In such cases the magnitude of the uncertainty ascribable to the measurement result may be significantly smaller than when that result is expressed in the relevant SI unit.

“In such cases the magnitude of the uncertainty ascribable to the measurement result may be significantly smaller than when that result is expressed in the relevant SI unit.”

Probably not a substantial claim: may not pass S3 (load-bearing).

If the input estimates xi are uncorrelated, Eq. (A-3) of Appendix A may be written as Eq. (D-1).

“For example, if the input estimates x i are uncorrelated, Eq. (A-3) of Appendix A may be written as (D-1)”

Probably not a substantial claim: may not pass S3 (load-bearing).

If a test method is employed at NIST to obtain measurement results for reasons other than those described above, it is expected that the uncertainties of these measurement results will be evaluated and reported according to section 2 of the NIST policy.

“If a test method is employed at NIST to obtain measurement results for reasons other than those described above, it is expected that the uncertainties of these measurement results will be evaluated and reported according to section 2 of the NIST policy (see Appendix C).”

• cites Appendix CNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

In many cases a measurand Y is not measured directly, but is determined from N other quantities X1...XN through a functional relation f.

“In many cases a measurand Y is not measured directly, but is determined from N other quantities X 1 , X 2 , . . ., X N through a functional relation f: Y f (X 1 , X 2 , . . ., X N ).”

Probably not a substantial claim: may not pass S3 (load-bearing).

As pointed out in the Guide, the result of a measurement is sometimes expressed in terms of the adopted value of a measurement standard or in terms of a conventional reference value rather than in terms of the relevant unit of the SI.

“As pointed out in the Guide, the result of a measurement is sometimes expressed in terms of the adopted value of a measurement standard or in terms of a conventional reference value rather than in terms of the relevant unit of the SI.”

• cites GuideNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Classified as probably not a substantial claim.

The approach to evaluating and expressing the uncertainty of a measurement result on which the NIST policy and this Technical Note are based is applicable to evaluating and expressing the uncertainty of the estimated value of a measurand that is defined by a standard method of measurement.

“The approach to evaluating and expressing the uncertainty of a measurement result on which the NIST policy and this Technical Note are based is applicable to evaluating and expressing the uncertainty of the estimated value of a measurand that is defined by a standard method of measurement.”

Probably not a substantial claim: may not pass S3 (load-bearing).

NIST policy on the use of units that are not part of the SI requires that SI units be stated first, with the units that are not part of the SI in parentheses.

“This situation is similar to the NIST policy on the use of units that are not part of the SI: the SI units must be stated first, with the units that are not part of the SI in parentheses (see subsection D.6.2).”

Classified as probably not a substantial claim. May combine two claims.

The function f of Eq. (A-1) should express not simply a physical law but a measurement process, and in particular, it should contain all quantities that can contribute a significant uncertainty to the measurement result.

“Thus the function f of Eq. (A-1) should express not simply a physical law but a measurement process, and in particular, it should contain all quantities that can contribute a significant uncertainty to the measurement result.”

Probably not a substantial claim: may not pass S3 (load-bearing).

NIST Special Publication 811, 1995 Edition, gives guidance on the use of the SI and on the rules and style conventions regarding quantity and unit symbols.

“NIST Special Publication 811, 1995 Edition [D.3], gives guidance on the use of the SI and on the rules and style conventions regarding quantity and unit symbols.”

• cites [D.3]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

The development of the Guide is providing further impetus to the worldwide adoption of the CIPM approach.

“The development of the Guide is providing further impetus to the worldwide adoption of the CIPM approach.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Execution of test methods according to these standards, both in the characterization stage and in subsequent measurement programs, often calls for the expression of uncertainties in terms of defined measures of repeatability and reproducibility.

“Execution of test methods according to these standards, both in the characterization stage and in subsequent measurement programs, often calls for the expression of uncertainties in terms of defined measures of repeatability and reproducibility.”

Probably not a substantial claim: may not pass S3 (load-bearing).

ISO 3534-1 views the concept of precision as encompassing both repeatability and reproducibility.

“Further, it views the concept of precision as encompassing both repeatability and reproducibility (see subsections D.1.1.2and D.1.1.3)”

• cites [D.2]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

Included among the quantities Xi are corrections (or correction factors) as described in subsection 5.2, as well as quantities that take into account other sources of variability, such as different observers, instruments, samples, laboratories, and times at which observations are made.

“Included among the quantities X i are corrections (or correction factors) as described in subsection 5.2, as well as quantities that take into account other sources of variability, such as different observers, instruments, samples, laboratories, and times at which observations are made (e.g., different days).”

Probably not a substantial claim: may not pass S3 (load-bearing).

The CIPM approach is based on Recommendation INC-1 (1980) of the Working Group on the Statement of Uncertainties.

“The CIPM approach is based on Recommendation INC-1 (1980) of the Working Group on the Statement of Uncertainties [3].”

• cites [3]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The CIPM approach has come into use in a significant number of areas at NIST and is becoming accepted in U.S. industry.

“Equally important, the CIPM approach has come into use in a significant number of areas at NIST and is also becoming accepted in U.S. industry.”

Probably not a substantial claim: may not pass S3 (load-bearing).

If the standard uncertainty from an outside source is known to be composed of components obtained from both Type A and Type B evaluations but the magnitudes of the individual components are unknown, then one may indicate this by using (A,B) rather than (B) in a table such as D.1.

“If the standard uncertainty from an outside source is known to be composed of components obtained from both Type A and Type B evaluations but the magnitudes of the individual components are unknown, then one may indicate this by using (A,B) rather than (B) in a table such as D.1.”

Probably not a substantial claim: may not pass S3 (load-bearing).

As pointed out in the Guide, the t-distribution is often tabulated in quantiles.

“As pointed out in the Guide, the t-distribution is often tabulated in quantiles.”

• cites GuideNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.