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Anatech Electronics

Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results
(from the NIST website)

Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results  - RF CafeI when I originally posted NIST Technical Note 1297, it had the name "Essentials of Expressing Measurement Uncertainty." Since that time, the NIST website changed its link to the updated version which now goes by the title of "Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results." It includes a lot of new data; in fact, it has been nearly totally re-written. This is a valuable reference for anyone who needs to understand the proper method for calculating measurement uncertainties.

BTW, a "measureand" is: A quantity or object  intended to be measured.

NIST Technical Note 1297

1994 Edition

Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results

Barry N. Taylor and Chris E. Kuyatt

Note: U.S. Government documents are in the public domain and may be freely distributed so long as content is not changed. This document is being made available for the convenience of RF Cafe visitors.

Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results

Preface to the 1994 Edition

The previous edition, which was the first, of this National Institute of Standards and Technology (NIST) Technical Note (TN 1297) was initially published in January 1993. A second printing followed shortly thereafter, and in total some 10 000 copies were distributed to individuals at NIST and in both the United States at large and abroad — to metrologists, scientists, engineers, statisticians, and others who are concerned with measurement and the evaluation and expression of the uncertainty of the result of a measurement. On the whole, these individuals gave TN 1297 a very positive reception. We were, of course, pleased that a document intended as a guide to NIST staff was also considered to be of significant value to the international measurement community.

Several of the recipients of the 1993 edition of TN 1297 asked us questions concerning some of the points it addressed and some it did not. In view of the nature of the subject of evaluating and expressing measurement uncertainty and the fact that the principles presented in TN 1297 are intended to be applicable to a broad range of measurements, such questions were not at all unexpected.

It soon occurred to us that it might be helpful to the current and future users of TN 1297 if the most important of these questions were addressed in a new edition. To this end, we have added to the 1993 edition of TN 1297 a new appendix — Appendix D — which attempts to clarify and give additional guidance on a number of topics, including the use of certain terms such as accuracy and precision. We hope that this new appendix will make this 1994 edition of TN 1297 even more useful than its predecessor.

We also took the opportunity provided us by the preparation of a new edition of TN 1297 to make very minor word changes in a few portions of the text. These changes were made in order to recognize the official publication in October 1993 of the ISO Guide to the Expression of Uncertainty in Measurement on which TN 1297 is based (for example, the reference to the Guide was updated); and to bring TN 1297 into full harmony with the Guide (for example, "estimated correction" has been changed to simply "correction," and can be asserted to lie" has been changed to "is believed to lie"). September 1994 Barry N. Taylor Chris E. Kuyatt


Foreword (to the 1993 Edition)

Results of measurements and conclusions derived from them constitute much of the technical information produced by NIST. It is generally agreed that the usefulness of measurement results, and thus much of the information that we provide as an institution, is to a large extent determined by the quality of the statements of uncertainty that accompany them. 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.

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. 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.

To address this issue, in July 1992 I appointed a NIST Ad Hoc Committee on Uncertainty Statements and charged it with recommending to me a NIST policy on this important topic. The members of the Committee were:

  • D. C. Cranmer Materials Science and Engineering Laboratory
  • K. R. Eberhardt Computing and Applied Mathematics Laboratory
  • R. M. Judish Electronics and Electrical Engineering Laboratory
  • R. A. Kamper Office of the Director, NIST/Boulder Laboratories
  • C. E. Kuyatt Physics Laboratory
  • J. R. Rosenblatt Computing and Applied Mathematics Laboratory
  • J. D. Simmons Technology Services
  • L. E. Smith Office of the Director, NIST; Chair
  • D. A. Swyt Manufacturing Engineering Laboratory
  • B. N. Taylor Physics Laboratory
  • R. L. Watters Chemical Science and Technology Laboratory

This action was motivated in part by the emerging international consensus on the approach to expressing uncertainty in measurement recommended by the International Committee for Weights and Measures (CIPM). The movement toward the international adoption of the CIPM approach for expressing uncertainty is driven to a large extent by the global economy and marketplace; its worldwide use will allow measurements performed in different countries and in sectors as diverse as science, engineering, commerce, industry, and regulation to be more easily understood, interpreted, and compared.

At my request, the Ad Hoc Committee carefully reviewed the needs of NIST customers regarding statements of uncertainty and the compatibility of those needs with the CIPM approach. It concluded that the CIPM approach could be used to provide quantitative expressions of measurement uncertainty that would satisfy our customers’ requirements. The Ad Hoc Committee then recommended to me a specific policy for the implementation of that approach at NIST. I enthusiastically accepted its recommendation and the policy has been incorporated in the NIST Administrative Manual. (It is also included in this Technical Note as Appendix C.)

To assist the NIST staff in putting the policy into practice, two members of the Ad Hoc Committee prepared this Technical Note. I believe that it provides a helpful discussion of the CIPM approach and, with its aid, that the NIST policy can be implemented without excessive difficulty. Further, I believe that because NIST statements of uncertainty resulting from the policy will be uniform among themselves and consistent with current international practice, the policy will help our customers increase their competitiveness in the national and international marketplaces.

January 1993

John W. Lyons Director, National Institute of Standards and Technology


1. Introduction

1.1 In October 1992, a new policy on expressing measurement uncertainty was instituted at NIST. This policy is set forth in Statements of Uncertainty Associated With Measurement Results, Appendix E, NIST Technical Communications Program, Subchapter 4.09 of the Administrative Manual (reproduced as Appendix C of these Guidelines).

1.2 The new NIST policy is based on the approach to expressing uncertainty in measurement recommended by the CIPM1 in 1981 [1] and the elaboration of that approach given in the Guide to the Expression of Uncertainty in Measurement (hereafter called the Guide), which was prepared by individuals nominated by the BIPM, IEC, ISO, or OIML [2].1 The CIPM approach is founded on Recommendation INC-1 (1980) of the Working Group on the Statement of Uncertainties [3]. This group was convened in 1980 by the BIPM as a consequence of a 19772 request by the CIPM that the BIPM study the question of reaching an international consensus on expressing uncertainty in measurement. The request was initiated by then CIPM member and NBS Director E. Ambler. A 19852 request by the CIPM to ISO asking it to develop a broadly applicable guidance document based on Recommendation INC-1 (1980) led to the development of the Guide. It is at present the most complete reference on the general application of the CIPM approach to expressing measurement uncertainty, and its development is giving further impetus to the worldwide adoption of that approach.

1.3 Although the Guide represents the current international view of how to express uncertainty in measurement based on the CIPM approach, it is a rather lengthy document. We have therefore prepared this Technical Note with the goal of succinctly presenting, in the context of the new NIST policy, those aspects of the Guide that will be of most use to the NIST staff in implementing that policy. We have also included some suggestions that are not contained in the Guide or policy but which we believe are useful. However, none of the guidance given in this Technical Note is to be interpreted as NIST policy unless it is directly quoted from the policy itself. Such cases will be clearly indicated in the text.

1.4 The guidance given in this Technical Note is intended to be applicable to most, if not all, NIST measurement results, including results associated with – international comparisons of measurement standards, – basic research, – applied research and engineering, – calibrating client measurement standards, – certifying standard reference materials, and – generating standard reference data. Since the Guide itself is intended to be applicable to similar kinds of measurement results, it may be consulted for additional details. Classic expositions of the statistical evaluation of measurement processes are given in references [4 -7].

2. Classification of Components of Uncertainty

2.1 In general, the result of a measurement is only an approximation or estimate of the value of the specific quantity subject to measurement, that is, the measurand, and thus the result is complete only when accompanied by a quantitative statement of its uncertainty.

2.2 The uncertainty of the result of a measurement generally consists of several components which, in the CIPM approach, may be grouped into two categories according to the method used to estimate their numerical values: A. those which are evaluated by statistical methods, B. those which are evaluated by other means.

2.3 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." The nature of an uncertainty component is conditioned by the use made of the corresponding quantity, that is, on how that quantity appears in the mathematical model that describes the measurement process. When the corresponding quantity is used in a different way, a "random" component may become a "systematic" component and vice versa. Thus the terms "random uncertainty" and "systematic uncertainty" can be misleading when generally applied. An alternative nomenclature that might be used is

      "component of uncertainty arising from a random effect,"

      "component of uncertainty arising from a systematic effect,"

where a random effect is one that gives rise to a possible random error in the current measurement process and a systematic effect is one that gives rise to a possible systematic error in the current measurement process. 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.

NOTE – The difference between error and uncertainty should always be borne in mind. For example, the result of a measurement after correction (see subsection 5.2) can unknowably be very close to the unknown value of the measurand, and thus have negligible error, even though it may have a large uncertainty (see the Guide [2]).

2.4 Basic to the CIPM approach is representing each component of uncertainty that contributes to the uncertainty of a measurement result by an estimated standard deviation, termed standard uncertainty with suggested symbol ui , and equal to the positive square root of the estimated variance u2i.

2.5 It follows from subsections 2.2 and 2.4 that an uncertainty component in category A is represented by a statistically estimated standard deviation si, equal to the positive square root of the statistically estimated variance s2i, and the associated number of degrees of freedom νi . For such a component the standard uncertainty is ui = si. The evaluation of uncertainty by the statistical analysis of series of observations is termed a Type A evaluation (of uncertainty).

2.6 In a similar manner, an uncertainty component in category B is represented by a quantity uj , which may be considered an approximation to the corresponding standard deviation; it is equal to the positive square root of u2j , which may be considered an approximation to the corresponding variance and which is obtained from an assumed probability distribution based on all the available information (see section 4). Since the quantity u2j is treated like a variance and uj like a standard deviation, for such a component the standard uncertainty is simply uj. The evaluation of uncertainty by means other than the statistical analysis of series of observations is termed a Type B evaluation (of uncertainty).

2.7 Correlations between components (of either category) are characterized by estimated covariances [see Appendix A, Eq. (A-3)] or estimated correlation coefficients.

3. Type A Evaluation of Standard Uncertainty A

Type A evaluation of standard uncertainty may be based on any valid statistical method for treating data. Examples are calculating the standard deviation of the mean of a series of independent observations [see Appendix A, Eq. (A5)]; using the method of least squares to fit a curve to data in order to estimate the parameters of the curve and their standard deviations; and carrying out an analysis of variance (ANOVA) in order to identify and quantify random effects in certain kinds of measurements. If the measurement situation is especially complicated, one should consider obtaining the guidance of a statistician. The NIST staff can consult and collaborate in the development of statistical experiment designs, analysis of data, and other aspects of the evaluation of measurements with the Statistical Engineering Division, Computing and Applied Mathematics Laboratory. Inasmuch as this Technical Note does not attempt to give detailed statistical techniques for carrying out Type A evaluations, references [4 -7], and reference [8] in which a general approach to quality control of measurement systems is set forth, should be consulted for basic principles and additional references.

4. Type B Evaluation of Standard Uncertainty

4.1 A Type B evaluation of standard uncertainty is usually based on scientific judgment using all the relevant information available, which may include

– previous measurement data,

– experience with, or general knowledge of, the behavior and property of relevant materials and instruments,

– manufacturer's specifications,

– data provided in calibration and other reports, and

– uncertainties assigned to reference data taken from handbooks.

Some examples of Type B evaluations are given in subsections 4.2 to 4.6.

4.2 Convert a quoted uncertainty that is a stated multiple of an estimated standard deviation to a standard uncertainty by dividing the quoted uncertainty by the multiplier.

4.3 Convert a quoted uncertainty that defines a confidence interval having a stated level of confidence (see subsection 5.5), such as 95 or 99 percent, to a standard uncertainty by treating the quoted uncertainty as if a normal distribution had been used to calculate it (unless otherwise indicated) and dividing it by the appropriate factor for such a distribution. These factors are 1.960 and 2.576 for the two levels of confidence given (see also the last line of Table B.1 of Appendix B).

4.4 Model the quantity in question by a normal distribution and estimate lower and upper limits a and a+ such that the best estimated value of the quantity is (a+ + a-)/2 (i.e., the center of the limits) and there is 1 chance out of 2 (i.e., a 50 percent probability) that the value of the quantity lies in the interval a- to a+. Then uj ≈ 1.48a, where a = (a+ - a-)/2 is the half-width of the interval.

4.5 Model the quantity in question by a normal distribution and estimate lower and upper limits a- and a+ such that the best estimated value of the quantity is (a+ + a-)/2 and there is about a 2 out of 3 chance (i.e., a 67 percent probability) that the value of the quantity lies in the interval a- to a+. Then uj ≈ a, where a = (a+ - a-)/2.

Click here for the full Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results PDF document.

 

 

Posted December 17, 2020

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