ISO/TC 69/SC 6/WG 7 - Statistical methods to support measurement uncertainty evaluation

ISO 21748:2017 gives guidance for - evaluation of measurement uncertainties using data obtained from studies conducted in accordance with ISO 5725‑2, and - comparison of collaborative study results with measurement uncertainty (MU) obtained using formal principles of uncertainty propagation (see Clause 14). ISO 5725‑3 provides additional models for studies of intermediate precision. However, while the same general approach may be applied to the use of such extended models, uncertainty evaluation using these models is not incorporated in this document. ISO 21748:2017 is applicable to all measurement and test fields where an uncertainty associated with a result has to be determined. ISO 21748:2017 does not describe the application of repeatability data in the absence of reproducibility data. ISO 21748:2017 assumes that recognized, non-negligible systematic effects are corrected, either by applying a numerical correction as part of the method of measurement, or by investigation and removal of the cause of the effect. The recommendations in this document are primarily for guidance. It is recognized that while the recommendations presented do form a valid approach to the evaluation of uncertainty for many purposes, it is also possible to adopt other suitable approaches. In general, references to measurement results, methods and processes in this document are normally understood to apply also to testing results, methods and processes.

ISO/TS 17503:2015 describes the estimation of uncertainties on the mean value in experiments conducted as crossed designs, and the use of variances extracted from such experiments and applied to the results of other measurements (for example, single observations). ISO/TS 17503:2015 covers balanced two-factor designs with any number of levels. The basic designs covered include the two-way design without replication and the two-way design with replication, with one or both factors considered as random. Calculations of variance components from ANOVA tables and their use in uncertainty estimation are given. In addition, brief guidance is given on the use of restricted maximum likelihood estimates from software, and on the treatment of experiments with small numbers of missing data points. Methods for review of the data for outliers and approximate normality are provided. The use of data obtained from the treatment of relative observations (for example, apparent recovery in analytical chemistry) is included.

ISO/TR 13587:2012 is concerned with three basic statistical approaches for the evaluation and interpretation of measurement uncertainty: the frequentist approach including bootstrap uncertainty intervals, the Bayesian approach, and fiducial inference. The common feature of these approaches is a clearly delineated probabilistic interpretation or justification for the resulting uncertainty intervals. For each approach, the basic method is described and the fundamental underlying assumptions and the probabilistic interpretation of the resulting uncertainty are discussed. Each of the approaches is illustrated using two examples including an example from the ISO/IEC Guide 98-3 (Uncertainty of measurement ? Part 3: Guide to the expression of uncertainty in measurement (GUM:1995)). This document also includes a discussion of the relationship between the methods proposed in GUM Supplement 1 and these three statistical approaches.

ISO/TS 21749:2005 follows the approach taken in the Guide to the expression of the uncertainty of measurement (GUM) and establishes the basic structure for stating and combining components of uncertainty. To this basic structure, it adds a statistical framework using the analysis of variance (ANOVA) for estimating individual components, particularly those classified as Type A evaluations of uncertainty, i.e. based on the use of statistical methods. A short description of Type B evaluations of uncertainty (non-statistical) is included for completeness. ISO/TS 21749:2005 covers experimental situations where the components of uncertainty can be estimated from statistical analysis of repeated measurements, instruments, test items or check standards. It provides methods for obtaining uncertainties from single-, two- and three-level nested designs only. More complicated experimental situations where, for example, there is interaction between operator effects and instrument effects or a cross effect, are not covered. ISO/TS 21749:2005 is not applicable to measurements that cannot be replicated, such as destructive measurements or measurements on dynamically varying systems (such as fluid flow, electronic currents or telecommunications systems). It is not particularly directed to the certification of reference materials (particularly chemical substances) and to calibrations where artefacts are compared using a scheme known as a "weighing design". For certification of reference materials, see ISO Guide 35. When results from interlaboratory studies can be used, techniques are presented in the companion guide ISO/TS 21748. The main difference between ISO/TS 21748 and this Technical Specification is that the ISO/TS 21748 is concerned with reproducibility data (with the inevitable repeatability effects), whereas this Technical Specification concentrates on repeatability data and the use of the analysis of variance for its treatment. ISO/TS 21749:2005 is applicable to a wide variety of measurements, for example, lengths, angles, voltages, resistances, masses and densities.

ISO 21748:2010 gives guidance for evaluation of measurement uncertainties using data obtained from studies conducted in accordance with ISO 5725-2:1994; comparison of collaborative study results with measurement uncertainty (MU) obtained using formal principles of uncertainty propagation. (ISO 5725-3:1994 provides additional models for studies of intermediate precision. However, while the same general approach may be applied to the use of such extended models, uncertainty evaluation using these models is not incorporated in ISO 21748:2010.) ISO 21748:2010 is applicable in all measurement and test fields where an uncertainty associated with a result has to be determined. It does not describe the application of repeatability data in the absence of reproducibility data. ISO 21748:2010 assumes that recognized, non-negligible systematic effects are corrected, either by applying a numerical correction as part of the method of measurement, or by investigation and removal of the cause of the effect. The recommendations in ISO 21748:2010 are primarily for guidance. It is recognized that while the recommendations presented do form a valid approach to the evaluation of uncertainty for many purposes, it is also possible to adopt other suitable approaches. In general, references to measurement results, methods and processes in ISO 21748:2010 are normally understood to apply also to testing results, methods and processes.

TS 21748:2004 gives guidance for the evaluation of measurement uncertainties using data obtained from studies conducted in accordance with ISO 5725-2, and for the comparison of collaborative study results with measurement uncertainty obtained using formal principles of uncertainty propagation. TS 21748:2003 is applicable in all measurement and test fields where an uncertainty associated with a result has to be determined, but does not describe the application of repeatability data in the absence of reproducibility data. The recommendations in this document are primarily for guidance.