1. Scope

The procedures in this chapter are intended for test laboratories, calibration laboratories, and scientific laboratories that report results of measurements from on-going or well-documented processes.
Evaluation of uncertainty is an on-going process that can consume time and resources. It requires familiarity with data analysis techniques, particularly statistical analysis. Therefore, it is important for laboratory personnel who are approaching uncertainty analysis for the first time to be aware of the resources required and to carefully lay out a plan for data collection and analysis.
This document follows the approach taken in the Guide to the Expression of the Uncertainty of Measurement (GUM) to stating and combining components of uncertainty. To this basic structure, it adds a statistical framework for estimating individual components, particularly those which are classified as type A uncertainties. It also covers cases where the reported value is an average of measurements made on primary or secondary variables in the measurement process.
The present document is not well suited to the certification of reference materials (particularly chemical substances), and to calibrations where artifacts are intercompared using a scheme known as a "weighing design". Both of these areas require more specific guidance than is given in this document and will be treated in a future document.

The document covers experimental situations where the components of uncertainty can be estimated from measurements on the test items itself, measurements on a check standard, nested designs for two and three levels of uncertainty components. More complicated experimental situations, for example where operators are crossed with instruments, are not covered in the present docment.

Some laboratories, such as test laboratories, may not have the resources to undertake detailed uncertainty analyses even though, increasingly, quality management standards such as the ISO 9000 series are requiring that all measurement results be accompanied by statements of uncertainty. Other situations where uncertainty analyses are problematical are:
  • One of a kind measurements
  • Dynamic measurements that depend strongly on the application for the measurement
What can be done in these situations? Organizations, such as the International Standards Organization (ISO) are investigating simplifed methods for dealing with this problem based on repeatability and reproducibility measures from interlaboratory tests.

2. Normative references

Normative references for this document are:

  • ISO 3534-Part 1: General vocabulary
  • ISO 3435-Part 2: Statistical terms
  • ISO 3435-Part 3: Design of experiments
  • ISO 5725-Part 1: Accuracy of measurement methods and results: General principles and definitions
  • ISO 5725-Part 2: Accuracy of measurement methods and results: Basic method for the determination of repeatability and reproducibility of a standard measurement method
  • ISO 5725-Part 3: Accuracy of measurement methods and results: Intermediate measures of precision of a standard measurement method
  • ISO 5725-Part 4: Accuracy of measurement methods and results: Basic methods for the determination of trueness of a standard measurement method
  • ISO 5725-Part 5: Accuracy of measurement methods and results: Alternative methods for the determination of the precision of a standard measurement method
  • ISO 5725-Part 6: Accuracy of measurement methods and results: Use in practice of accuracy values
  • ISO 11095: Linear calibration using reference materials

3. Definitions

  • Uncertainty - a parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the quantity being measured.

  • Type A evaluation of uncertainty - quantification of uncertainty component using statistical methods.

  • Type B evaluation - quantification of uncertainty component using non-statistical methods.

  • Standard uncertainty - standard deviation associated with a single component of uncertainty.

  • Sensitivity coefficient - coefficient showing the relationship between a single uncertainty component and the standard deviation of a result.

  • Combined standard uncertainty - standard deviation associated with the result of a particular measurement or series of measurements that takes into account one or more components of uncertainty.

  • Expanded uncertainty - combined standard uncertainty multiplied by an appropriate critical value from the t-distribution which depends upon the degrees of freedom in the combined standard uncertainty and the desired level of coverage.

  • Effective degrees of freedom - degrees of freedom associated with a standard deviation composed of two or more components of variance and computed using the Welch-Satterthwaite approximation.

  • Level-1 standard deviation - repeatability standard deviation describing the distribution of short-term measurements under repeatability conditions.

  • Level-2 standard deviation - standard deviation describing the distribution of measurement results over intermediate time-intervals such as day-to-day.

    Note - this standard deviation is a function of the between-day standard deviation and the repeatability standard deviation.

  • Level-3 standard deviation - standard deviation describing the distribution of measurement results over the long-term such as run-to-run.

    Note - this standard deviation is a function of the between-run standard deviation, the between-day standard deviation and the repeatability standard deviation.

  • Between-day standard deviation - standard deviation describing the distribution of intermediate-term (day-to-day) fluctuations in the measurement process.

  • Between-run standard deviation - standard deviation describing the distribution of long-term (run-to-run) fluctuations in the measurement process.

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