Overview
ISO/TR 13587:2012 - "Three statistical approaches for the assessment and interpretation of measurement uncertainty" - is a Technical Report from ISO that compares and explains three probabilistic frameworks for evaluating measurement uncertainty: the frequentist approach (including bootstrap uncertainty intervals), the Bayesian approach, and fiducial inference. Each approach is described with its underlying assumptions, probabilistic interpretation of uncertainty intervals, and illustrated with worked examples (including an example from the GUM and a gauge-block calibration example).
Keywords: ISO/TR 13587:2012, measurement uncertainty, frequentist, Bayesian, fiducial, bootstrap, GUM, uncertainty evaluation.
Key Topics
- Three statistical paradigms: clear descriptions of frequentist, Bayesian and fiducial methods for uncertainty assessment and interpretation.
- Bootstrap methods: practical discussion of bootstrap uncertainty intervals as a frequentist resampling tool.
- Probabilistic interpretation: explanation of what uncertainty intervals mean under each statistical approach.
- Assumptions and limitations: statements of the fundamental assumptions behind each method and when they are applicable.
- Worked examples: multiple examples including one from ISO/IEC Guide 98-3 (GUM) and a detailed calibration example (gauge block), demonstrating implementation and comparison of results.
- Relation to GUM Supplement 1: discussion of how Monte Carlo propagation (GUMS1) relates to the three approaches.
- Terminology and notation: alignment with ISO statistics vocabulary (ISO 3534 series) and GUM definitions.
Applications
ISO/TR 13587:2012 is practical for professionals who need rigorous, interpretable uncertainty statements:
- Metrologists and National Metrology Institutes evaluating and reporting measurement uncertainty.
- Calibration laboratories and testing facilities seeking defensible uncertainty intervals for calibration and conformity assessment.
- Laboratory managers and assessors involved in accreditation (e.g., ISO/IEC 17025) who need to justify uncertainty methods.
- Statisticians and measurement scientists comparing inference frameworks or selecting methods for complex measurement models.
Practical uses include uncertainty budgeting, calibration reports (e.g., gauge-block calibration), uncertainty propagation, and methodological selection between Monte Carlo, Bayesian posterior intervals, bootstrap intervals, or fiducial intervals.
Related Standards
- ISO/IEC Guide 98-3 (GUM) - Guide to the expression of uncertainty in measurement.
- ISO/IEC Guide 98-3:2008/Supplement 1 (GUMS1) - Monte Carlo propagation of distributions.
- ISO 3534-1 / ISO 3534-2 - Statistics vocabulary and symbols.
- ISO/IEC 17025 - Laboratory accreditation requirements (context for uncertainty reporting).
This Technical Report helps users choose and interpret uncertainty evaluation methods with a clear probabilistic basis, improving consistency and transparency in measurement reporting.