ISO/IEC Guide 98-3:2008/Suppl 2:2011 PDF

Overview

ISO/IEC Guide 98-3:2008/Suppl.2:2011 (JCGM 102:2011) extends the GUM (Guide to the expression of uncertainty in measurement, GUM:1995) to measurement models with any number of input and output quantities, including real and complex quantities. It formalizes two complementary approaches for multivariate uncertainty evaluation: a generalized GUM uncertainty framework and a Monte Carlo method (propagation of distributions). The Supplement provides practical procedures to produce coverage regions (multivariate analogues of coverage intervals) such as hyper-ellipsoids and hyper-rectangles, and gives guidance to approximate the smallest coverage region from Monte Carlo results. The document is identical in content to JCGM 102:2011.

Key topics and technical requirements

• Multivariate measurement models: Guidance for explicit and implicit models with any number of outputs; real or complex-valued quantities are covered.
• Two propagation approaches:
  • Generalized GUM framework: Linearization, sensitivity coefficients, and covariance propagation for vector outputs.
  • Monte Carlo method: Implementation details for sampling input distributions, number of trials, drawing techniques, and discrete representation of output distributions.
• Coverage regions: Procedures to construct multivariate coverage regions for a prescribed coverage probability:
  • Hyper-ellipsoidal and hyper-rectangular regions.
  • Method to approximate the smallest coverage region from Monte Carlo samples.
• Practical computation issues: Estimation of mean vectors and covariance matrices, adaptive Monte Carlo procedures, numerical tolerances, and validation of the GUM framework using Monte Carlo.
• Supporting material: Treatment of multivariate t-distributions, coordinate transformations, complex derivatives, and worked examples (e.g., resistance/reactance, temperature measurements).

Practical applications and users

Who benefits:

• Metrologists and calibration laboratories applying uncertainty budgets to multivariate results.
• Test and measurement engineers working with vector outputs (e.g., complex impedance, multi-sensor arrays).
• Statisticians and data scientists implementing propagation-of-uncertainty in software.
• Standards bodies and conformity assessment bodies needing rigorous multivariate uncertainty reporting.

Typical uses:

• Reporting joint uncertainty for multi-parameter measurements.
• Producing multivariate coverage regions for compliance and decision-making.
• Validating linearized uncertainty estimates against Monte Carlo simulations.
• Designing adaptive Monte Carlo workflows for accurate uncertainty characterization.

Related standards

• ISO/IEC Guide 98-3 (GUM:1995) - Guide to the expression of uncertainty in measurement
• ISO/IEC Guide 98 series (Parts 1, 3, 4) and JCGM guidance documents (e.g., Supplement 1 on Monte Carlo)
• VIM (International Vocabulary of Metrology) for terms and definitions

This Supplement is essential when you need robust, standardized methods to quantify and report measurement uncertainty for multivariate and complex-valued outputs using either the GUM framework or Monte Carlo propagation.