ISO TS 28037-2010 PDF

Full title and description

ISO/TS 28037:2010 — Determination and use of straight-line calibration functions. This Technical Specification provides guidance on deriving, validating and using straight-line (Y = A + B X) calibration functions from measurement data, including evaluation of parameter estimates, their uncertainties and covariances, and procedures for prediction (inverse evaluation) and forward evaluation.

Abstract

ISO/TS 28037:2010 addresses calibration functions of the straight-line form Y = A + B X. It describes methods for estimating the parameters A and B from paired measurement data (xi, yi) using appropriate least-squares approaches that account for heteroscedasticity and non-negligible x‑errors, treats general covariance matrices for the data, and gives procedures for validating the calibration, computing uncertainties and covariances of the estimated parameters, and using those results to predict X from a measured Y (and vice versa).

General information

• Status: Published (Technical Specification); reviewed and confirmed in 2021 and listed for revision — expected to be replaced by an International Standard (ISO 28037) currently under publication activity.
• Publication date: 2010-09 (Edition 1, 2010).
• Publisher: International Organization for Standardization (ISO).
• ICS / categories: 03.120.30 (Statistics — application of statistical methods).
• Edition / version: Edition 1 (2010).
• Number of pages: 63 pages (English edition).

Scope

The Technical Specification covers straight-line calibration functions of the form Y = A + B X and the statistical treatment of measurement data used to determine the parameters A and B. It considers different uncertainty structures (including heteroscedastic data and non‑negligible x‑uncertainties), presents least‑squares estimation methods appropriate to each case, gives techniques for validating the straight‑line model, and sets out procedures to compute and propagate the uncertainties and covariances of parameter estimates for prediction and forward evaluation.

Key topics and requirements

• Definition and formulation of straight-line calibration functions (Y = A + B X).
• Estimation of parameters A (intercept) and B (slope) using least‑squares methods adapted to the uncertainty structure of the data.
• Treatment of heteroscedastic measurement errors and non‑negligible x‑uncertainties; use of general covariance matrices for data.
• Validation tests and diagnostics for the appropriateness of straight‑line calibration models.
• Evaluation of standard uncertainties and covariance of parameter estimates, including formulas and worked examples for common special cases.
• Procedures for inverse evaluation (predicting X from measured Y) and forward evaluation, with uncertainty propagation.

Typical use and users

Practitioners in metrology and calibration laboratories, measurement scientists, statisticians supporting calibration work, quality managers in manufacturing and test laboratories, and researchers who need to develop or apply linear calibration functions and quantify the associated measurement uncertainty. The Technical Specification aids those who must choose appropriate least‑squares methods, validate calibration models, and produce uncertainty statements for calibration results and predictions.

Related standards

ISO/TS 28037 references and builds on established metrology and statistical guidance including ISO/IEC Guide 98-3 (the Guide to the Expression of Uncertainty in Measurement — GUM) and ISO 3534‑1 (statistics vocabulary and symbols). It is also practically related to laboratory accreditation and calibration standards such as ISO/IEC 17025 (general requirements for the competence of testing and calibration laboratories).

Keywords

straight-line calibration; calibration function; Y = A + B X; least squares; parameter estimation; uncertainty evaluation; covariance; inverse prediction; forward evaluation; metrology; calibration laboratory.

FAQ

Q: What is this standard?

A: ISO/TS 28037:2010 is a Technical Specification that gives methods and guidance for determining and using straight‑line calibration functions and for evaluating the uncertainties and covariances of the fitted parameters.

Q: What does it cover?

A: It covers statistical methods for estimating the intercept and slope of straight‑line calibration functions from paired measurement data, special cases and general covariance treatments, validation of the calibration model, and procedures to predict X from Y (and vice versa) together with uncertainty propagation.

Q: Who typically uses it?

A: Metrology and calibration laboratories, calibration service providers, statisticians and technical staff responsible for establishing calibration functions and reporting measurement uncertainty, and auditors assessing calibration methods.

Q: Is it current or superseded?

A: As published in September 2010 the Technical Specification remains a published, valid document; it was last reviewed and confirmed in 2021. ISO has developed an International Standard, ISO 28037 (Edition 1, 2026), to replace ISO/TS 28037:2010 — ISO 28037 was listed as under publication (final production steps) on ISO’s catalogue. Users should check the ISO catalogue or national bodies for the current publication status and obtain ISO 28037 once available for the definitive consolidated requirements.

Q: Is it part of a series?

A: It is produced by ISO/TC 69/SC 6 (measurement methods and results) and sits among ISO guidance documents on measurement uncertainty and statistical methods; it is not formally a numbered multi‑part series but is closely related to other ISO documents on uncertainty and calibration practice.

Q: What are the key keywords?

A: Straight-line calibration, least squares, uncertainty, covariance, prediction, inverse evaluation, metrology, calibration function.