ISO 8466-2:2001 PDF

Water quality — Calibration and evaluation of analytical methods and estimation of performance characteristics — Part 2: Calibration strategy for non-linear second-order calibration functions

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Title (English):

ISO 8466-2:2001

Water quality — Calibration and evaluation of analytical methods and estimation of performance characteristics — Part 2: Calibration strategy for non-linear second-order calibration functions

Document status:: Active
Format:: Electronic (PDF)
Number of pages:: 12
Publication date:: November 1, 2001
Edition:: ISO IS 8466 edition 2 version 1
ICS:: 13.060.01

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Description (English):

It is not always possible to accurately describe the relationship between a set of calibration points with a rectilinear curve, even by decreasing the working range. Instead of the linear regression analysis, a least-squares fit to a second-order polynomial is applied (see test for linearity in 4.1.3 of ISO 8466-1:1990[1]). Using this fit, it is possible to calculate not only the calibration function but also the confidence interval associated with it. This part of ISO 8466 is intended primarily for use in method development and may not necessarily be applicable to all routine analyses.

Technical details

Technical committee: ISO/TC 147/SC 2 - Physical, chemical and biochemical methods
SKU: ISO 8466-2:2001

Abstract

Overview

ISO 8466-2:2001 - Water quality: Calibration strategy for non-linear second‑order calibration functions - provides guidance for calibrating analytical methods when a straight‑line (linear) fit is inadequate. Instead of linear regression, the standard prescribes a least‑squares fit to a second‑order polynomial to determine the calibration function and associated confidence intervals. It is intended primarily for method development in water, wastewater and sludge analysis and may not be required for all routine analyses.

Key topics and technical requirements

Working range selection
- Define the practical objective and place expected sample concentrations near the centre of the working range.
- Ensure lower limit is distinguishable from blanks (above limit of quantitation).
Homogeneity of variances
- Use replicate measurements at lowest and highest standards (recommended N = 10 equidistant standards).
- Apply a one‑sided F‑test (see Annex A) to check variance homogeneity; reduce working range if variances differ significantly.
Second‑order calibration
- Fit response y to y = a + b x + c x² using least squares to estimate coefficients a, b, c.
- Diagnose fit adequacy by plotting residuals (y − ŷ) vs concentration.
- Degrees of freedom for residual standard deviation: f = N − 3.
Performance characteristics
- Residual standard deviation (s_y) quantifies scatter about the quadratic fit.
- Sensitivity (e) at concentration x: e = b + 2 c x; instrument sensitivity at the working‑range centre x0: E = b + 2 c x0.
- Standard deviation of the procedure (s_x0) = s_y / E and relative standard deviation (V%) = (s_x0 / x0) × 100.
Single‑valued calibration requirement
- Test for maxima/minima: stationary point x* = −b / (2 c). If x* lies inside the working range the function is not single‑valued and must not be used.
Sample analysis
- Invert the quadratic to obtain sample concentration x̂ from measured response ŷ (different algebraic solutions for positive/negative curvature).
- Estimate the confidence interval of x̂ by propagating both measurement error and calibration uncertainty.

Applications and users

Method developers and validation teams in environmental and water quality laboratories
Quality managers and accreditation bodies assessing analytical performance
Environmental chemists, instrument manufacturers, and laboratories confronting non‑linearity in calibration
Use cases: method validation, estimation of limits of quantitation, performance comparison, reporting confidence intervals for non‑linear calibrations

Related standards

ISO 8466‑1: Statistical evaluation of the linear calibration function - use when linear regression is appropriate.
Refer to Annex A of ISO 8466‑2 for F‑table values used in variance testing.

Keywords: ISO 8466-2:2001, water quality calibration, second‑order polynomial, non‑linear calibration, residual standard deviation, instrument sensitivity, F‑test, confidence interval.

Related standards

Mentioned in the description and other ISO standards

Abstract

Overview

Key topics and technical requirements

Working range selection
- Define the practical objective and place expected sample concentrations near the centre of the working range.
- Ensure lower limit is distinguishable from blanks (above limit of quantitation).
Homogeneity of variances
- Use replicate measurements at lowest and highest standards (recommended N = 10 equidistant standards).
- Apply a one‑sided F‑test (see Annex A) to check variance homogeneity; reduce working range if variances differ significantly.
Second‑order calibration
- Fit response y to y = a + b x + c x² using least squares to estimate coefficients a, b, c.
- Diagnose fit adequacy by plotting residuals (y − ŷ) vs concentration.
- Degrees of freedom for residual standard deviation: f = N − 3.
Performance characteristics
- Residual standard deviation (s_y) quantifies scatter about the quadratic fit.
- Sensitivity (e) at concentration x: e = b + 2 c x; instrument sensitivity at the working‑range centre x0: E = b + 2 c x0.
- Standard deviation of the procedure (s_x0) = s_y / E and relative standard deviation (V%) = (s_x0 / x0) × 100.
Single‑valued calibration requirement
- Test for maxima/minima: stationary point x* = −b / (2 c). If x* lies inside the working range the function is not single‑valued and must not be used.
Sample analysis
- Invert the quadratic to obtain sample concentration x̂ from measured response ŷ (different algebraic solutions for positive/negative curvature).
- Estimate the confidence interval of x̂ by propagating both measurement error and calibration uncertainty.

Applications and users

Method developers and validation teams in environmental and water quality laboratories
Quality managers and accreditation bodies assessing analytical performance
Environmental chemists, instrument manufacturers, and laboratories confronting non‑linearity in calibration
Use cases: method validation, estimation of limits of quantitation, performance comparison, reporting confidence intervals for non‑linear calibrations

Related standards

ISO 8466‑1: Statistical evaluation of the linear calibration function - use when linear regression is appropriate.
Refer to Annex A of ISO 8466‑2 for F‑table values used in variance testing.

Keywords: ISO 8466-2:2001, water quality calibration, second‑order polynomial, non‑linear calibration, residual standard deviation, instrument sensitivity, F‑test, confidence interval.

ISO 8466-2:2001 PDF

Technical details

Abstract

Overview

Key topics and technical requirements

Applications and users

Related standards

Related standards

Abstract

Overview

Key topics and technical requirements

Applications and users

Related standards

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