Overview
ISO 7066-2:1988 provides internationally recognized procedures for the assessment of uncertainty when calibrating flow measurement devices that exhibit non-linear calibration relationships. It specifies how to fit quadratic, cubic or higher-order polynomial expressions to calibration data using the least-squares criterion and how to evaluate the uncertainty associated with the resulting calibration curve. The standard complements ISO 7066-1, which covers linear calibration relationships.
Key topics and technical requirements
- Polynomial curve fitting: Procedures for fitting polynomials (bo + b1x + b2x2 + … + bmxm) to non-linear calibration data using least-squares (polynomial or curvilinear regression).
- Selection of polynomial degree: Incremental testing of degree m, computation of residual standard deviation (sr), and selection of the optimum degree based on statistical significance (95% confidence) of added coefficients using Student’s t test.
- Uncertainty evaluation: Calculation of the random component of uncertainty for predicted values (95% confidence), combining systematic and random components, and expressions for variances of coefficients (annexes A and B).
- Computational guidance: Use of standard regression library routines or the orthogonal polynomial method (Annex B); a FORTRAN program is provided (Annex C). A finite-difference method (Annex E) is suggested for uniformly spaced x when a computer is unavailable.
- Practical cautions: No extrapolation beyond data range; avoid overfitting and spurious oscillations from excessive polynomial degree; consider variable transformations (e.g., reciprocal) or segmented fits when appropriate.
- Annexes: Informative annexes on regression methods (A), orthogonal polynomials (B), example program (C), worked examples (D) and finite-difference guidance (E) (these annexes are non-normative).
Applications
- Calibration laboratories assessing uncertainty in flow meter calibrations when responses are non-linear.
- Instrument manufacturers developing calibration curves and uncertainty budgets for flow devices.
- Metrology institutes and test houses establishing traceable calibration services for liquid and gas flow instruments.
- Engineers needing statistically justified calibration models and uncertainty estimates for flow measurement systems.
Who should use this standard
- Metrologists, calibration engineers, laboratory managers, and quality assurance personnel involved in flow measurement and calibration.
- Developers of calibration software and statistical routines for flow instrumentation.
Related standards
- ISO 7066-1 - Assessment of uncertainty in the calibration and use of flow measurement devices (linear calibration relationships).
- ISO 5168 - Measurement of fluid flow - Estimation of uncertainty of a flow-rate measurement (referenced for uncertainty principles).
Keywords: ISO 7066-2, calibration uncertainty, flow measurement, non-linear calibration, polynomial fitting, least-squares, orthogonal polynomials, regression, calibration curve.
Open preview (PDF)Assessment of uncertainty in the calibration and use of flow measurement devices — Part 2: Non-linear calibration relationships
