ISO 7066-2:1988

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.