Use of Welch-Satterthwaite Approximation in Calibration of Voltage Standards - ASQ

Use of Welch-Satterthwaite Approximation in Calibration of Voltage Standards

In certifying banks of solid state voltage standards, the customer is provided with predictive equations that are used to predict mean voltage and uncertainty in voltage. These equations are provided for both the bank average and the individual standards constituting the bank over the period of certification, which is typically a year. Use of the Welch-Satterthwaite Approximation (W-SA) can significantly reduce the number of calibrations required to provide satisfactory levels of uncertainty for the bank average. We first review the standard approach in metrology for expressing the uncertainty in a measurement system. We provide an intuitive discussion of the W-SA along with examples of its use and information on its usefulness when there are only a few degrees of freedom. A case study involving a bank of four solid state voltage standards is presented in detail. We also propose an analysis technique that can be used to investigate the usefulness and potential limitations of the W-SA when estimating measurement uncertainties. The analysis technique can be used to estimate approximation error, sampling error, and the coverage probabilities of confidence intervals computed using the W-SA.

Key Words: Degrees of Freedom; Uncertainty.

By STEPHEN V. CROWDER AND STUART L. KUPFERMAN, Sandia National Laboratories, Albuquerque, NM 87185


THE global economy rests on an almost invisible foundation of measurements and standards. The basis of the structure is the International System of Units (SI), the modern metric system, which is the coherent system of units adopted and recommended by the General Conference of Weights and Measures (CGPM). In the United States, the federal government has the constitutional responsibility to provide the weights and measures for the nation. This responsibility is vested in the National Institute of Standards and Technology (NIST). NIST is the highest level in the hierarchy of primary, secondary, and lower level standards and calibration laboratories. These laboratories collaborate to assign values to the standards and instruments used to make accurate measurements on shop floors, in production facilities, and in research and development laboratories.

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