Covariance Matrix Evaluation in Correlated Type B Measurement Uncertainty Propagation
Evaluating input covariance matrices in Type B propagation prevents underestimating multi-channel variance and ensures valid system uncertainty limits.
GUM Guide
Procedural Framework
International consensus document providing rules for evaluating and expressing the uncertainty of measurement results across all levels of precision. Statistical methods defined in the gum guide classify components of uncertainty into Type A and Type B categories. Type A evaluations use the statistical analysis of series of observations.
Procedures for Type B evaluations rely on other sources like calibration certificates or manufacturer specifications.
Uncertainty Categorization
Quantifying the reliability of a measurement requires identifying every source of error from the instrument to the environment. The gum guide provides a standardized approach to combine these individual components into a single numerical value. Each source must be characterized by a probability distribution.
Mathematical Model
Calculating the combined standard uncertainty requires establishing a functional relationship between input quantities and the final measurand. Sensitivity coefficients help determine how much each input contributes to the total variation. Correlation between inputs must be accounted for using covariance terms.
Reporting Format
Final results are expressed as an expanded uncertainty by multiplying the combined standard uncertainty by a coverage factor. Most applications of the gum guide use a coverage factor of two to provide a confidence interval of approximately ninety five percent. The result ensures that measurement data is comparable across different laboratories.