A Monte Carlo Analysis of the Effects of Covariance on Propagated Uncertainties

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A Monte Carlo Analysis of the Effects of Covariance on Propagated Uncertainties (156.57 KB)

Reports of calibration typically provide total combined uncertainties at each individual calibration point with no information describing the correlation among those uncertainties. This affects the ability of the user of the report of calibration to make an accurate determination of propagated uncertainty values. Although covariance is known to affect propagated uncertainties, in those cases where there is insufficient information to evaluate the covariance it is generally taken to be zero even when the assumption is unlikely to be true. When correlation coefficients are allowed to vary from zero, the resulting shape of the propagated uncertainty curve varies depending on the specific combination of correlation coefficient values. When combinations of correlation coefficients are chosen at random a wide range of propagated uncertainty curves are obtained. This type of Monte Carlo simulation is not intended to recreate the physical insight withheld by the provider of the report of calibration however it does demonstrate the magnitude of the problem faced by the user of the calibration certificate. In particular the paper discusses the impact that the absence of correlation coefficient information has on the propagation of uncertainty curves for an Au/Pt thermocouple calibration. Furthermore this paper discusses the possibility of a maximum likelihood estimator for propagation of uncertainty curves where information about the degree of correlation among uncertainties is not provided. The simulations show that uncertainty in the degree of correlation between the variances of calibration points may have a demonstrably significant impact on the overall uncertainty of the calibration.