Analysis and Comparison of Hyper-Ellipsoidal and Smallest Coverage Regions for Multivariate Monte Carlo Measurement Uncertainty Analysis Simulation Datasets

Abstract

Traditionally metrology systems have been analysed for measurement uncertainties in terms of the frequency statistics-based Guide to the Uncertainty in Measurement (GUM); however, a key challenge in the application of the GUM has been in terms of its inherent limitations and internal inconsistencies with Type A and Type B uncertainties in adequately and accurately determining appropriate coverage intervals and regions for measurement uncertainty results. Subsequently in order to address these particular issues the Bayesian statistical-based GUM supplements for univariate and multivariate models were developed that supersede the original GUM and which resolve these challenges. In this paper, a GUM supplement 2 uncertainty analysis for a multivariate oil pressure balance model is numerically implemented using an experimental dataset, and then the multivariate Monte Carlo method simulation results are processed in order to construct and study the corresponding optimal hyper-ellipsoidal and smallest coverage regions for bivariate and trivariate distributions with new proposed numerical algorithms for specified probability levels. The results are then further investigated in order to study the accuracy, validity limits and potential confidence region implications for measurement models that exhibit non-Gaussian joint probability density function distributions.