Research Article

Numerical analysis of the accuracy of bivariate quantile distributions utilizing copulas compared to the GUM supplement 2 for oil pressure balance uncertainties

University of South Africa, Department of Mechanical and Industrial Engineering, Private Bag X6, Florida 1710, South Africa

^* ramnav@unisa.ac.za

Received: 12 June 2017
Accepted: 12 September 2017

Abstract

In the field of pressure metrology the effective area is A_e = A₀ (1 + λP) where A₀ is the zero-pressure area and λ is the distortion coefficient and the conventional practise is to construct univariate probability density functions (PDFs) for A₀ and λ. As a result analytical generalized non-Gaussian bivariate joint PDFs has not featured prominently in pressure metrology. Recently extended lambda distribution based quantile functions have been successfully utilized for summarizing univariate arbitrary PDF distributions of gas pressure balances. Motivated by this development we investigate the feasibility and utility of extending and applying quantile functions to systems which naturally exhibit bivariate PDFs. Our approach is to utilize the GUM Supplement 1 methodology to solve and generate Monte Carlo based multivariate uncertainty data for an oil based pressure balance laboratory standard that is used to generate known high pressures, and which are in turn cross-floated against another pressure balance transfer standard in order to deduce the transfer standard's respective area. We then numerically analyse the uncertainty data by formulating and constructing an approximate bivariate quantile distribution that directly couples A₀ and λ in order to compare and contrast its accuracy to an exact GUM Supplement 2 based uncertainty quantification analysis.