Comparison of the GUM and Monte Carlo measurement uncertainty techniques with application to effective area determination in pressure standards

A common measurement model for a gas operated piston-cylinder based pressure standard effective area is the well known integral equation formulation originally developed by Dadson of the NPL. However a problem with directly applying this exact mathematical model is that it cannot be easily cast into a functional form suitable for application of the Guide to the expression of Uncertainty in Measurement (GUM) which is reliant on the concept of sensitivity coefficients without various simplifications. In this paper, we examine the standard approximations that are currently necessary in order to directly apply the GUM for a pressure standard effective area uncertainty determination. We also compare and contrast this to the exact effective area uncertainty results obtained through the direct application of the Monte Carlo Method (MCM) which has recently been published as Supplement 1 to the GUM. Based on these investigations we also draw some preliminary conclusions on the relative merits on the extent to which the shape of the piston and cylinder radii and whose uncertainties may vary along the engagement length of the piston-cylinder may be modeled and incorporated into a piston-cylinder's effective area uncertainty calculation. © EDP Sciences 2010.