A Monte Carlo simulation investigation on the effect of the probability distribution of input quantities on the effective area of a pressure balance and its uncertainty

Abstract

The present manuscript demonstrates the effect of the variation of input Probability Distributions Functions (PDF) on the output PDF of the effective area in case of a pressure balance using Monte Carlo Method (MCM). Pressure balances are the basic units used for the establishment of measurement capabilities in National Metrology Institutes (NMIs) and require diligent characterization in order to achieve the lowest possible measurement uncertainties. MCM is a preferred alternative method for the estimation of measurement uncertainty which is primarily based on the propagation of probability distributions. In MCM, the assignment of probability density functions (PDF) of the input quantities is the most significant factor which directly influences the PDF of the output quantities. The assignment of these PDFs needs to be made judiciously depending upon several factors. To illustrate this, the authors have taken a secondary pressure standard, characterized it experimentally and estimated its effective area and the associated measurement uncertainty using MCM. The influence of input PDFs into the output PDF of the measurand was investigated by tentatively assigning different probability distributions for all input quantities, and observed their effect on the probability distribution of effective area. Quantitative analysis was also performed in all cases of the assumed distribution of input quantities. The results thus obtained are discussed in detail.