Fig. 7

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Verification and validation of proposed method using normalized errors of applied pressures demonstrating that ∥En ∥ ≤1 ∀ n ∈ [1, … , 10] laboratory standard pressure balance generated pressures and transfer standard pressure balance cross-floated area measurements. The pressures P1 through to P10 correspond to pressures from 50 MPa through to 500 MPa at 50 MPa steps and the En values for each of these pressures indicates the corresponding normalized error. When calculating the En value for each pressure the known reference pressure Pref is determined from the laboratory standard pressure balance whilst the calibrated pressure Pcal is determined from the transfer standard pressure balance using the bivariate copula that models and summarizes the information of the calibrated pressure balance's zero-pressure area A0 and distortion coefficient λ. Due to the fact that all of the En values are smaller than unity this then means that the results and uncertainties that were calculated for the calibrated pressure balance when tested against the reference pressure balance are statistically consistent and hence provides proof that the proposed method of using copulas to model and summarize bivariate probability density functions has been verified and validated.
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