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

Ramnath, Vishal

doi:10.1051/ijmqe/2010013

Cited by 8 publications

(3 citation statements)

References 4 publications

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“…Many reports have been published on the calculation of the effective area dimensionally and calculated the uncertainty using MCM and LPU. However, none of them compared the values of effective area and uncertainty calculated from the dimensional, MCM, and LPU methods [7,[25][26][27][28][29]. After the invention of MCM, metrology scientists and many industries as well have been using MCM to calculate the uncertainty [25,30].…”

Section: Introductionmentioning

confidence: 99%

Evaluation of effective area of air piston gauge with limitations in piston–cylinder dimension measurements

et al. 2021

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The air piston gauge (APG) has been established at the National Physical Laboratory, India (NPLI) for Pascal realization since 2002. The APG at NPLI has been considered a transfer pressure standard because it has been calibrated against the primary pressure standard, i.e. ultrasonic interferometer manometer. As per existing international protocol, the APG establishment as a primary standard, the effective area (A e) of piston–cylinder (p–c) assembly and masses must be directly traceable to SI units. We have calculated A e and associated uncertainty of p–c assembly using the theory of rarefaction gas dynamics, which is based on dimension measurements. The value of A e is obtained for varying temperatures and radii of piston and cylinder in their respective uncertainty limits. The variation of the cylinder's inner radius within its uncertainty limit of 0.7 µm includes the expected effective area, i.e. 3.356 775 (5) cm2. The effective area’s expected values are obtained for the cylinder’s radius of 10.338 00 (2) mm, which is approximately 0.65 µm away from the value obtained from dimensional measurements and well within the uncertainty limit. Therefore, to get the effective area of 3.356 775 (5) cm2, the uncertainty of the cylinder’s radius should be at least one order less (similar to piston’s radius) than that of the present value. The precision in dimension measurement of the cylinder's internal radius is the critical parameter for effective area calculation of p–c assembly.

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Section: Introductionmentioning

confidence: 99%

Evaluation of effective area of air piston gauge with limitations in piston–cylinder dimension measurements

et al. 2021

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“…We investigate the application of the use of quantile functions for pressure balance effective areas by considering the geometry data specified in Figure 2 which was previously reported by Ramnath [17]. Due to the fact that all of the three models that we have considered utilize a radial symmetry assumption we assume constant representative values for corresponding piston/cylinder radii along the engagement length by using the standard uncertainties for the external diameter d corresponding to the piston and the internal diameter D corresponding to the cylinder as u(D) = 100 nm and u(d) = 170 nm respectively.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Application of quantile functions for the analysis and comparison of gas pressure balance uncertainties

Ramnath

2017

Int. J. Metrol. Qual. Eng.

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Abstract. Traditionally in the field of pressure metrology uncertainty quantification was performed with the use of the Guide to the Uncertainty in Measurement (GUM); however, with the introduction of the GUM Supplement 1 (GS1) the use of Monte Carlo simulations has become an accepted practice for uncertainty analysis in metrology for mathematical models in which the underlying assumptions of the GUM are not valid. Consequently the use of quantile functions was developed as a means to easily summarize and report on uncertainty numerical results that were based on Monte Carlo simulations. In this paper, we considered the case of a piston-cylinder operated pressure balance where the effective area is modelled in terms of a combination of explicit/implicit and linear/non-linear models, and how quantile functions may be applied to analyse results and compare uncertainties from a mixture of GUM and GS1 methodologies.

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“…Alternatives to linear least squares limitations and incorporation of possible nonlinear and correlation effects for confidence limit estimation on the model parameters include the well known Monte Carlo techniques such as the boot strap method as originally discussed in Press et al [8] and later by Cox and Siebert [9] from a general implementation perspective, and more recently by Ramnath [10] who utilized and fully developed these alternatives for the computation of the effective area uncertainty determination of apex piston-cylinder based pressure standards by a direct Monte Carlo numerical simulation for a primary scientific pressure standard characterization.…”

Section: (M + C)g A(p A)[1 + φ(T)] = (M + C)g A(p B)[1 + φ(T )]mentioning

confidence: 99%

Determination of pressure balance distortion coefficient and zero-pressure effective area uncertainties

Ramnath

2011

Int. J. Metrol. Qual. Eng.

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Abstract. The behaviour of piston-cylinder operated pressure balances is characterized by the distortion coefficient λ and zero-pressure effective area A0 which model the variation of a pressure balance's area in terms of the applied pressure. This paper determines the uncertainties in λ and A0 when utilizing the method of cross-floating with another pressure balance standard whose parameters and associated uncertainties are known. A limitation that is frequently encountered in many attempts of the uncertainty analysis for a pressure balance is that no readily accessible uncertainty quantification framework for the distortion coefficient is present. As a result the uncertainty in a pressure balance's area at elevated applied pressures is typically underestimated in the absence of this uncertainty information. We firstly review the uncertainty formulation for a pressure balance generated pressure involving correlation effects in terms of an implicit multivariate matrix equation approach and then utilizing the resulting solution present the methodology to consistently perform the uncertainty analysis for λ and A0.

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

Cited by 8 publications

References 4 publications

Evaluation of effective area of air piston gauge with limitations in piston–cylinder dimension measurements

Evaluation of effective area of air piston gauge with limitations in piston–cylinder dimension measurements

Application of quantile functions for the analysis and comparison of gas pressure balance uncertainties

Determination of pressure balance distortion coefficient and zero-pressure effective area uncertainties

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