Monte Carlo Simulations Applied to Uncertainty in Measurement

On the Uncertainty of the EN12354-1: Estimate of the Flanking Sound Reduction Index Due to the Uncertainty of the Input Data

Building Acoustics ◽

10.1260/135101009789877059 ◽

2009 ◽

Vol 16 (3) ◽

pp. 199-231 ◽

Cited By ~ 5

Author(s):

Jeffrey Mahn ◽

John Pearse

Keyword(s):

Monte Carlo ◽

Probability Density Function ◽

Monte Carlo Simulations ◽

Input Data ◽

Vibration Reduction ◽

Uncertainty In Measurement ◽

Sound Reduction ◽

Expression Of Uncertainty ◽

Lognormal Probability ◽

Reduction Index

Equations to calculate the uncertainty of the EN12354-1 estimate of the flanking sound reduction index due to the uncertainty of the input data are derived using the method of the ISO Guide to the Expression of Uncertainty in Measurement (GUM). The uncertainty equations have been validated using Monte Carlo simulations. It is shown that the magnitude of the uncertainty depends on the uncertainty of the resonant sound reduction indices of the elements, the uncertainty of the vibration reduction index and the uncertainty of the equivalent absorption lengths and areas of the elements. However, equations could not be derived to calculate the uncertainty of the EN12354 estimate of the apparent sound reduction index which has a lognormal probability density function and is therefore outside of the scope of the method of GUM. Monte Carlo simulations must be used to calculate the uncertainty of the apparent sound reduction index. It is recommended that guidance for calculating and declaring the uncertainty is included in future versions of EN12354, ISO10848 and ISO15712.

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Low-voltage EDS of magnesium ferrite Dendrites in a FEG-SEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100164854 ◽

1996 ◽

Vol 54 ◽

pp. 478-479

Author(s):

Matthew T. Johnson ◽

Ian M. Anderson ◽

Jim Bentley ◽

C. Barry Carter

Keyword(s):

Monte Carlo ◽

Quantitative Analysis ◽

Monte Carlo Simulations ◽

Cross Section ◽

Spatial Resolution ◽

Low Voltage ◽

Magnesium Ferrite ◽

X Ray ◽

Interaction Volume ◽

Ferrite Spinel

Energy-dispersive X-ray spectrometry (EDS) performed at low (≤ 5 kV) accelerating voltages in the SEM has the potential for providing quantitative microanalytical information with a spatial resolution of ∼100 nm. In the present work, EDS analyses were performed on magnesium ferrite spinel [(MgxFe1−x)Fe2O4] dendrites embedded in a MgO matrix, as shown in Fig. 1. spatial resolution of X-ray microanalysis at conventional accelerating voltages is insufficient for the quantitative analysis of these dendrites, which have widths of the order of a few hundred nanometers, without deconvolution of contributions from the MgO matrix. However, Monte Carlo simulations indicate that the interaction volume for MgFe2O4 is ∼150 nm at 3 kV accelerating voltage and therefore sufficient to analyze the dendrites without matrix contributions.Single-crystal {001}-oriented MgO was reacted with hematite (Fe2O3) powder for 6 h at 1450°C in air and furnace cooled. The specimen was then cleaved to expose a clean cross-section suitable for microanalysis.

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