Propagation of measurement

K. Faber and B.R. Kowalski, Propagation of measurement errors for the validation of predictions obtained by principal component regession and partial least squares. J. Chemom., 11 (1997) 181-238. 

The propagation of measurement and calculation errors can also be a problem. In general, experimental errors in boundary conditions at the bottom of the column and calculation errors in the model are propagated along the stripping section. Introduced... 

We can consider the propagation of measure resulting from a numerical discretization deflned by the composition of these two pieces. For a scheme [HOJ, we have the distribution first propagated under Hamiltonian dynamics, and then the momenta are evolved as the solution to the Ornstein-Uhlenbeck process, which clearly will preserve the Gibbs measure... 

This approach assumes the constancy of AH over the temperature range that is, its accuracy depends largely on the linearity of flie vant Hoff regression. Estimation of AS from R X intercept of the regression, as implied by equation [13.21.2.15], is invalid due to the large propagation of measurement errors encountered in extrapolating the 1/T (x-... 

Propagation of uncertainty allows us to estimate the uncertainty in a calculated result from the uncertainties of the measurements used to calculate the result. In the equations presented in this section the result is represented by the symbol R and the measurements by the symbols A, B, and C. The corresponding uncertainties are sr, sa, sb) and sq. The uncertainties for A, B, and C can be reported in several ways, including calculated standard deviations or estimated ranges, as long as the same form is used for all measurements. 

Given the complexity of determining a result s uncertainty when several measurements are involved, it is worth examining some of the reasons why such calculations are useful. A propagation of uncertainty allows us to estimate an ex-... 

A propagation of uncertainty also helps in deciding how to improve the uncertainty in an analysis. In Example 4.7, for instance, we calculated the concentration of an analyte, obtaining a value of 126 ppm with an absolute uncertainty of 2 ppm and a relative uncertainty of 1.6%. How might we improve the analysis so that the absolute uncertainty is only 1 ppm (a relative uncertainty of 0.8%) Looking back on the calculation, we find that the relative uncertainty is determined by the relative uncertainty in the measured signal (corrected for the reagent blank)... 

A standard solution of Mn + was prepared by dissolving 0.250 g of Mn in 10 ml of concentrated HNO3 (measured with a graduated cylinder). The resulting solution was quantitatively transferred to a 100-mL volumetric flask and diluted to volume with distilled water. A 10-mL aliquot of the solution was pipeted into a 500-mL volumetric flask and diluted to volume, (a) Express the concentration of Mn in parts per million, and estimate uncertainty by a propagation of uncertainty calculation, (b) Would the uncertainty in the solution s concentration be improved... 

Tables 4—6 Ust ASTM methods used for the characterization of PB and PMP. A number of specialized methods were developed for testing particular articles manufactured from polyolefins several of these determine the performance of PB and PMP film, including the measurement of the film s dart impact strength and tear strength. Dart impact strength is measured by dropping a heavy dart with a round tip on a stretched film. Tear resistance, which reflects the film s resistance to tear propagation, is measured with the Ehnendorf tear tester. Two values for the tear strength are usually reported, one in the machine dkection of the film and the other in the transverse dkection. Pipes manufactured from PB are tested by pressurizing them internally with water the time-to-burst failure is determined at various temperatures (46). The standard test method for haze and luminous transmittance (ASTM D1003) is used for the measurement of PMP optical characteristics.

Acoustic Measurements. Measurement of the propagation of ultrasonic acoustic waves has been found useful for determining the viscoelastic properties of thin films of adhesives. In this method, the specimen is clamped between transmitting and receiving transducers. The change in pulse shape between successive reverberation of the pulse is dependent on the viscoelastic properties of the transmitting material. Modulus values can be calculated (267,268). 

Metal deck assembhes are tested by UL for under-deck fire hazard by usiag their steiaer tunnel (ASTM E84). The assembly, exposed to an under-deck gas flame, must not allow rapid propagation of the fire down the length of the tuimel. FM uses a calorimeter fire-test chamber to evaluate the hazard of an under-deck fire. The deck is exposed to a gas flame and the rate of heat release is measured and correlated to the rate of flame propagation. A different FM test assesses the damage to roof iasulations exposed to radiant heat. 

Explosion Isolation For all equipment systems protected by design safety measures it is also necessary to prevent the propagation of an explosion from these protected vessels into operating areas or equipment connectedviainterconnectingpipeline. Such an approach is referred to as explosion isolation. 

Systematic Operating Errors Fifth, systematic operating errors may be unknown at the time of measurements. Wriile not intended as part of daily operations, leaky or open valves frequently result in bypasses, leaks, and alternative feeds that will add hidden bias. Consequently, constraints assumed to hold and used to reconcile the data, identify systematic errors, estimate parameters, and build models are in error. The constraint bias propagates to the resultant models. 

The velocity of current or voltage waves in any medium is called the velocity of propagation of electricity in that medium. The velocity of electromagnetic waves (electricity) through a conductor is a measure of line or conductor parameters through which it propagates and is represented by... 

This test code specifies procedures for evaiuation of uncertainties in individuai test measurements, arising from both random errors and systematic errors, and for the propagation of random and systematic uncertainties... 

Polarization effects are another feature of Raman spectroscopy that improves the assignment of bands and enables the determination of molecular orientation. Analysis of the polarized and non-polarized bands of isotropic phases enables determination of the symmetry of the respective vibrations. For aligned molecules in crystals or at surfaces it is possible to measure the dependence of up to six independent Raman spectra on the polarization and direction of propagation of incident and scattered light relative to the molecular or crystal axes. 

Burning velocity The velocity of propagation of a flame burning through a flammable gas-air mixture. This velocity is measured relative to the unbumed gases immediately ahead of the flame front. Laminar burning velocity is a fundamental property of a gas-air mixture. 

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