Table 24.2 presents global mean values of the parameters in (24.29), along with estimates of the uncertainty associated with each parameter, as suggested by Penner et al. (1994). [Pg.1069]

We also want estimates of the uncertainties of the parameters Equations (2-99) and (2-101), repeated here, provide these. [Pg.249]

An explanation of the erroneous estimate of stoichiometric number may be that Equations 6 and 7 contain a number of flexible parameters such as v, Kbutane, Kbutenes and the exponents of partial pressures of both butane and butenes. In addition the equation is nonlinear with respect to these parameters, and the parameters are highly correlated. In those situations it is extremely difficult to obtain precise estimates of parameters, even with well-developed nonlinear regression computer programs. Uncertainty associated with the estimate of stoichiometric number may arise from the fact that the assumptions made when Equations 6 and 7 [Pg.104]

The cell parameters of the trigonal phase can now be calculated at each pressure for which the monoclinic unit-cell was measured. The estimated uncertainties given in Table A3 were obtained from the components of the variance-covariance matrices of the fits (Table A2) through Equations (7) and (8). Note that for the unit-cell parameters, the variance-covariance matrix used in Equation (7) is that of the fit of the cubes of the unitcell parameters, yielding estimates of the uncertainty of the cubes of extrapolated unitcell [Pg.99]

The estimation of measurement uncertainty is an alternative to validation if a quantitative result is used for the assessment of the development process. In this case only one parameter of the validation is needed. The precision of the analysis is sometimes taken as a quality figure instead of a validation. But precision cannot replace validation because in this case the environment, i.e. the sample preparation is neglected and precision is [Pg.76]

Although different fitting methods may produce estimates of parameters with the same uncertainties, the methods may differ greatly in reliability. It is thus of prime importance to choose an accurate method that has the greatest robustness for the application being considered. [Pg.65]

A simple procedure to overcome the problem of the small region of convergence is to use a two-step procedure whereby direct search optimization is used to initially to bring the parameters in the vicinity of the optimum, followed by the Gauss-Newton method to obtain the best parameter values and estimates of the uncertainty in the parameters (Kalogerakis and Luus, 1982). [Pg.155]

In bubble columns, the estimation of parameters is more difficult than in the case of either gas-solid or solid-liquid fluidized beds. Major uncertainties in the case of bubble columns are due to the essential differences between solid particles and gas bubbles. The solid particles are rigid, and hence the solid-hquid (or gas-solid) interface is nondeformable, whereas the bubbles cannot be considered as rigid and the gas-liquid interface is deformable. Further, the effect of surface active agents is much more pronounced in the case of gas-liquid interfaces. This leads to uncertainties in the prediction of all the major parameters such as terminal bubble rise velocity, the relation between bubble diameter and terminal bubble rise velocity, and the relation between hindered rise velocity and terminal rise velocity. The estimation procedure for these parameters is reviewed next. [Pg.42]

A large data base has been amassed relative to the analysis of milk samples for 1-131. The data are presented here along with the "theoretical" estimates of systematic uncertainty In each of the parameters of concern In order to provide the reader with a review of the type of data required for experiment redesign and optimization. This historical data might be used to establish an a-priori LLD estimate of a measurement system. [Pg.254]

It is difficult to make a quantitative estimate of the uncertainty in the result coming from the model dependence of the approach. In the analysis several assumptions must be made, such as the radial shape of the density oscillations and the actual values of the optical model parameters. [Pg.108]

What is more difficult is the estimation of the uncertainties of the resulting values of the strain components. These arise from three sources, the uncertainties in the measurement of the low-symmetry cell parameters, the uncertainty in the pressure of that measurement, and the uncertainties in the values of the extrapolated cell parameters of the high-symmetry phase. The variance Vy,v (= square of the estimated uncertainty) of the extrapolated volume Vr of the high-symmetry phase is given by (see Angel 2000, Eqn. 15) [Pg.92]

In order to estimate the uncertainties in a model s predictions (the ut in Eq. (21)) for consistency checking, one must have estimates of the uncertainties in the model s input parameters. In the 20th century, model input uncertainties [Pg.42]

It can be argued that the main advantage of least-squares analysis is not that it provides the best fit to the data, but rather that it provides estimates of the uncertainties of the parameters. Here we sketch the basis of the method by which variances of the parameters are obtained. This is an abbreviated treatment following Bennett and Franklin.We use the normal equations (2-73) as an example. Equation (2-73a) is solved for <2o- [Pg.46]

It should be stressed that, in any experiment for which there is to be a least-squares refinement of parameters, intended to yield not only the best possible parameter values but also respectable estimates of their uncertainties and a test of the validity of the model, it is vital to take the trouble to analyze the methods and the circumstances of the experiment carefully in order to get the best possible values of the a priori weights. [Pg.671]

Abstract Every analytical result should be expressed with some indication of its quality. The uncertainty as defined by Eurachem ( parameter associated with the result of a measurement that characterises the dispersion of the values that could reasonably be attributed to the,. .., quantity subjected to measurement ) is a good tool to accomplish this goal in quantitative analysis. Eurachem has produced a guide to the estimation of the uncertainty attached to an analytical result. Indeed, the estimation of the total uncertainty by using uncertainty propagation laws is com-ponents-dependent. The estimation of some of those components is based on subjective criteria. The identification of the uncertainty sources and of their importance, [Pg.62]

Local sensitivity information has numerous applications in uncertainty analysis, parameter estimation, experimental design, mechanism investigation and mechanism reduction. Uncertainty analysis, a quantitative study of the effect of parameter uncertainties on the solution of models, is [Pg.320]

The estimates obtained by applying Eqs. 8-10 are intended to give a first estimate of the measurement uncertainty associated with a particular parameter. If such estimates of the uncertainty are found to be a significant contribution to the overall uncertainty for the method, further study of the effect of the parameters is advised, to establish the true relationship between changes in the parameter and the result of the method. However, if the uncertainties are found to be small compared to other uncertainty components (i.e. the uncertainties associated with precision and trueness) then no further study is required. [Pg.89]

Method validation is a process used to confirm that an analytical procedure employed for a specific test is suitable for the intended use. The examples above show that the estimation of measurement uncertainty is a viable alternative to validation. The estimation of measurement uncertainty can be used to confirm that an analytical procedure is suitable for the intended use. If the estimation of measurement uncertainty is used together with validations both the uncertainty estimation and the validation have their own place in a developmental environment. The major advantages of measurement uncertainty are that it is fast and efficient. Normally, if the analytical method is understood by the laboratory very similar results are found for the estimation of uncertainty and for the classical variation of critical parameters, namely, validation. The decision on how to perform a validation should be made on a case to case basis depending on experience. [Pg.79]

© 2019 chempedia.info