Errors measuring

Two generally accepted models for the vapor phase were discussed in Chapter 3 and one particular model for the liquid phase (UNIQUAC) was discussed in Chapter 4. Unfortunately, these, and all other presently available models, are only approximate when used to calculate equilibrium properties of dense fluid mixtures. Therefore, any such model must contain a number of adjustable parameters, which can only be obtained from experimental measurements. The predictions of the model may be sensitive to the values selected for model parameters, and the data available may contain significant measurement errors. Thus, it is of major importance that serious consideration be given to the proper treatment of experimental measurements for mixtures to obtain the most appropriate values for parameters in models such as UNIQUAC. 

There are two types of measurement errors, systematic and random. The former are due to an inherent bias in the measurement procedure, resulting in a consistent deviation of the experimental measurement from its true value. An experimenter s skill and experience provide the only means of consistently detecting and avoiding systematic errors. By contrast, random or statistical errors are assumed to result from a large number of small disturbances. Such errors tend to have simple distributions subject to statistical characterization. 

The method used here is based on a general application of the maximum-likelihood principle. A rigorous discussion is given by Bard (1974) on nonlinear-parameter estimation based on the maximum-likelihood principle. The most important feature of this method is that it attempts properly to account for all measurement errors. A discussion of the background of this method and details of its implementation are given by Anderson et al. (1978). 

If there is sufficient flexibility in the choice of model and if the number of parameters is large, it is possible to fit data to within the experimental uncertainties of the measurements. If such a fit is not obtained, there is either a shortcoming of the model, greater random measurement errors than expected, or some systematic error in the measurements. 

The maximum-likelihood method is not limited to phase equilibrium data. It is applicable to any type of data for which a model can be postulated and for which there are known random measurement errors in the variables. P-V-T data, enthalpy data, solid-liquid adsorption data, etc., can all be reduced by this method. The advantages indicated here for vapor-liquid equilibrium data apply also to other data. 

The measurement error for conventional motor fuels is around 0.3 points and 0.7 points for the RON and the MON respectively. The RON is the characteristic more often used and more widespread than the MON moreover, when the octane number is used without reference either procedure, it is taken to be the RON. 

A new one-dimensional mierowave imaging approaeh based on suecessive reeonstruetion of dielectrie interfaees is described. The reconstruction is obtained using the complex reflection coefficient data collected over some standard waveguide band. The problem is considered in terms of the optical path length to ensure better convergence of the iterative procedure. Then, the reverse coordinate transformation to the final profile is applied. The method is valid for highly contrasted discontinuous profiles and shows low sensitivity to the practical measurement error. Some numerical examples are presented. 

However the forms of the curves in fig. 5 are not fully symraetrieal. There are several causes for this nonlinear behaviour. For instance even small un-symmetrics in the coil construction or measurement errors caused by small differences in the position of the coil to the underground or the direction of coil movement influence the measured data and results in mistakes. 

For interpretation of measuring results, calibration characteristics obtained on the samples in advance is used in the above instruments. However, if number of impediment factors increases, the interpretation of the signals detected becomes more complicated in many times. This fact causes the position that the object thickness T and crack length I are not taken into consideration in the above-mentioned instruments. It is considered that measuring error in this case is not significant. 

Now we study measuring errors as a result of ignoring the influence of parameters T and I. To do the study we have performed the necessary calculation according to the following methods. 

The component of the relative measuring error of crack depth measuring is calculated because real parameter p is replaced by its limit value ... 

Analogous methods are used to calculated the measuring error related to inexact measuring of voltage Ur and/or Up. It is counted that the value of U is determined with measuring error 5%. The measuring error 5hu-, Shut at too low and high value of U are separately analyzed. 

The measuring error of crack depth by means of electropotential devices is considered to be approximately 10%[2]. The research work performed gives us an opportunity to maintain it that is practice such a measuring error can be higher in many times et some probably combinations of parameters h, I, T. 

The procedure of testing must include measurements which have to provide reliable information about the quality of the object to be tested. The list of characteristics of measurement errors is selected on the basis of the required end results, methods of its calculation, form of presentation of the accuracy factors, reliability of the end result. These factors are of utmost attention in attestation of the procedure of testing. 

In assessment of characteristics of measurement error all components of this error must be taken into account and supported by the results of experimental investigations. 

When we report the result of a measurement a , there are two things a person reading the report wants to know the magnitude (size) of the measurement and the reliability of the measurement (its scatter ). If measuring errors are random, as they very frequently are, the magnitude is best expressed as the arithmetic mean p of N repeated tr ials xi... 

When designing and evaluating an analytical method, we usually make three separate considerations of experimental error. First, before beginning an analysis, errors associated with each measurement are evaluated to ensure that their cumulative effect will not limit the utility of the analysis. Errors known or believed to affect the result can then be minimized. Second, during the analysis the measurement process is monitored, ensuring that it remains under control. Finally, at the end of the analysis the quality of the measurements and the result are evaluated and compared with the original design criteria. This chapter is an introduction to the sources and evaluation of errors in analytical measurements, the effect of measurement error on the result of an analysis, and the statistical analysis of data. 

Determinate errors may be divided into four categories sampling errors, method errors, measurement errors, and personal errors. 

The maximum determinate measurement error for equipment or instrument as reported by the manufacturer. 

Measurement Errors for Class A Glassware Class B Glassware... 

Balance Capacity (g) Measurement Error Pipet Range Volume (mL or ixL)=> Measurement Error ( %)... 

Determinate measurement errors can be minimized by calibration. A pipet can be calibrated, for example, by determining the mass of water that it delivers and using the density of water to calculate the actual volume delivered by the pipet. Although glassware and instrumentation can be calibrated, it is never safe to assume that the calibration will remain unchanged during an analysis. Many instruments, in particular, drift out of calibration over time. This complication can be minimized by frequent recalibration. 

Determine the uncertainty for the gravimetric analysis described in Example 8.1. (a) How does your result compare with the expected accuracy of 0.1-0.2% for precipitation gravimetry (b) What sources of error might account for any discrepancy between the most probable measurement error and the expected accuracy ... 

The relative measurement error in concentration, therefore, is determined by the magnitude of the error in measuring the cell s potential and by the charge of the analyte. Representative values are shown in Table 11.7 for ions with charges of+1 and +2, at a temperature of 25 °C. Accuracies of 1-5% for monovalent ions and 2-10% for divalent ions are typical. Although equation 11.22 was developed for membrane electrodes, it also applies to metallic electrodes of the first and second kind when z is replaced by n. 

Relationship Between Measurement Error in Potential and Relative Error in Concentration... 

Accuracy The accuracy of a controlled-current coulometric method of analysis is determined by the current efficiency, the accuracy with which current and time can be measured, and the accuracy of the end point. With modern instrumentation the maximum measurement error for current is about +0.01%, and that for time is approximately +0.1%. The maximum end point error for a coulometric titration is at least as good as that for conventional titrations and is often better when using small quantities of reagents. Taken together, these measurement errors suggest that accuracies of 0.1-0.3% are feasible. The limiting factor in many analyses, therefore, is current efficiency. Fortunately current efficiencies of greater than 99.5% are obtained routinely and often exceed 99.9%. 

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