Error defined

Figure 6.31 compares the measured heat transfer coefficient by Lee and Mudawar (2005b) in two-phase flow of R-134a to predictions based on previous studies. The predictive accuracy of a correlation was measured by the mean absoiute error, defined as... 

However, since we are to implement negative feedback, we base our decision on the error defined as... 

The difference between the true result and the measured value. It is conveniently expressed as an absolute error, defined as the actual difference between the true result and the experimental value in the same units. Alternatively, the relative error may be computed, i.e. the error expressed as a percentage of the measured value or in parts per thousand. ... 

C Variance-covariance matrix of observation errors, defined ko... 

The authors also define a standard error although differently from the one previously given in equation 12. For that reason, when speaking about the standard error defined in reference [4] it will be indicated as the relative standard deviation of the experiments (RSD) since in fact that is what is calculated. 

Since the corrections are now known, the error measure can be computed from (3.69). The same value can be obtained from (3.77) using the equation error defined by (3.80), i.e.,... 

For A — tp, a in each case, the quantities AA denote the differences A A = ACh3 — AChl, and the quantities (AA/ = (AA)pulse(y/5Aj + 8A )(8(AA)) are our hnal results for the induced time delays or width differences of the peaks between BATSE channels 1 and 3. The first set of parentheses in the latter expression denotes the statistical error (where 8A( denotes the statistical error in determining A in the ith channel) the second set of parentheses denotes the ui theoretical systematic error, defined as 8(AA) = (8A)pulse — (AA). ... 

Error count increased by severe system error (defined in the tool)... 

Analysis of the shape of error surfaces. To conclude this section, we consider a more quantitative approach to error estimation. The first step is to estimate the accuracy of the individual data points this can either be done by analysis of the variability of replicate measurements, or from the variation of the fitted result. From that, one can assess the shape of the error surface in the region of the minimum. The procedure is straightforward the square root of the error, defined as the SSD, is taken as a measure of the quality of the fit. A maximum allowed error is defined which depends on the reliability of the individual points, for example, 30% more than with the best fit, if the points are scattered by about 30%. Then each variable (not the SSD as before) is minimised and also maximised. A further condition is imposed that the sum of errors squared (SSD) should not increase by more than the fraction defined above. This method allows good estimates to be made of the different accuracy of the component variables, and also enables accuracy to be estimated reliably even in complex analyses. Finally, it reveals whether parameters are correlated. This is an important matter since it happens often, and in some extreme cases where parameters are tightly correlated it leads to situations where individual constants are effectively not defined at all, merely their products or quotients. Correlations can also occur between global and local parameters. 

For precipitates of asymmetrical charge types, such as MA2 and MjA, expressions for relative precision are more complicated. Christopherson, excluding the effect of dilution, indicated that the relative titration error, defined by ( inflection — V)IV (where inflection is the titrant volume to the inflection point and V is the equivalence-point volume), is generally... 

This algorithm is based on eliminating the effect of error, defined as... 

Use of the optically thin value of the mean beam length yields values of gas emissivities or exchange areas that are too high. It is thus necessary to introduce a dimensionless constant P < 1 and define some new average mean beam length such that KLm = P mo-For the case of parallel plates, we now require that the mean beam length exactly predict the gas emissivity for a third value of KL. In this example we find p = -An[2Es(KL)]/2KL and for KL = 0.193095 there results p = 0.880. The value p = 0.880 is not wholly arbitrary. It also happens to minimize the error defined by the so-called shape correction factor ( ) = [9(.s /dAi]/ l - for all KL > 0. The... 

Modified Woods-Saxon Potential Coulombian Potential. - In Figure 2 the maximum absolute error, defined as Err = -log10 Eaccurate - Ecomputed, in the computation of all resonances E ,n — 1(1)4 obtained with another potential in (121), for step length equal to = and for the methods mentioned above, is shown. This potential is... 

The true solutions to the Woods-Saxon bound-states problem were obtained correct to fourteen decimal places using the analytic solution and the numerical results obtained using the above mentioned methods were compared with this true solution. In Figure 3 we present the maximum absolute error, defined as Err = — og o Eaccurate — ECOmputed, in the computation of the eigevnalues E ,n = 0(4) 12, for step length equal to h =... 

In the above relation OP s is the steady state value, or the bias of the manipulated variable, and e is the error defined as difference between PV and setpoint ... 

Before choosing the critical value, one specifies one s tolerance for Type I errors, defined as erroneous rejection of the null hypothesis when it is true. Type I errors are sometimes called/fltoe positives or false rejections. Regardless of the choice of the critical value, there is always the probability of a Type I error. For large enough critical values, this probability is small and generally can be tolerated. The tolerable probability that one specifies is called the significance level of the test and is usually denoted by a. In radioanalytical chemistry, it is common to set a = 0.05. If O = 0.05, then analyte-free samples should produce false positive results at a rate of only about one per twenty measurements. 

System Error Message Error count increased by severe system error (defined in the tool) Every second "CheckSys" Tool Message to pager with error number According to SOP "Problem Management" According to appropriate GxP regulations... 

Measurement error defines the measurement error (la) for each performance parameter. 

Figure 3 shows that the minimized square errors defined by Eq. (20) for the cSTO-T/rG, cSTO-7/cG, and cSTO-NreG expansions for Is-cSTO, firom which one can see that... 

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