Accuracy evaluation requirements

Much effort has been devoted to producing fast and efficient numerical integration techniques, and there is a very wide variety of methods now available. The efficiency of an integration routine depends on the number of function evaluations, required to achieve a given degree of accuracy. The number of evaluations depends both on the complexity of the computation and on the number of integration step lengths. The number of steps depends on both the na-... 

In summaty, HOz and ROz radical concentrations are substantially greater than those of OH, typically by several orders of magnitude. There are several different approaches to measuring these peroxy radicals, and the results from these are in overall agreement as to the magnitude of the concentrations and their diurnal variation. However, there have not been a significant number of intercomparison studies of these methods, so evaluation of the absolute accuracies will require further work. 

The determination of crystal structure in synthetic polymers is often made difficult by the lack of resolution in the diffraction data. The diffuseness of the reflections observed in most x-ray fiber patterns results from the small size and imperfect lattice nature of the polymer crystallites. Resolution of individual reflections is also made difficult from misorientation of the crystallites about the fiber axis. This lack of resolution leads to poor accuracy in measurement of peak positions. In particular, this lack of accuracy makes determination of layer line heights difficult with a corresponding loss of significant figures in evaluation of the repeat distance for the molecular conformation. In the case of helical conformations, the repeat distance may be of considerable length or, as we shall show, indeterminate and, in effect, nonperiodic. This evaluation requires high accuracy in measurements of layer line heights. 

The results of research on the NMR spectra of elements with different isotopic composition have been reported. (95) The particular interest of these investigations lies in the possibility of applying perturbation theory to account for the contribution of vibrational states to the shielding of nuclei. (96, 97) In addition, the measurement of nuclear g factors of isotopic pairs, with great accuracy, is required for evaluating small hyperfine structure anomalies. (39,98)... 

In many computational codes, second derivatives are evaluated numerically (this is also the case of CRYSTAL). This evaluation requires high numerical accuracy in the determination of the total energy. In particular, the lattice deformations involved in calculating lattice constants, which generally reduce the local symmetry, make basis set flexibility (additional sp shells, polarization functions, and so on) necessary. Consequently, a good basis set for the determination of total energy and lattice parameters may be inadequate for the more demanding estimation of these second derivatives. 

The latest methodical development [51] is an automatic evaluation method of the video frames, by which the true macroscopic elongation of the sample can be determined with an accuracy of 3 decimals. Such high accuracy is required for thermoplastic materials that fail at low elongations ( 0.1). The method extracts the grating of the fiducial marks on the sample from the actual video image, computes the ID correlation function [52,53], and evaluates its long period . 

Step 6 Evaluate the ANN model If the estimation generated by the model lies within acceptable accuracy then, proceed to the next step. Otherwise repeat Steps 2 to 6 all over again until the estimation produced falls within the acceptable accuracy. For various applications, accuracy level requirements would be different and are judged subjectively by the user. 

The shear viscosity is a tensor quantity, with components T] y, t],cz, T)yx> Vyz> Vzx> Vzy If property of the whole sample rather than of individual atoms and so cannot be calculat< with the same accuracy as the self-diffusion coefficient. For a homogeneous fluid the cor ponents of the shear viscosity should all be equal and so the statistical error can be reducf by averaging over the six components. An estimate of the precision of the calculation c then be determined by evaluating the standard deviation of these components from tl average. Unfortunately, Equation (7.89) cannot be directly used in periodic systems, evi if the positions have been unfolded, because the unfolded distance between two particl may not correspond to the distance of the minimum image that is used to calculate the fore For this reason alternative approaches are required. 

With the Industrial Revolution, life became more complex but it was not until World War II that reliability engineering was needed to keep the complex airplanes, tanks, vehicles and ships operating. Of particular concern was the reliability of radar. Prior to this time equipment was known qualitatively to be reliable or unreliable. To quantify reliability requires collecting statistics on part failures in order to calculate the mean time to failure and the mean time to repair. Since then, NASA and the military has included reliability specifications in procurements thereby sustaining the collection and evaluation of data build statistical accuracy although it adds to the cost. 

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