THE PROBLEM OF THE NUMBER OF COMPUTATION POINTS in VS .NET Drawer UPCA in VS .NET THE PROBLEM OF THE NUMBER OF COMPUTATION POINTS THE PROBLEM OF THE NUMBER OF COMPUTATION POINTSUCC - 12 Recognizer In .NETUsing Barcode Control SDK for .NET Control to generate, create, read, scan barcode image in VS .NET applications.Table 15.7 Point 1 2 3 4 5 6 7 8 Generate UPC-A Supplement 2 In Visual Studio .NETUsing Barcode printer for Visual Studio .NET Control to generate, create UPC Code image in .NET framework applications.Results from Hong s method with four variables for Culmann slope c(kPa) 2.445 5.863 4.333 4.333 4.333 4.333 4.333 4.333 (deg) 15.667 15.667 12.556 19.167 15.667 15.667 15.667 15.667 (kN/m3 ) 19.333 19.333 19.333 19.333 17.445 20.863 19.333 19.333 (deg) 20.000 20.000 20.000 20.000 20.000 20.000 18.367 21.663 M (kPa) 0.636 4.054 1.274 3.978 2.701 2.381 2.900 2.521 Mest = Sum of M p = p 0.112 0.138 0.132 0.118 0.112 0.138 0.125 0.125 2.576 1.202UPC-A Supplement 2 Scanner In .NET FrameworkUsing Barcode decoder for VS .NET Control to read, scan read, scan image in .NET applications.Variance = Sum of M2 p (Mest)2 = = 1.097, = 2.350 H = 10 m, = 26 deg Barcode Printer In Visual Studio .NETUsing Barcode generation for .NET Control to generate, create bar code image in .NET applications.Points far from Mean for Large n Read Barcode In .NET FrameworkUsing Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in .NET applications.Lind s, Haar s, and Hong s methods give results superior to those from FOSM methods with little or no increase in computational effort. Because they use fewer points than the original point-estimate methods, they may be somewhat less accurate for some functions, but limited testing indicates that they are usually quite satisfactory. All the methods locate the points at or near the surface of a hypersphere or hyperellipsoid that encloses the points from the original Rosenblueth method. The radius of the hypersphere is proportional toMaking Universal Product Code Version A In Visual C#.NETUsing Barcode printer for .NET framework Control to generate, create UPCA image in .NET framework applications.x3 x2 Encoding UPC-A In VS .NETUsing Barcode maker for ASP.NET Control to generate, create GS1 - 12 image in ASP.NET applications.Figure 15.13 Distribution of evaluation points for three uncertain variables. The variables have been normalized by subtracting the mean and dividing by the standard deviation. (a) Coordinate system, (b) black squares are the eight points in the original Rosenblueth procedure, (c) ellipses are circular arcs de ning a sphere circumscribed around the Rosenblueth points, (d) black dots are the intersections of the circumscribed sphere with the coordinate axes, which are the six points in the Harr and Hong procedures. (Christian, J. T. and Baecher, G. B., 2002, The Point-Estimate Method with Large Numbers of Variables, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 126, No. 15, pp. 1515 1529, reproduced by permission of John Wiley & Sons.)UCC - 12 Printer In Visual Basic .NETUsing Barcode maker for Visual Studio .NET Control to generate, create UPC A image in VS .NET applications.POINT ESTIMATE METHODS Draw EAN / UCC - 14 In Visual Studio .NETUsing Barcode creation for .NET Control to generate, create EAN128 image in Visual Studio .NET applications.X3 X2 Code 128 Code Set B Encoder In VS .NETUsing Barcode creator for .NET framework Control to generate, create Code 128 image in .NET applications.X3 X2 Data Matrix 2d Barcode Generation In .NET FrameworkUsing Barcode maker for .NET Control to generate, create DataMatrix image in .NET framework applications.Figure 15.13 (continued )Printing Industrial 2 Of 5 In .NET FrameworkUsing Barcode generator for .NET framework Control to generate, create Standard 2 of 5 image in VS .NET applications.THE PROBLEM OF THE NUMBER OF COMPUTATION POINTS Code128 Generator In Visual C#.NETUsing Barcode creator for .NET framework Control to generate, create Code 128C image in VS .NET applications.1E +07 1E +06 1E +05 2n 1E +04 1E +03 1E +02 1E +01 1E +00 0 5 10 15 Number of Uncertain Quantities 20 (n 3+ 3n = 2)/2Generating Code39 In Visual Basic .NETUsing Barcode printer for VS .NET Control to generate, create Code 3 of 9 image in .NET applications.Number of Calculations Encoding USS Code 39 In Visual Studio .NETUsing Barcode generator for ASP.NET Control to generate, create Code 39 image in ASP.NET applications.2n + 1 UCC.EAN - 128 Drawer In JavaUsing Barcode creator for Java Control to generate, create GS1-128 image in Java applications.Figure 15.14 Numbers of calculations by various algorithms. (Christian, J. T. and Baecher, G. B., 2002, The Point-Estimate Method with Large Numbers of Variables, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 126, No. 15, pp. 1515 1529, reproduced by permission of John Wiley & Sons.)UPC - 13 Drawer In JavaUsing Barcode printer for Java Control to generate, create UPC - 13 image in Java applications.n in Harr s method and nearly so in Lind s and Hong s. It is possible that, when n is large, the values of the xi s at which the evaluation is to take place may be so many standard deviations away from the means that they are outside the range of meaningful de nition of the variables. Figure 15.15 shows what happens in a case of normalized uncorrelated and unskewed variables. The four black points are the points in the conventional Rosenblueth procedure for two variables. The four open points on the circle drawn through the black points are the evaluation points that would be used in the Harr, Hong, or Lind procedures. There is obviously no advantage in doing this for two variables as four points are needed in either case. However, if there were nine variables, a reduction from 512 to 18 evaluations would be well worth the effort. The outer circle in Figure 15.15 represents a two-dimensional section through the nine-dimensional hypersphere, and the evaluation points now lie three standard deviations form the mean. Thus, critical values of the variables will be located far from the region where the distributions are known best. In Table 15.8, which gives the coordinates of the points to be used in the analysis with four uncertain variables triangularly distributed, it is clear that the values of some of the variables are quite close to the limits of their triangular distributions. If there were seven variables, Table 15.9 shows that the values of all the variables would fall outside the bounds of their distributions. Figure 15.16 is the same as Figure 15.4, except that the locations of the evaluation points for cases with 5 and 10 variables are shown. The evaluations fall far out along the tails of the distribution, where the values of the distribution are known poorly.Draw Bar Code In C#.NETUsing Barcode creation for .NET Control to generate, create bar code image in Visual Studio .NET applications.Printing EAN128 In Visual Studio .NETUsing Barcode creation for ASP.NET Control to generate, create GTIN - 128 image in ASP.NET applications.