The proof is similar to that of Theorem 3 and is omitted here. Hence we have that the sum of elementwise product of \(p_1, p_2\) and \(p_3\), no matter whether they are distinct or not, is equal to zero, which implies the second-order orthogonality of \(P_c\). Ye KQ, Li W, Sudjianto A (2000) Algorithmic construction of optimal symmetric Latin hypercube desings. When using RAND(), I get at most 2 different solutions. One of the constraintss bound has to vary within a range everytime the worksheet is visited. Ye KQ (1998) Orthogonal column Latin hypercubes and their application in computer designs. Mike, I have an optimization model and using excel optimizer. Yang JY, Liu MQ (2012) Construction of orthogonal and nearly orthogonal Latin hypercube designs from orthogonal designs. Sun FS, Liu MQ, Lin DKJ (2009) Construction of orthogonal Latin hypercube designs. Steinberg DM, Lin DKJ (2006) A construction method for orthogonal Latin hypercube designs. Santner TJ, Williams BJ, Notz WI (2003) The design and analysis of computer experiments. Pang F, Liu MQ, Lin DKJ (2009) A construction method for orthogonal Latin hypercube designs with prime power levels. McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Lin CD, Mukerjee R, Tang B (2009) Construction of orthogonal and nearly orthogonal Latin hypercube designs. Lin CD, Bingham D, Sitter RR, Tang B (2010) A new and flexible method for constructing designs for computer experiments. Technometrics 49:45–55įang KT, Li R, Sudjianto A (2006) Design and modeling for computer experiments. Commun Stat Theory Methods 34:417–428Ĭioppa TM, Lucas TW (2007) Efficient nearly orthogonal and space-filling Latin hypercubes. Biometrika 96:51–65īutler NA (2005) Supersaturated Latin hypercube designs. This analysis is the first attempt to propagate parameter uncertainties of modern multi-group libraries, which are used to feed advanced lattice codes that perform state of the art resonant self-shielding calculations such as DRAGONv4.Bingham D, Sitter RR, Tang B (2009) Orthogonal and nearly orthogonal designs for computer experiments. Output uncertainty assessment is based on the tolerance limits concept, where the sample formed by the code calculations infers to cover 95% of the output population with at least a 95% of confidence. The quasi-random LHS allows a much better coverage of the input uncertainties than simple random sampling (SRS) because it densely stratifies across the range of each input probability distribution. The chosen sampling strategy for the current study is Latin Hypercube Sampling (LHS). The aim is to propagate multi-group nuclide uncertainty by running the DRAGONv4 code 500 times, and more » to assess the output uncertainty of a test case corresponding to a 17 x 17 PWR fuel assembly segment without poison. This library is based on JENDL-4 data, because JENDL-4 contains the largest amount of isotopic covariance matrixes among the different major nuclear data libraries. A statistical methodology is employed for such purposes, where cross-sections of certain isotopes of various elements belonging to the 172 groups DRAGLIB library format, are considered as normal random variables. These new designs facilitate exploratory analysis of stochastic simulation models in which there is considerable a priori uncertainty about the forms of the responses. = and 2-group homogenized macroscopic cross-sections predictions. This paper presents new Latin hypercube designs with minimal correlations between all main, quadratic, and two-way interaction effects for a full second-order model.
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