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Technical Brief

Sample Size Determination in NT-Net Quasi-Monte Carlo Simulation

[+] Author and Article Information
Wenzhen Huang

Mechanical Engineering Department,
University of Massachusetts Dartmouth,
285 Old Westport Rd.,
North Dartmouth, MA 02747
e-mail: whuang@umassd.edu

Contributed by the Computers and Information Division of ASME for publication in the Journal of Computing and Information Science in Engineering. Manuscript received April 30, 2012; final manuscript received March 7, 2013; published online May 14, 2013. Assoc. Editor: Xiaoping Qian.

J. Comput. Inf. Sci. Eng 13(3), 034501 (May 14, 2013) (7 pages) Paper No: JCISE-12-1072; doi: 10.1115/1.4024026 History: Received April 30, 2012; Revised March 07, 2013

Monte Carlo (MC) technique prevails in probabilistic design simulation, such as in statistical tolerance analysis and synthesis. A quasi-Monte Carlo (e.g., number theoretic net method (NT-net)) with better computation efficiency over MC has recently attracted interests in application. In spite of a comprehensive case study (Huang et al., 2004, “Tolerance Analysis for Design of Multistage Manufacturing Processes Using Number-Theoretical Net Method (NT-net),” Int. J. Flexible Manuf. Syst., 16, pp. 65–90 and Zhou et al., 2001, “Sequential Algorithm Based on Number Theoretic Method for Tolerance Analysis and Synthesis,” ASME J. Manuf. Sci. Eng., 123(3), pp. 490–493) for comparison between NT-net and MC, a method for sample size determination of NT-net is still not available. Combinatorial theory and the solution of occupancy problem are used for estimating equivalent sample sizes of MC and NT-net, allowing the NT-net sample size determination in application. A multivariate Chebyshev polynomial with variant coefficients is used to represent generic design functions for validation. The results are verified by case studies.

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Figures

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Fig. 1

Comparison of discrepancies

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Fig. 2

Sample points distribution: (a) NT-net and grid-net; (b) MC and grid-net

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Fig. 3

Sample distributions in subspace

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Fig. 4

Illustration of ESS: 3D cube cells generated by NT-net (a) and points generated by MC (b)

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Fig. 5

m/n versus n at confidence level 0.9 (left) and ESS ratio (m/n) surface (right)

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Fig. 6

Relative error envelope of Chebyshev polynomials: std (left); mean (right)

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Fig. 7

Relative error envelope of specified functions: std (left); mean (right)

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Fig. 8

Computation efficiency and accuracy comparison for mean estimation of F(x,y,z,t) = sinx+cosy+sinz*sint+x2+xy+y3+zt with ±1σ and ±3σ boundaries

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Fig. 9

Computation efficiency and accuracy comparison for std estimation of F(x,y,z,t) = sinx+cosy+sinz*sint+x2+xy+y3+zt with ±1σ and ±3σ boundaries

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