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.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Fig. 1

Comparison of discrepancies

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 3

Sample distributions in subspace

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
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

Grahic Jump Location
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




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In