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

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.