Sample Size Determination in NT Net Quasi Monte Carlo Simulation

Abstract

Monte Carlo (MC) technique prevails in probabilistic design simulation, such as in statistical tolerance analysis and synthesis. A quasiMonte Carlo (e.g., number theoretic net method (NTnet)) 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 NumberTheoretical Net Method (NTnet),â€‌ 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,â€‌ ASME J. Manuf. Sci. Eng., 123(3), pp. 490–493) for comparison between NTnet and MC, a method for sample size determination of NTnet is still not available. Combinatorial theory and the solution of occupancy problem are used for estimating equivalent sample sizes of MC and NTnet, allowing the NTnet 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.