Multilevel design of experiments for statistical moment and probability calculation

A procedure for statistical moment estimation and reliability analysis using design of experiment (DOE) is proposed. A numerical method of finding the optimal levels and weights of DOE for statistical moment estimation is established and applied to three- and five-level cases. The four statistical moments of the system response function are then calculated from the full-factorial DOE, and the probability distribution of the system response function is obtained using the empirical distribution systems such as the Pearson system. The proposed method is tested through several examples and compared with other analysis methods, including the previous developments of a three-level full-factorial design. The results show that it relieves much of the difficulties met in the previous method and provides good accuracy compared to other methods for various input distributions.