Abstract
The paper gives a new method to identify significant effects in two-level factorial experiments, and compares the new method with the exiting methods using Monte Carlo simulation. The existing methods only perform well under the assumption of effect sparsity, but the new method performs well without effect sparsity.
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References
Box, G.E.P., Hunter, W.G., Hunter, J.S. Statistics for Experiment. Wiley, New York, 1978
Box, G.E.P., Meyer, R.D. An analysis for unreplicated fractional factorials. Technometrics, 28: 11–18 (1986)
Daniel, C. Use of half-normal plots in interpreting fractorial two-level experiments. Technometrics, 1: 311–341 (1959)
Daniel, C. Applications of Statistics to industrial experimentation. Wiley, New York, 1976
Dong, F. On the identification of active contrasts in unreplicated fractional factorials. Statist Sinica, 3: 209–217 (1993)
Le N.D., Zamer R.H. A global test for effects in 2k factorial design without replicates. Journal of Statistical Computation and Simulation, 41: 41–54 (2007)
Lenth, R.S. Quick and easy analysis of unreplicated factorials. Technometrics, 31: 469–473 (1989)
Li, P., Zhao, S.L., Zhang, R.C. A cluster analysis selection strategy for supersaturated designs. Comput. Statist. Data An., 54: 1605–1612 (2010)
Variyath, A.M., Abraham, B., Chen, J. Analysis of performance measures in experimental designs using Jackknife. J. Quality Tech., 37: 91–100 (2005)
Wu, C.F.J., Hamada, M.S. Experiments: Planning, Analysis, and Optimization, 2nd ed. Wiley, New York, 2009
Zahn, D.A. Modifications of and revised critical values for the half-normal plot. Technometrics, 17: 189–200 (1975)
Zahn, D.A. An empirical study of the half-normal plot. Technometrics, 17: 201–211 (1975)
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The authors would like to thank the referees for their valuable comments and structural suggestions for improving the paper.
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This paper is supported by the National Natural Science Foundation of China (Nos. 11771250, 11371223).
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Li, H., Zhao, Sl. Identifying Significant Effects in Unreplicated Regular Two-level Factorial Experiments. Acta Math. Appl. Sin. Engl. Ser. 36, 816–824 (2020). https://doi.org/10.1007/s10255-020-0981-9
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DOI: https://doi.org/10.1007/s10255-020-0981-9