A criterion for selecting a two level fractional factorial design

Document Type : Original Paper


Department of Statistics, University of Kurdistan, Sanandaj, Iran


Application of fractional factorial design is common in experiments with a large number of factors. Choosing the appropriate fraction is an important issue in the fractional designs literature. There are different criteria based on different perspectives. In this paper, a criterion based on minimization of a weighted function of the mean squared error matrix of the least squares estimators of a pre-specified model is introduced. In two-level fractional designs, the criterion for the uniform weight function is calculated and shown to be equivalent to the well-known $ D $-optimal design. Finally, the method is described with examples.


Main Subjects

[1] Box G. E. P. and Hunter J. S., The 2^k fractional factorial designs: part I, Technometrics, 3 (1961a),311-351.
[2] Box G. E. P. and Hunter J. S., The 2^k fractional factorial designs: part II, Technometrics, 3 (1961b), 449-458.
[3] Cheng C. S., Orthogonal arrays with variable numbers of symbols, Ann. Stat., 8 (1980), 447-453.
[4] Fedorov V. V., Theory of optimal experiments, Academic Press, New York, (1972).
[5] Lehmann E. L. and Romano J., Testing Statistical Hypotheses, Springer, New York, (2005).
[6] Lin D. K. J. and Zhou J., D-optimal minimax fractional factorial designs, Can. J. Stat., 41 (2013), 325-340.
[7] Pukelsheim F., Optimal design of experiments, Wiley, New York, (1993).
[8] Rao C. R., Linear Statistical Inference and its Applications, Wiley, New York, (1973).
[9] Tang B. and Zhou J., Existence and construction of two-level orthogonal arrays for estimating main effects and some specified two-factor interactions, Stat. Sin., 19 (2009), 1193-1201.
[10] Wilmut M. and Zhou J., D-optimal minimax design criterion for two-level fractional factorial designs, J. Stat. Plan. Inference., 141 (2011), 576-587.
[11] Wu C. F. J. and . Hamada M. S, Experiments: planning, analysis and optimization, Wiley, New York,(2009).
[12] Yin Y. and Zhou J., Minimax design criterion for fractional factorial designs, Ann. Inst. Stat. Math. 67 (2015), 673-685.