April 2021
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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.