%0 Journal Article %T A criterion for selecting a two level fractional factorial design %J Journal of Advanced Mathematical Modeling %I Shahid Chamran University of Ahvaz %Z 2251-8088 %A Esmailzadeh, Nabaz %A Ramezani, Shayda %D 2021 %\ 04/21/2021 %V 11 %N 1 %P 61-68 %! A criterion for selecting a two level fractional factorial design %K Fractional factorial design %K optimal design %K Two level design %R 10.22055/jamm.2021.29978.1731 %X 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. %U https://jamm.scu.ac.ir/article_16745_6698e991c76432ff2d69f1d50dc23fcd.pdf