ADV MATH SCI JOURNAL 8 printed version electronic version D-OPTIMAL MINIMAX CRITERION FOR TWO-LEVEL FRACTIONAL FACTORIAL SPLIT PLOT DESIGNS A. J. SAKA 1 , A. A. OLOSUNDE, AND B. B. ADEOYE ABSTRACT. In this paper, the D-optimal minimax criterion of two-level fractional factorial split-plot designs were constructed and a general form of the loss function for the criterion was provided. This was used in searching for optimal designs. The optimum designs were obtained via the algorithm developed in python programming language among many designs constructed. As such, the resulting designs are called D-optimal minimax two-level fractional factorial split plot designs. The efficiency of D-optimal minimax designs was felt when compared with both A- and D-optimal designs. 1. I NTRODUCTION Factorial designs are useful to study the effects of two or more factors with their interactions effects in an experiment. In every complete trial or replicate of an experiment, all possible combinations of the levels of the factors are investigated. As the numbers of factors increase, the numbers of runs required for a full replicate of the design rapidly outgrows the resources of experimenters. As such, fractional factorial designs are then employed to screen the factors and identify those with significant effects. At times, it may be impossible to perform the trial in a complete random 1 corresponding author 2010 Mathematics Subject Classification. 62K10; 20A05. Key words and phrases. Factorial Designs, Fractional Factorial Designs, Split Plots Design, Fractional Factorial Split Plot Designs and D-optimal minimax. 103