In the design of statistical experiments, situations may arise when resource constraints hinder the use of factorial designs for process improvement. This paper explores how 9, 18 and 27-run orthogonal arrays compare against each other and against a proposed experimental plan referred to as a 'Segmented Fractional Plan' when used to fractionate 3 3 and 3 4 factorial experiments. Based on the analysis of 8 responses from 6 factorial experiments, it was observed that to identify the process setting that produces the desired product quality, with a reduced number of experimental runs, the segmented fractional plan can perform as well or better than some orthogonal arrays thus, providing an option for fractionating 3 3 and 3 4 factorial experiments.