Computer-Aided Design of Fractional Factorial Experiments Given A List of Feasible Observations

Abstract

When attributes of experimental units serve as independent variables, locating the units possessing the required combinations of attribute values for an experimental design can be a serious practical problem. Often, however, data sets of observable experimental units exist. A computer-aided design methodology is presented which determines which two-level factorial and orthogonal fractional factorial designs are feasible, given the data set of observable experimental units. Contrary to usual practice, the number of factors to consider is an explicit experiment planning variable in the methodology. All combinations of ten and fewer factors and 2¹⁰ and fewer observations (in steps of powers of 2) are represented by a feasibility matrix. For a given set of observable experimental units, the design methodology attempts to map which cells of the matrix are feasible. Dependency relationships among feasibility matrix cells are stated which allow implicit enumeration of cells. An example taken from highway safety research is used to demonstrate use of the design methodology. Lastly, search times for random data sets indicate seven or fewer factors can be searched at low cost, but the cost for more than seven factors is dependent upon data-set size.