Generation of Two-Level Cost Optimal Fractional Factorials

It is assumed that, in a 2k factorial experiment, there are different costs per observation at each of the factor combinations. When the number of factors, k, increases, the total number of observations in the full factorial increases rapidly as does the expense of observing all observations in the full factorial. If the experimenter can assume certain classes of higher-order interactions are negligible, then advantage may be taken by observing measurements from an orthogonal fractional factorial. For any “1/2p” fraction of the full factorial, a 2k-p experiment, there are 2p feasible orthogonal fractions that could be selected at random. This paper develops an algorithm for generating the minimum cost such fraction in an efficient way. The problem is formulated as a mathematical programming problem subject to a resolution III constraint (main effects unconfounded). Computational experience is presented.