Irregular Fractions of the 2 n Factorial Experiments

The development of fractional replicate plans which consist of irregular fractions of factorial experiments is presented. The method of constructing irregular fraction plans is developed for the general s n factorial experiment. However, the plans which are found to be of greatest practical value are plans for the 3/2 m replicate of the 2 n experiment. Although these plans introduce correlations between some of the estimates, the correlations do not affect individual tests on the parameters. Some irregular fraction plans permit the estimation of main effects and two-factor interactions with fewer trials than is required with an orthogonal plan. A straightforward procedure for obtaining estimates of the main effects and “important” interactions and estimates of their variances, covariances and correlation coefficients is presented for the 3/2 m replicate plans.