Regular fractional factorial plans were introduced by Finney in 1945 as a means for reducing the number of observations necessary to estimate a particular set of effects. These plans frequently suffer from the same shortcoming as complete factorial plans in that the require far more observations than there are effects to be estimated. A method for reducing the number of observations involves the use of irregular fractional factorial plans.

This dissertation is primarily an extension of the work begun in the early sixties by P.W.M. John and S. Addleman, concerning irregular fractional plans which are obtained by either omitting observations from regular fractional plans, or adding observations to regular fractional plans. A procedure for either adding or omitting these observations is described, and the properties of the irregular fractional plans which result are examined. For each plan, it is shown how the effects to be estimated must be arranged in alias sets, if they are to be uniquely estimable. The variance properties of these estimates are discussed. Also included is a listing of some useful irregular fractional factorial plans.