Partially replicated fractional factorial designs

Abstract

In this paper we consider screening experiments where m factors are to be studied using n experimental runs and where m is relatively large compared to n. In such experimental settings unreplicated fractional factorial (FF) designs are often used. Unreplicated FF designs have received a good deal of study over the past 15 years because they present problems in terms of use and analysis. One major problem with unreplicated FF design is the lack of reliable estimates for experimental error. Because of this a number of methods have been developed for identifying significant effects which include both graphical and more objective methods. However, there does not seem to be a clear winner among the methods suggested. In this paper we suggest as an alternative the use of partially replicated FF designs. The use of partial replication provides a non-model dependent estimate for pure error which allows for simpler and more standard methods for identifying significant effects through the use of F-and T-tests for lack of fit and individual contrasts. To illustrate the possibilities we focus on 16 run designs and provide some partially replicated designs for 4 ≤ m ≤ 11. We compare our proposed designs in terms of the A-optimality criterion and Estimation Capacity to regular unreplicated FF and Generalized Minimum Aberration non-regular FF designs. Our results indicate that partially replicated FF are competitive in terms of the criteria mentioned.