Construction Of Optimal Split-plot Designs For Various Design Scenarios

Replication,randomization and blocking are three fundamental principles that need to be considered in the experiment design.When performing fractional factorial experiments in a completely random order is impractical,the fractional factorial split-plot designs are suitable choices.It is well recognized that the more lower order effects at lower order confounding,the better the designs.Based on this principle,statisticians have put forward a number of design criteria,including the GMC criterion.From this viewpoint,this thesis considers the construction of optimal regular two-level fractional factorial split-plot designs.The optimality criteria for two different designs scenarios are proposed.Under the newly proposed optimality criteria,the theoretical construction methods of optimal regular two-level fractional factorial split-plot designs are proposed.In addition,we also explore the theoretical construction methods of some optimal regular two-level fractional factorial split-plot designs under the widely adopted general minimum lower order confounding criterion.And we obtain the construction method of GMC-FFSP design under some range.At the end of this paper,we also discuss the differences between these three criteria and analysis their applicable conditions.