Analyzing Unreplicated Blocked or Split-Plot Fractional Factorial Designs

In many industrial settings, experimental replication is sacrificed for run size. This can present serious difficulties in the analysis. Further restrictions are often placed on the experiment due to the inability or cost of completely randomizing the run order. Two situations where this arises are in blocked fractional factorial experiments and fractional factorial split-plot designs. Two existing methods of analysis for completely randomized experiments are extended to handle the restricted randomization. The methods are applied to industrial examples and their performance evaluated through simulation.