Detailed Wordlength Pattern of Regular Fractional Factorial Split-Plot Designs in Terms of Complementary Sets

With reference to regular fractional factorial split-plot designs, we consider a detailed wordlength pattern taking due cognizance of the distinction between the whole-plot and sub-plot factors. A generalized version of the MacWilliamsʹ identity is employed to express the detailed wordlength pattern in terms of complementary sets. Several special features make this result intrinsically different from the corresponding one in classical fractional factorial designs where all factors have the same status. An application to robust parameter designs is indicated and examples given.