On sum composition of fractional factorial designs |
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Authors: | J. Joiner B.L. Raktoe W.T. Federer |
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Affiliation: | Tracor-Jitco Co , University of Guelph and Cornell University |
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Abstract: | Combinatorial extension and composition methods have been extensively used in the construction of block designs. One of the composition methods, namely the direct product or Kronecker product method was utilized by Chakravarti [1956] to produce certain types of fractional factorial designs. The present paper shows how the direct sum operation can be utilized in obtaining from initial fractional factorial designs for two separate symmetrical factorials a fractional factorial design for the corresponding asymmetrical factorial. Specifically, we provide some results which are useful in the construction of non-singular fractional factorial designs via the direct sum composition method. In addition a modified direct sum method is discussed and the consequences of imposing orthogonality are explored. |
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Keywords: | sum composition fractional factorial designs estimability orthogonality |
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