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Block plan for a fractional 2m factorial design derived from a 2r factorial design

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Summary

For a given fractional 2m factorial (2m-FF) designT, the constitution of a block plan to divideT intok (2r−1<k≦2r) blocks withr block factors each at two levels is proposed and investigated. The well-known three norms of the confounding matrix are used as measures for determining a “good” block plan. Some theorems concerning the constitution of a block plan are derived for a 2m-FF design of odd or even resolution. Two norms which may be preferred over the other norm are slightly modified. For each value ofN assemblies with 11≦N≦26, optimum block plans fork=2 blocks with block sizes [N/2] andN−[N/2] minimizing the two norms are presented forA-optimal balanced 24-FF designs of resolutionV given by Srivastava and Chopra (Technometrics,13, 257–269).

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Authors and Affiliations

  1. Kobe University, Kobe, Japan

    Teruhiro Shirakura

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  1. Teruhiro Shirakura
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Shirakura, T. Block plan for a fractional 2m factorial design derived from a 2r factorial design. Ann Inst Stat Math 38, 145–159 (1986). https://doi.org/10.1007/BF02482507

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  • DOI: https://doi.org/10.1007/BF02482507

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