Abstract
In the absence of four-factor and higher order interactions, we present a series of search designs for 2m factorials (m≥6) which allow the search of at most k (=1,2) nonnegligible three-factor interactions, and the estimation of them along with the general mean, main effects and two-factor interactions. These designs are derived from balanced arrays of strength 6. In particular, the nonisomorphic weighted graphs with 4 vertices in which two distinct vertices are assigned with integer weight ω (1≤ω≤3), are useful in obtaining search designs for k=2. Furthermore, it is shown that a search design obtained for each m≥6 is of the minimum number of treatments among balanced arrays of strenth 6. By modifying the results for m≥6, we also present a search design for m=5 and k=2.
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References
Box, G. E. P., Hunter, W. S. and Hunter, J. S. (1978). Statistics for Experiments, Wiley, New York.
Ghosh, S. (1980). On main effect plus one plans for 2m factorials, Ann. Statist., 8, 922–930.
Ghosh, S. (1981). On some new search designs for 2m factorial experiments, J. Statist. Plann. Inference, 5, 381–389.
Gupta, B. C. (1988). A bound connected with 26 factorial search designs of resolution 3.1, Comm. Statist. Theory Methods, 17, 3137–3144.
Gupta, B. C. and Carvajal, S. S. R. (1984). A necessary condition for the existence of main effect plus one plan for 2m factorials, Comm. Statist. Theory Methods, 13, 567–580.
Ohnishi, T. and Shirakura, T. (1985). Search designs for 2m factorial experiments, J. Statist. Plann. Inference, 11, 241–245.
Shirakura, T. (1991). Main effect plus one or two plans for 2m factorials, J. Statist. Plann. Inference, 27, 65–74.
Shirakura, T. and Ohnishi, T. (1985). Search designs for 2m factorials derived from balanced arrays of strength 2(ℓ+1) and AD-optimal search designs, J. Statist. Plann. Inference, 11, 247–258.
Shirakura, T. and Tazawa, S. (1986). Enumeration and representation of nonisomorphic weighted graphs, Kobe J. Math., 3, 299–235.
Shirakura, T. and Tazawa, S. (1991). Series of main effect plus one or two plans for 2m factorials when three-factor and higher order interactions are negligible, J. Japan Statist. Soc. (to appear).
Srivastava, J. N. (1972). Some general existence conditions for balanced arrays of strength t and 2 symbols, J. Combin. Theory Ser. A, 13, 198–206.
Srivastava, J. N. (1975). Designs for searching non-negligible effects, A Survey of Statistical Design and Linear Models (ed. J. N.Srivastava), 507–519, North-Holland, Amsterdam.
Srivastava, J. N. (1977). Optimal search design, or designs optimal under bias free optimality criteria, Statistical Decision Theory and Related Topics II (eds. S. S.Gupta and D. S.Moore), 375–409, Academic Press, New York.
Srivastava, J. N. and Ghosh, S. (1976). A series of balanced 2m factorial designs of resolution V which allow search and estimation of one extra unknown effect, Sankyā Ser. B, 38, 280–289.
Srivastava, J. N. and Ghosh, S. (1977). Balanced 2m factorial designs of resolution V which allow search and estimation of one unknown effect, 4≤m≤8, Comm. Statist. Theory Methods, 6, 141–166.
Srivastava, J. N. and Gupta, B. C. (1979). Main effect plan for 2m factorials which allow search and estimation of one unknown effect, J. Statist Plann. Inference, 3, 259–265.
Yamamoto, S., Shirakura, T. and Kuwada, M. (1975). Balanced arrays of strength 2ℓ and balanced fractional 2m factorial designs, Ann. Inst. Statist. Math., 27, 143–157.
Yamamoto, S., Shirakura, T. and Kuwada, M. (1976). Characteristic polynomials of the in-formation matrices of balanced fractional 2m factorial designs of higher (2ℓ+1) resolution, Essays in Probability and Statistics, Birthday volume in honor of Prof. Ogawa (eds. S.Ikeda, T.Hayakawa, H.Hudimoto, M.Okamono, M.Siotani and S.Yamamoto), 73–94, Shinko-Tsusho, Tokyo.
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Shirakura, T., Tazawa, S. A series of search designs for 2m factorial designs of resolution V which permit search of one or two unknown extra three-factor interactions. Ann Inst Stat Math 44, 185–196 (1992). https://doi.org/10.1007/BF00048681
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DOI: https://doi.org/10.1007/BF00048681