Regular fractional factorial designs with minimum aberration and maximum estimation capacity.

*(English)*Zbl 0927.62076Summary: Using the approach of finite projective geometry, we make a systematic study of estimation capacity, a criterion of model robustness, under the absence of interactions involving three or more factors. Some general results, providing designs with maximum estimation capacity, are obtained.

In particular, for two-level factorials, it is seen that constructing a design with maximum estimation capacity calls for choosing points from a finite projective geometry such that the number of lines is maximized and the distribution of these lines among the chosen points is as uniform as possible. We also explore the connection with minimum aberration designs under which the sizes of the alias sets of two-factor interactions which are not aliased with main effects are the most uniform possible.

In particular, for two-level factorials, it is seen that constructing a design with maximum estimation capacity calls for choosing points from a finite projective geometry such that the number of lines is maximized and the distribution of these lines among the chosen points is as uniform as possible. We also explore the connection with minimum aberration designs under which the sizes of the alias sets of two-factor interactions which are not aliased with main effects are the most uniform possible.

##### Keywords:

resolution; upper weak majorization; weak minimum aberration; capacity; projective geometry
PDF
BibTeX
Cite

\textit{C.-S. Cheng} and \textit{R. Mukerjee}, Ann. Stat. 26, No. 6, 2289--2300 (1998; Zbl 0927.62076)

Full Text:
DOI

##### References:

[1] | BOSE, R. C. 1947. Mathematical theory of the sy mmetrical factorial design. Sankhy a 8 107 166. Z. k p · Zbl 0038.09601 |

[2] | BOX, G. E. P. and HUNTER, J. S. 1961. The 2 fractional factorial designs. Technometrics 3 311 351, 449 458. Z. n m · Zbl 0100.14406 |

[3] | CHEN, H. and HEDAy AT, A. S. 1996. 2 fractional factorial designs with weak minimum aberration. Ann. Statist. 24 2536 2548. Z. n k · Zbl 0867.62066 |

[4] | CHEN, J. 1992. Some results on 2 fractional factorial designs and search for minimum aberration designs. Ann. Statist. 20 2124 2141. Z. · Zbl 0770.62063 |

[5] | CHEN, J., SUN, D. X. and WU, C. F. J. 1993. A catalogue of two-level and three-level fractional factorial designs with small runs. Internat. Statist. Rev. 61 131 145. Z. n k · Zbl 0768.62058 |

[6] | CHEN, J. and WU, C. F. J. 1991. Some results on s fractional factorial designs with minimum aberration or optimal moments. Ann. Statist. 19 1028 1041. Z. · Zbl 0725.62068 |

[7] | CHENG, C. S., STEINBERG, D. M. and SUN, D. X. 1998. Minimum aberration and model robustness for two-level factorial designs. J. Roy. Statist. Soc. Ser. B. To appear. Z. n m FRANKLIN, M. F. 1984. Constructing tables of minimum aberration p designs. Technometrics 26 225 232. Z. k p JSTOR: |

[8] | FRIES, A. and HUNTER, W. G. 1980. Minimum aberration 2 designs. Technometrics 22 601 608. Z. n m JSTOR: · Zbl 0453.62063 |

[9] | SUEN, C.-Y., CHEN, H. and WU, C. F. J. 1997. Some identities on q designs with application to minimum aberration designs. Ann. Statist. 25 1176 1188. · Zbl 0898.62095 |

[10] | SUN, D. X. 1993. Estimation capacity and related topics in experimental designs. Ph.D. dissertation, Univ. Waterloo. Z. n m TANG, B. and WU, C. F. J. 1996. Characterization of minimum aberration 2 designs in terms of their complementary designs. Ann. Statist. 24 2549 2559. · Zbl 0867.62068 |

[11] | DEPARTMENT OF STATISTICS JOKA, DIAMOND HARBOUR ROAD 367 EVANS HALL 3860 P.O. BOX NO. 16757, ALIPORE POST OFFICE BERKELEY, CALIFORNIA 94720-3860 CALCUTTA 700 027 E-MAIL: Cheng@stat.Berkeley.edu INDIA E-MAIL: rmuk1@hotmail.com |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.