The Annals of Statistics

Optimal fractional factorial plans for main effects and specified two-factor interactions: a projective geometric approach

Aloke Dey and Chung-Yi Suen

Full-text: Open access

Abstract

Finite projective geometry is used to obtain fractional factorial plans for m-level symmetrical factorial experiments, where m is a prime or a prime power. Under a model that includes the mean, all main effects and a specified set of two-factor interactions, the plans are shown to be universally optimal within the class of all plans involving the same number of runs.

Article information

Source
Ann. Statist., Volume 30, Number 5 (2002), 1512-1523.

Dates
First available in Project Euclid: 28 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1035844986

Digital Object Identifier
doi:10.1214/aos/1035844986

Mathematical Reviews number (MathSciNet)
MR1936329

Zentralblatt MATH identifier
1016.62089

Subjects
Primary: 62K15: Factorial designs

Keywords
Galois field finite projective geometry universal optimality saturated plans

Citation

Dey, Aloke; Suen, Chung-Yi. Optimal fractional factorial plans for main effects and specified two-factor interactions: a projective geometric approach. Ann. Statist. 30 (2002), no. 5, 1512--1523. doi:10.1214/aos/1035844986. https://projecteuclid.org/euclid.aos/1035844986


Export citation

References

  • BOSE, R. C. and BUSH, K. A. (1952). Orthogonal array s of strength two and three. Ann. Math. Statist. 23 508-524.
  • CHIU, W. Y. and JOHN, P. W. M. (1998). D-optimal fractional factorial designs. Statist. Probab. Lett. 37 367-373.
  • DEY, A. and MUKERJEE, R. (1999a). Fractional Factorial Plans. Wiley, New York.
  • DEY, A. and MUKERJEE, R. (1999b). Inter-effect orthogonality and optimality in hierarchical models. Sankhy¯a Ser. B 61 460-468.
  • HEDAy AT, A. S. and PESOTAN, H. (1992). Two-level factorial designs for main effects and selected two-factor interactions. Statist. Sinica 2 453-464.
  • HEDAy AT, A. S. and PESOTAN, H. (1997). Designs for two-level factorial experiments with linear models containing main effects and selected two-factor interactions. J. Statist. Plann. Inference 64 109-124.
  • HIRSCHFELD, J. W. P. (1979). Projective Geometries over Finite Fields. Oxford Univ. Press.
  • KIEFER, J. (1975). Construction and optimality of generalized Youden designs. In A Survey of Statistical Designs and Linear Models (J. N. Srivastava, ed.) 333-353. North-Holland, Amsterdam.
  • SHOEMAKER, A. C., TSUI, K.-L. and WU, C. F. J. (1991). Economical experimentation methods for robust design. Technometrics 33 415-427.
  • SINHA, B. K. and MUKERJEE, R. (1982). A note on the universal optimality criterion for full rank models. J. Statist. Plann. Inference 7 97-100.
  • WU, C. F. J. and CHEN, Y. (1992). A graph-aided method for planning two-level experiments when certain interactions are important. Technometrics 34 162-175.
  • WU, C. F. J., ZHANG, R. and WANG, R. (1992). Construction of asy mmetric orthogonal array s of ty pe OA(sk, sm(sr1)n1 · · · (srt)nt). Statist. Sinica 2 203-219.
  • CLEVELAND, OHIO 44115