Skip to main content
SpringerLink
Log in

Optimal balanced 27 fractional factorial designs of resolutionV, withN≦42

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Summary

In this paper, we present a class of fractional factorial designs of the 27 series, which are of resolutionV. Such designs allow the estimation of the general mean, the main effects and the two factors interactions (29 parameters in all for the 27 factorial) assuming that the higher order effects are negligible. For every value ofN (the number of runs) such that 29≦N≦42, we give a resolutionV design that is optimal (with respect to the trace criterion) within the subclass of balanced designs. Also, for convenience of analysis, we present for each design, the covariance matrix of the estimates of the various parameters. As a by product, we establish many interesting combinatorial theorems concerning balanced arrays of strength four (which are generalizations of orthogonal arrays of strength four, and also of balanced incomplete block designs with block sizes not necessarily equal).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bose, R. C. and Srivastava, J. N. (1964a). Analysis of irregular factorial fractions,Sankhya, A,26, 117–144.

    MATH  MathSciNet  Google Scholar 

  2. Bose, R. C. and Srivastava, J. N. (1964b). Multidimensional partially balanced designs and their analysis, with applications to partially balanced factorial fractions,Sankhya, A,26, 145–168.

    MATH  MathSciNet  Google Scholar 

  3. Chopra, D. V. (1968). Investigations on the construction and existence of balanced fractional factorial designs of 2m series, Ph.D. Thesis, University of Nebraska.

  4. Kiefer, J. C. (1959). Optimum experimental designs,Jour. Roy. Stat. Soc., B,21, 273–319.

    MathSciNet  Google Scholar 

  5. Srivastava, J. N. (1971). Some general existence conditions for balanced arrays of strengtht and 2 symbols,Jour. Comb. Th., A,13, 198–206.

    Article  Google Scholar 

  6. Srivastava, J. N. (1970). Optimal balanced 2m fractional factorial designs,S. N. Roy Memorial Volume, University of North Carolina and Indian Statistical Institute, 227–241.

  7. Srivastava, J. N. and Chopra, D. V. (1971a). On the characteristic roots of the information matrix of 2m balanced factorial designs of resolutionV, with applications,Ann. Math. Statist.,42, 722–734.

    MATH  MathSciNet  Google Scholar 

  8. Srivastava, J. N. and Chopra, D. V. (1971b). Balanced optimal 2m fractional factorial designs of resolutionV, M=4, 5, 6,Technometrics,13, 257–269.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Wichita State University, Wichita, USA

    D. V. Chopra & J. N. Srivastava

  2. Colorado State University, Colorado, USA

    D. V. Chopra & J. N. Srivastava

Authors
  1. D. V. Chopra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. N. Srivastava
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Chopra, D.V., Srivastava, J.N. Optimal balanced 27 fractional factorial designs of resolutionV, withN≦42. Ann Inst Stat Math 25, 587–604 (1973). https://doi.org/10.1007/BF02479401

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02479401

Keywords

Search

Navigation