Skip to main content
Log in

An algorithm to generate near D-optimal designs for multiple response surface models

  • Published:
IIE Transactions

Abstract

An algorithm is proposed to generate near D-optimal designs for multiple response surface models, i.e., a first-order or second-order polynomial model for each response with cuboidal design regions. For a class of designs generated by the proposed algorithm, simulation results indicate that the designs generated are near D-optimal and do not depend on ∑. An example is given to demonstrate how multiresponse D-optimal designs can be used to provide benchmarks to other experimental designs for multiple response problems.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Lai, Y.J. and Chang, S.I. (1994) A fuzzy approach for multiresponse optimization: an off-line quality engineering problem. Fuzzy Sets and Systems, 63, 117–129.

    Google Scholar 

  2. Pignatiello, Jr, J.J. (1993) Strategies for robust multiresponse quality engineering. IIE Transactions, 25, 5–15.

    Google Scholar 

  3. Box, G.E.P. and Draper, N.R. (1987) Empirical Model-Building and Response Surfaces, Wiley, New York.

    Google Scholar 

  4. Khuri, A.I. and Cornell, J.A. (1987) Response Surfaces-Designs and Analyses, Marcel Dekker, New York.

    Google Scholar 

  5. St. John, R.C. and Draper, N.R. (1975) D-optimality for regression designs: a review. Technometrics, 17, 15–23.

    Google Scholar 

  6. Fedorov, V.V. (1972) Theory of Optimal Experiments, Academic Press, New York.

    Google Scholar 

  7. Cooray-Wijesinha, M.C. and Khuri, A.I. (1987) The sequential generation of multiresponse D-optimal designs when the variance-covariance matrix is not known. Communications in Statistics, Part B-Simulation and Computation, 16, 239–259.

    Google Scholar 

  8. Kiefer, J. (1959) Optimum experimental design. Journal of the Royal Statistical Society, B21, 272–319.

    Google Scholar 

  9. Wijesinha, M.C. (1984) Design of experiments for multiresponse models. Ph. D. thesis. Department of Statistics, University of Florida, Gainesville, FL.

    Google Scholar 

  10. Farrell, R.H., Kiefer, J. and Walbran, A. (1965) Optimum multivariate designs, in Proceedings of the Fifth Berkeley Symposium Math. Statist. Prob., 1, University of California Press, pp. 113–138.

    Google Scholar 

  11. Chang, S.I. (1994) Some properties of multiresponse D-optimal designs. Journal of Mathematical Analysis and Applications, 184, 256–262.

    Google Scholar 

  12. Bratley, P., Fox, B.L. and Schrage, L.E. (1987) A Guide to Simulation, Springer-Verlag, New York.

    Google Scholar 

  13. Kiefer, J. (1961) Optimum designs in regression problems II. Annals of Mathematical Statistics, 32, 381–405.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

CHANG , S. An algorithm to generate near D-optimal designs for multiple response surface models. IIE Transactions 29, 1073–1081 (1997). https://doi.org/10.1023/A:1018520923888

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018520923888

Keywords

Navigation