Evaluation of the Block Effects in Response Surface Designs with Random Block Effects over Cuboidal Regions

  • Published : 2000.12.01


In may experimental situations, whenever a block design is used, the block effect is usually considered to be fixed. There are, however, experimental situations in which it should be treated as random. The choice of a blocking arrangement for a response surface design can have a considerable effect on estimating the mean response and on the size of he prediction variance even if the experimental runs re the same. Therefore, care should be exercised in the selection of blocks. In this paper, in the presence of a random block effect, we propose a graphical method or evaluating the effect of blocking in response surface designs using cuboidal regions. This graphical method can be used to investigate how the blocking has influence on the prediction variance throughout all experimental regions of interest when this region is cuboidal, and compare the block effects in the cases of the orthogonal and non-orthogonal block designs, respectively.


  1. Sankhya, Series B v.52 Sequential Method of Conducting Rotatable Designs Adhikary, B.;Panda, R.
  2. Empirical Model-Building and Response Surfaces Box, G.E.P.;Draper, N.R.
  3. The Annals of Mathematical Statistics v.28 Multi-factor Experimental Designs for Exploring Response Surface Box, G.E.P.;Hunter, J.S.
  4. Calcutta Statistical Association Bulletin v.19 On Blocking Second Order Rotatable Designs Dey, A.;Das, M.N.
  5. Technometrics v.31 Graphical Assessment of the Prediction Capability of Response Surface Designs Giovannitti Jensen, A.;Myers, R.H.
  6. Technometrics v.34 Response Surface Models with Random Block Effects Khuri, A.I.
  7. Journal of Applied Statistics v.21 Effect of Blocking on the Estimation of a Response Surface
  8. Journal of Quality Technology v.28 Response Surface Models with Mixed Effects
  9. Computational Statistics & Data Analysis v.22 Quantile plots of the Rediction Variance for Response Surface Designs Khuri, A.I.;Kim, H.J.;Um, Y.H.
  10. Response Surface Methodology Myers, R.H.;Montgomery, D.C.
  11. Journal of Quality Technology v.24 Variance Dispersion Properties of Second-Order Response Surface Designs Myers, R.H.;Vining, G.G.;Giovannitti Jensen, A.
  12. The Korean Communications in Statistics v.5 no.3 A Graphical Method for Evaluating the Effect of Blocking in Response Surface Designs Using Cuboidal Regions Park, S.H.;Jang, D.H.
  13. Communications in Statistics - Theory and Methods v.28 no.7 Measures for Evaluating the Effect of Blocking in Response Surface Desings
  14. Communications in Statistics - Simulation and Computation v.28 no.2 A Graphical Method for Evaluating the Effect of Blocking in Response Surface Designs
  15. Journal of the Korean Society for Quality Management v.27 no.1 A Measure for Evaluating the Effect of Blocking in Response Surface Designs Using Cuboidal Regions
  16. paper presented at ASA Meetings Variance Dispersion Graphs for Cuboidal Regions Rozum, M.A.;Myers, R.H.
  17. Technometrics v.33 A Graphical Approach for Evaluating Response Surface Designs in Terms of the Mean Squared Error of Prediction Vining, G.G.;Myers, R.H.