Orthogonal blocking of regular and non-regular strength-3 designs
There is currently no general approach to orthogonally block two-level and multi-level orthogonal arrays and mixed-level orthogonal arrays. In this article, we present a mixed integer linear programming approach that seeks an optimal blocking arrangement for any type of regular and non-regular orthogonal array of strength 3. The strengths of the approach are that it is an exact optimization technique which guarantees an optimal solution, and that it can be applied to many problems where combinatorial methods for blocking orthogonal arrays cannot be used. By means of 54- and 64-run examples, we demonstrate that the mixed integer linear programming approach outperforms two benchmark techniques in terms of the number of estimable two-factor interaction contrasts. We demonstrate the generality of our approach by applying it to the most challenging instances in the catalog of all orthogonal arrays of strength 3 with up to 81 runs. Finally, we show that, for two-level fold-over designs involving many factors, the only way to arrange the runs in orthogonal blocks of size four is by grouping two pairs of fold-over pairs in each of the blocks.
|Date of creation:||Nov 2012|
|Contact details of provider:|| Postal: Prinsstraat 13, B-2000 Antwerpen|
Web page: https://www.uantwerp.be/en/faculties/applied-economic-sciences/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Butler, Neil A., 2004. "Minimum G2-aberration properties of two-level foldover designs," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 121-132, April.
When requesting a correction, please mention this item's handle: RePEc:ant:wpaper:2012026. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joeri Nys)
If references are entirely missing, you can add them using this form.