This article considers optimal foldover plans for nonregular designs. By using the indicator function, we define words with fractional lengths. The extended word-length pattern is then used to select among non-regular foldover designs. Some general properties of foldover designs are obtained using the indicator function. We prove that the full-foldover plan that reverses the signs of all factors is optimal for all-run and 20-run orthogonal designs. The optimal foldover plans for all 16-run (regular and nonregular) orthogonal designs are constructed and tabulated for practical use. Optimal foldover plans for higher-order orthogonal designs can be constructed in a similar manner.
Bibliographical noteFunding Information:
This research was supported by the SupercomputingInstitute for Digital Simulation and Advanced Computation at the University of Minnesota. The authors thank the editor, an associate editor, and the two referees for their helpful comments and sug-gestionsin improvingan earlier version of the manuscript.They also thank Boxin Tang for reading an early draft of the manuscript and making helpful comments. Wilialm Li’s research was also supported by a Research and Techaing Supplement from the Carlson School of Management, University of Minnesota. Dennis Lin is partially supported by National Security Agency grant MDA 904-02-1-0054.
- Extended word length pattern
- Foldover design
- Generalized resolution
- Indicator function
- Orthogonal design