A tutorial on randomizing versus not randomizing Split-Plot experiments

References

• Bailey, R. A., C. S. Cheng, and P. Kipnis. 1992. Construction of trend-resistant factorial designs. Statistica Sinica 2 (2):393–411.
   Web of Science ®Google Scholar
• Bertocci, F., L. Francalanci, R. De Luca, M. Bassani, F. Gelli, and P. Palchetti. 2018. Design of medical ultrasound probe: Measurement system for the characterization of reverberations. IEEE International Symposium on Medical Measurements and Applications (MeMeA), Rome, pp. 1–6.
   Google Scholar
• Bisgaard, S. 2008. Must a process be in statistical control before conducting designed experiments. Quality Engineering 20 (2):143–50. doi: 10.1080/08982110701826721.
   Google Scholar
• Box, G. E. P., and S. Jones. 1992. Split-plot designs for robust product experimentation. Journal of Applied Statistics 19 (1):3–26. doi: 10.1080/02664769200000001.
   Google Scholar
• Carrano, A. L., B. K. Thorn, and G. Lopez. 2006. An integer programming approach to the construction of trend-free experimental plans on split-plot designs. Journal of Manufacturing Systems 25 (1):39–44. doi: 10.1016/S0278-6125(06)80031-2.
   Web of Science ®Google Scholar
• Catelani, M., V. L. Scarano, and F. Bertocci. 2010. Implementation and characterization of a medical ultrasound phased array probe with new Pb-free soldering materials. IEEE Transactions on Instrumentation and Measurement 59 (10):2522–9. doi: 10.1109/TIM.2010.2057670.
   Web of Science ®Google Scholar
• Catelani, M., V. L. Scarano, F. Bertocci, and R. Berni. 2010. Optimization of the soldering process with ECAs in electronic equipment: Characterization measurement and experimental design. IEEE Transactions on Components, Packaging and Manufacturing Technology 1 (10):1616–26. doi: 10.1109/TCPMT.2011.2143412.
   Web of Science ®Google Scholar
• Cheng, C. S., and M. Jacroux. 1988. The construction of trend-free run orders of two-level factorial designs. Journal of the American Statistical Association 83 (404):1152–8. doi: 10.2307/2290148.
   Web of Science ®Google Scholar
• Cochran, W. G., and G. M. Cox. 1992. Experimental designs. 2nd ed. Somerset, NJ: John Wiley and Sons.
   Google Scholar
• Cox, D. R. 2009. Randomization in the design of experiments. International Statistical Review 77 (3):415–29. doi: 10.1111/j.1751-5823.2009.00084.x.
   Web of Science ®Google Scholar
• Daniel, C., and F. Wilcoxon. 1966. Fractional 2p−q plans robust against linear and quadratic trends. Technometrics 8 (2):259–78. doi: 10.2307/1266360.
   Google Scholar
• Goos, P., and B. Jones. 2011. Optimal design of experiments: a case study approach. 1st ed. Somerset, NY: John Wiley and Sons.
   Google Scholar
• Jones, B., and C. J. Nachtsheim. 2009. Split-plot designs: What, why, and how. Journal of Quality Technology 41 (4):340–61. doi: 10.1080/00224065.2009.11917790.
   Web of Science ®Google Scholar
• Kempthorne, O. 1955. The randomization theory of experimental inference. Journal of the American Statistical Association 50 (3):946–67. doi: 10.2307/2281178.
   Google Scholar
• Kowalski, S. M., P. Parker, and G. G. Vining. 2007. Tutorial: industrial split-plot experiment. Quality Engineering 19 (1):1–15. doi: 10.1080/08982110601057179.
   Google Scholar
• Núñez Ares, J., and P. Goos. 2019. An integer linear programing approach to find trend-robust run orders of experimental designs. Journal of Quality Technology 51 (1):37–50. doi: 10.1080/00224065.2018.1545496.
   Web of Science ®Google Scholar
• Tack, L., and M. Vandebroek. 2001. (Dt, C)-optimal run orders. Journal of Statistical Planning and Inference 98 (1–2):293–310. doi: 10.1016/S0378-3758(00)00299-8.
   Web of Science ®Google Scholar
• Tack, L., and M. Vandebroek. 2002. Trend-resistant and cost-effective block designs with fixed and random block effects. Journal of Quality Technology 34 (4):422–36. doi: 10.1080/00224065.2002.11980174.
   Web of Science ®Google Scholar
• Tack, L., and M. Vandebroek. 2004a. Budget constrained run orders in optimum design. Journal of Statistical Planning and Inference 124 (1):231–49. doi: 10.1016/S0378-3758(03)00193-9.
   Web of Science ®Google Scholar
• Tack, L., and M. Vandebroek. 2004b. Trend-resistant and cost-efficient cross-over designs for mixed models. Computational Statistics & Data Analysis 46 (4):721–46. doi: 10.1016/j.csda.2003.09.012.
   Web of Science ®Google Scholar
• Vining, G. G., and S. M. Kowalski. 2008. Exact inference for response surface designs within a split-plot structure. Journal of Quality Technology 40 (4):394–406. doi: 10.1080/00224065.2008.11917745.
   Web of Science ®Google Scholar