Split-plot designs: What, why, and how

Journal of Quality Technology

Volumn 41, Issue 4, 2009, Pages 340-361

  Jones, Bradley ^a   Nachtsheim, Christopher J ^b  

^a SAS INSTITUTE INC   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Block designs; Completely randomized designs; Factorial designs; Fractional factorial designs; Optimal designs; Random effects model; Random run order designs; Response surface designs; Robust parameter designs

Indexed keywords

RANDOM PROCESSES;

BLOCK DESIGNS; COMPLETELY RANDOMIZED DESIGNS; FACTORIAL DESIGN; FRACTIONAL FACTORIAL DESIGNS; OPTIMAL DESIGN; RANDOM EFFECTS MODEL; RESPONSE SURFACE DESIGNS; ROBUST PARAMETER DESIGN;

DESIGN;

EID: 70350181849     PISSN: 00224065     EISSN: None     Source Type: Journal    
DOI: 10.1080/00224065.2009.11917790     Document Type: Article

References (49)

1. ALMIMI, A. A.; KULAHCI, M.; and MONTGOMERY, D. C. (2008). "Follow-Up Designs to Resolve Confounding in Split-Plot Experiments". Journal of Quality Technology 40, pp. 154-166.
2. Anbari, F. T. and Lucas, J. M. (1994). "Super-Efficient Designs: How to Run Your Experiment for Higher Efficiencies and Lower Cost". ASQC Technical Conference Transactions, pp. 852-863.
3. Anbari, F. T. and Lucas, J. M. (2008). "Designing and Running Super-Efficient Experiments: Optimum Blocking with One Hard-to-Change Factor". Journal of Quality Technology 40, pp. 31-45.
4. Beckman, R. J.; Cook, R. D.; and Nachtsheim, C. J. (1987). "Diagnostics for Mixed-Model Analysis of Variance". Technometrics 29, pp. 413-426.
5. Bingham, D. and Sitter, R. R. (1999). "Minimum-Aberration Two-Level Fractional Factorial Split-Plot Designs". Technometrics 41, pp. 62-70.
6. Bingham, D. R. and Sitter, R. R. (2001). "Design Issues in Fractional Factorial Split-Plot Experiments". Journal of Quality Technology 33, pp. 2-15.
7. Bingham, D. and Sitter, R. R. (2003). "Fractional Factorial Split-Plot Designs for Robust Parameter Experiments". Technometrics 45, pp. 80-89.
8. Bingham, D. R.; Schoen, E. D.; and Sitter, R. R. (2004). "Designing Fractional Factorial Split-Plot Experiments with Few Whole-Plot Factors".Journal of the Royal Statistical Society, Series C 53, pp. 325-339.
9. q-r Split Plot Experiments". Journal of Quality Technology 32, pp. 39-56.
10. Box, G.; Hunter, W.; and Hunter, S. (2005). Statistics for Experimenters: Design, Innovation, and Discovery, 2nd edition. New York, NY: Wiley-Interscience.
11. Box, G. and Jones, S. (1992). "Split-Plot Designs for Robust Product Experimentation". Journal of Applied Statistics 19, pp. 3-26.
12. Box, G. and Meyer, R. D. (1986). "An Analysis for Unreplicated Fractional Factorials". Technometrics 28, pp. 11-18.
13. Daniel, C. (1959). "Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments". Technometrics 1, pp. 311-341.
14. Draper, N. R. and John, J. A. (1998). "Response Surface Designs Where Levels of Some Factors Are Difficult to Change". Australian and New Zealand Journal of Statistics 40, pp. 487-495.
15. FISHER, R. A. (1925). Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd.
16. Ganju, J. and Lucas, J. M. (1997). "Bias in Test Statistics when Restrictions in Randomization Are Caused by Factors". Communications in Statistics: Theory and Methods 26, pp. 47-63.
17. Ganju, J. and Lucas, J. M. (1999). "Detecting Randomization Restrictions Caused by Factors". Journal of Statistical Planning and Inference 81, pp. 129-140.
18. Ganju, J. and Lucas, J. M. (2005). "Randomized and Random Run Order Experiments". Journal of Statistical Planning and Inference 133, pp. 199-210.
19. GOOS, P. (2002). The Optimal Design of Blocked and Split-Plot Experiments. New York, NY: Springer.
20. GOOS, P. (2006). "Optimal Versus Orthogonal and Equivalent- Estimation Design of Blocked and Split-Plot Experiments". Statistica Neerlandica 60, pp. 361-378.
21. GOOS, P. and Donev, A. (2007). "Tailor-Made Split-Plot Designs for Mixture and Process Variables". Journal of Quality Technology 39, pp. 326-339.
22. GOOS, P.; Langhans, I.; and Vandebroek, M. (2006) "Practical Inference from Industrial Split-Plot Designs". Journal of Quality Technology 38, pp. 162-179.
23. GOOS, P. and Vandebroek, M. (2001). "Optimal Split-Plot Designs". Journal of Quality Technology 33, pp. 436-450.
24. GOOS, P. and Vandebroek, M. (2003). "D-Optimal Split-Plot Designs with Given Numbers and Sizes of Whole Plots". Technometrics 45, pp. 235-245.
25. GOOS, P. and Vandebroek, M. (2004). "Outperforming Completely Randomized Designs". Journal of Quality Technology 36, pp. 12-26.
26. GOOS, P.; Langhans, I.; and Vandebroek, M. (2006). "Practical Inference from Industrial Split-Plot Designs". Journal of Quality Technology 38, pp. 162-179.
27. Huang, P.; Dechang, C.; and Voelkel, J. O. (1998). "Minimum- Aberration Two-Level Split-Plot Designs". Technometrics 40, pp. 314-326.
28. Jones, B. and GOOS, P. (2007). "A Candidate-Set-Free Algorithm for Generating D-optimal Split-Plot Designs". Applied Statistics 56, pp. 347-364.
29. Jones, B. and GOOS, P. (2009). "D-Optimal Split-Split-Plot Designs". Biometrika 96, pp. 67-82.
30. k Factorial Experiments with Hard-To-Change and Easy-To-Change Factors". Journal of Quality Technology 34, pp. 411-421.
31. Kackar, A. N. and Harville, D. A. (1984). "Approximations for Standard Errors of Estimators of Fixed and Random Effects in Mixed Linear Models". Journal of the American Statistical Association 79, pp. 963-974.
32. Kenward, M. G. and Roger, J. H. (1997) "Small Sample Inference for Fixed Effects from Restricted Maximum Likelihood" Biometrics 53, pp. 983-997.
33. Kowalski, S. M. (2002). "24 Run Split-Plot Experiments for Robust Parameter Design". Journal of Quality Technology 34, pp. 399-410.
34. Kowalski, S. M.; Cornell, J. A.; and Vining, G. G. (2002). "Split-Plot Designs and Estimation Methods for Mixture Experiments with Process Variables". Technometrics 44, pp. 72-79.
35. Kowalski, S. and Vining, G. G. (2001). "Split-Plot Experimentation for Process and Quality Improvement". In Frontiers in Statistical Quality Control 6, H. Lenz (ed.), pp. 335-350. Heidelberg: Springer-Verlag.
36. Kutner, M.; Nachtsheim, C. J.; Neter, J.; and LI, W. (2005). Applied Linear Statistical Models. Chicago, IL: McGraw-Hill/Irwin.
37. Letsinger, J. D.; Myers, R. H.; and Lentner, M. (1996). "Response Surface Methods for Bi-Randomization Structures". Journal of Quality Technology 28, pp. 381-397.
38. Lewis, D. K.; Hutchens, C.; and Smith, J. M. (1997). " Experimentation for Equipment Reliability Improvement". In Statistical Case Studies for Industrial Process Improvement, V. Czitrom and P. D. Spagon (eds.), pp. 387-401. Philadelphia, PA: ASA and SIAM.
39. Loeppky, J. L. and Sitter, R. R. (2002). "Analyzing Unreplicated Blocked or Split-Plot Fractional Factorial Designs". Journal of Quality Technology 43, pp. 229-243.
40. Meyer, R. K. and Nachtsheim, C. J. (1995). "The Coordinate Exchange Algorithm for Constructing Exact Optimal Exponential Designs". Technometrics 37, pp. 60-69.
41. McLeod, R. G. and Brewster, J. F. (2004). "The Design of Blocked Fractional Factorial Split-Plot Experiments". Technometrics 46, pp. 135-146.
42. McLeod, R. G. and Brewster, J. F. (2008). "Optimal Foldover Plans for Two-Level Fractional Factorial Split-Plot Designs". Journal of Quality Technology 40, pp. 227-240.
43. Montgomery, D. C. (2008). Design and Analysis of Experiments, 7th ed. New York, NY: John Wiley and Sons.
44. Taguchi, G. (1987). System of Experimental Design. White Plains, NY: Kraus International Publications.
45. Trinca, L. A. and Gilmour, S. G. (2001). "Multistratum Response Surface Designs". Technometrics 43, pp. 25-33.
46. Vining, G. G.; Kowalski, S. M.; and Montgomery, D. C. (2005). "Response Surface Designs Within a Split-Plot Structure". Journal of Quality Technology 37, pp. 115-129.
47. Vining, G. G. and Kowalski, S. M. (2008). "Exact Inference for Response Surface Designs Within a Split-Plot Structure". Journal of Quality Technology 40, pp. 394-406.
48. Webb, D. F.; Lucas, J. M.; and Borkowski, J. J. (2004). "Factorial Experiments when Factor Levels Are Not Necessarily Reset". Journal of Quality Technology 36, pp. 1-11.
49. Yates, F. (1935) "Complex Experiments, with Discussion". Journal of the Royal Statistical Society, Series B 2, pp. 181-223.