Identifying effects under a split-plot design structure

Journal of Chemometrics

Volumn 19, Issue 1, 2005, Pages 5-15

  Langhans, Ivan ^a,b   Goos, Peter ^a,c   Vandebroek, Martina ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b CQ Consultancy   (Belgium)

^c UNIVERSITY OF ANTWERP   (Belgium)

Author keywords

Design of experiments; GLS; Randomization; Reset error; Split plot; Type I error; Type II error

Indexed keywords

ERRORS; RANDOM PROCESSES;

COMPLETELY RANDOMIZED DESIGNS; DESIGN STRUCTURE; GLS; PROPERTY; RANDOMISATION; RESET ERROR; SPLIT PLOT DESIGNS; SPLIT-PLOT; TYPE II ERROR; TYPE-I ERROR;

DESIGN OF EXPERIMENTS;

EID: 23044470354     PISSN: 08869383     EISSN: None     Source Type: Journal    
DOI: 10.1002/cem.900     Document Type: Article

References (32)

1. Yates F. The principles of orthogonality and confounding in replicated experiments. J. Agric. Sci. 1933; 23: 108-148.
2. Montgomery DC. Design and Analysis of Experiments. Wiley: Chichester, 2001; 13.
3. q-r split plot experiments. J. Qual. Technol. 2000; 32: 39-56.
4. Huang P, Chen D, Voelkel J. Minimum-aberration two-level split-plot designs. Technometrics 1998; 40: 314-326.
5. Bingham D, Sitter RR. Minimum-aberration two-level fractional factorial split-plot designs. Technometrics 1999; 41: 62-70.
6. Bingham DR, Sitter RR. Design issues in fractional factorial split-plot designs. J. Qual. Technol. 2001; 33: 2-15.
7. Goos P, Vandebroek M. Optimal split-plot designs. J. Qual. Technol. 2001; 33: 436-450.
8. Goos P, Vandebroek M. D-optimal split-plot designs with given numbers sizes of whole plots. Technometrics 2003; 45: 235-245.
9. Goos P, Vandebroek M. Outperforming completely randomized designs. J. Qual. Technol. 2004; 36: 12-26.
10. Trinca LA, Gilmour SG. Multi-stratum response surface designs. Technometrics 2001; 43: 25-33.
11. Kowalski SM, Cornell JA, Vining GG. Split-plot designs and estimation methods for mixture experiments with process variables. Technometrics 2002; 44: 72-79.
12. Vining GG, Kowalski SM, Montgomery DC. Response surface designs within a spilit-plot structure. J. Qual. Tech. 2005; 37: 115-129.
13. Cornell JA. Analyzing data from mixture experiments containing process variables: a split-plot approach. J. Qual. Technol. 1988; 20: 2-23.
14. Box GEP, Jones SP. Split-plot designs for robust product experimentation. J. Appl. Statist. 1992; 19: 3-26.
15. k-p × s prototype experiments. Technometrics 1997; 39: 52-62.
16. Anbari FT, Lucas JM. Super-efficient designs: how to run your experiment for higher efficiency and lower cost. ASQC Tech. Conf. Trans. 1994; 852-863.
17. Ganju J, Lucas JM. Bias in test statistics when restrictions in randomization are caused by factors. Commun. Statist.: Theory Methods 1997; 26: 47-63.
18. Ganju J, Lucas JM. Detecting randomization restrictions caused by factors. J. Statis. Plan. Infer. 1999; 81: 129-140.
19. Ganju J, Lucas JM. Randomized and random run order experiments. J. Statis. Plan. Infer. 2005; 133: 199-210.
20. k factorial experiments with hard-to-change and easy-to-change factors. J. Qual. Technol. 2002; 34: 411-421.
21. Webb D, Lucas JM, Borkowski JJ. Factorial experiments when factor levels are not necessarily reset. J. Qual. Technol. 2004; 36: 1-11.
22. Myers RH, Montgomery DC, Vining GG, Borror CM, Kowalski SM. Response surface methodology: a retrospective and current literature survey. J. Qual. Tech. 2004; 36(1): 53-77.
23. Goos P. The Optimal Design of Blocked and Split-plot Experiments. Springer: New York, 2002.
24. Goos P, Langhans I, Vandebroek M. Practical inference from industrial split-plot designs. Res. Rep. 0407, Department of Applied Economics, Katholieke Universiteit Leuven, 2004.
25. Sahni NS, Isaksson T, Naes T. The use of experimental design methodology multivariate analysis to determine critical control points in a process. Chemometrics Intell. Lab. Syst. 2001; 56: 105-201.
26. Kenward MG, Roger JH. Small sample inference for fixed effects from restricted maximum likelihood. Biometrics 1997; 53: 983-997.
27. Letsinger JD, Myers RH, Lentner M. Response surface methods for bi-randomization structures. J. Qual. Technol. 1996; 28: 381-397.
28. Kempthorne O. The Design and Analysis of Experiments. Wiley: New York, 1952.
29. Nelson LS. What do low F ratios tell you? J. Qual. Technol. 1985; 17: 237-238.
30. Davison JJ. Response surface designs and analysis for birandomization error structures. PhD Thesis, Virginia Polytechnic Institute and State University, 1995.
31. Neter J, Kutner MH, Nachtsheim CJ, Wasserman W. Applied Linear Statistical Models. McGraw-Hill: New York, 1996; 164-166.
32. Bisgaard S, De Pinho A. The error structure of split-plot experiments. Qual. Eng. 2004; 16: 671-675.