# THE STEPWISE RESPONSE REFINEMENT SCREENER (SRRS) AND ITS APPLICATIONS TO ANALYSIS OF FACTORIAL EXPERIMENTS

### Frederick Kin Hing Phoa

#### Abstract

Two-level supersaturated designs are very useful in the screening experiments and the common goal is to identify sparse but dominant active factors with low cost. Recently, a new analysis procedure called the Stepwise Response Refinement Screener (SRRS) method is proposed to screen important effects. This paper extends this method to the two-level nonregular fractional factorial designs. The applications to several reallife examples suggest that the SRRS method is able to retrieve similar results as the existing methods do. Simulation studies show that compared to existing methods in the literature, the SRRS method performs well in terms of the true model identification rate and the average model size.

#### References

- Beattie, S., Fong, D., and Lin, D. (2002). A two-stage bayesian model selection strategy for supersaturated designs. Technometrics, 44:55-63.
- Box, G. and Meyer, R. (1986). An analysis for unreplicated fractional factorials. Technometrics, 28:11-18.
- Candes, E. and Tao, T. (2007). The dantzig selector: statistical estimation when p is much larger than n. Annals of Statistics, 35:2313-2351.
- Chipman, H., Hamada, H., and Wu, C. (1997). A bayesian variable-selection approach for analyzing designed experiments with complex aliasing. Technometrics, 39:372-381.
- Li, R. and Lin, D. (2003). Analysis methods for supersaturated design: some comparisons. Journal of Data Science, 1:249-260.
- Phoa, F. (2011). The stepwise response refinement screener (srrs). (in review).
- Phoa, F., Pan, Y., and Xu, H. (2009a). Analysis of supersaturated designs via the dantzig selector. Journal of Statistical Planning and Inference, 139:2362-2372.
- Phoa, F., Wong, W., and Xu, H. (2009b). The need of considering the interactions in the analysis of screening designs. Journal of Chemometrics, 23:545-553.
- Phoa, F. and Xu, H. (2009). Quater-fraction factorial design constructed via quaternary codes. Annals of Statistics, 37:2561-2581.
- Phoa, F., Xu, H., and Wong, W. (2009c). The use of nonregular fractional factorial designs in combination toxicity studies. Food and Chemical Toxicology, 47:2183- 2188.
- Plackett, R. and Burman, J. (1946). The design of optimum multifactorial experiments. Biometrika, 33:305-325.
- Vander-Heyden, Y., Jimidar, M., Hund, E., Niemeijer, N., Peeters, R., Smeyers-Verbeke, J., D.L., M., and Hoogmartens, J. (1999). Determination of system suitability limits with a robustness test. Journal of Chromatography A, 845:145-154.
- Wu, C. and Hamada, M. (2000). Experiments: Planning, Analysis, and Parameter Design Optimization. Wiley, New York.
- Zhang, Q., Zhang, R., and Liu, M. (2007). A method for screening active effects in supersaturated designs. Journal of Statistical Planning and Inference, 137:235-248.
- Zhang, R., Phoa, F., Mukerjee, R., and Xu, H. (2011). A trigonometric approach to quaternary code designs with application to one-eighth and one- sixteenth fractions. Annals of Statistics, 39:931-955.

#### Paper Citation

#### in Harvard Style

Kin Hing Phoa F. (2012). **THE STEPWISE RESPONSE REFINEMENT SCREENER (SRRS) AND ITS APPLICATIONS TO ANALYSIS OF FACTORIAL EXPERIMENTS** . In *Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,* ISBN 978-989-8425-98-0, pages 157-161. DOI: 10.5220/0003711101570161

#### in Bibtex Style

@conference{icpram12,

author={Frederick Kin Hing Phoa},

title={THE STEPWISE RESPONSE REFINEMENT SCREENER (SRRS) AND ITS APPLICATIONS TO ANALYSIS OF FACTORIAL EXPERIMENTS},

booktitle={Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,},

year={2012},

pages={157-161},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003711101570161},

isbn={978-989-8425-98-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,

TI - THE STEPWISE RESPONSE REFINEMENT SCREENER (SRRS) AND ITS APPLICATIONS TO ANALYSIS OF FACTORIAL EXPERIMENTS

SN - 978-989-8425-98-0

AU - Kin Hing Phoa F.

PY - 2012

SP - 157

EP - 161

DO - 10.5220/0003711101570161