ON THE DEVELOPMENT OF MINIMAX LOSS AUGMENTED BOX-BEHNKEN DESIGN ROBUST TO TWO MISSING OBSERVATIONS

  • Oluchukwu C. Asogwa Department of Mathematics and Statistics, Alex Ekwueme Federal University Ndufu Alike, Nigeria
  • Oluwaseun A. Otekunrin Department of Statistics, University of Ibadan
Keywords: Robustness of designs, Missing observations, Third-order designs

References

Ahmad, T., Akhtar, M. and Gilmour, S. G. (2012). Multilevel augmented pairs second-order response surface designs and their robustness to missing data. Communications in Statistics - Theory and Methods, 41(3), 43752. DOI: https://doi.org/10.1080/03610926.2010.513783

Ahmad, T., and Gilmour, S. G. (2010). Robustness of subset response surface designs to missing observations. Journal of Statistical Planning and Inference,140(1), 92103. DOI: https://doi.org/10.1016/j.jspi.2009.06.011

Akhtar, M., and Prescott, P. (1986). Response surface designs robust to missing observations. Communications in Statistics-Simulation and Computation, 15(2), 345-363. DOI: https://doi.org/10.1080/03610918608812512

Akram, M. (2002). Central Composite Designs Robust to three missing observations, A Ph. D Thesis in Statistics, Islamia University, Baha-walpur, Pakistan.

Alrweili, H., Georgiou, S., and Stylianou, S. (2019). Robustness of response surface designs to missing data. Quality and Reliability Engineering International, 35(5), 12881296. DOI: https://doi.org/10.1002/qre.2524

Andrews, D. F., and Herzberg, A. M. (1979). The robustness and optimality of response surface designs. Journal of Statistical Planning and Inference, 3, 249-257. DOI: https://doi.org/10.1016/0378-3758(79)90016-8

Angelopoulos P, Evangelaras H, and Koukouvinos, C. (2014). Small, balanced, efficient and near-rotatable central composite designs,Journalof Statistical Planning and Inference. 139, 2010-2013. DOI: https://doi.org/10.1016/j.jspi.2008.09.001

Arshad, H. M., Akhtar, M., and Gilmour, S. G. (2012). Augmented Box-Behnken designs for fitting third-order response surfaces. Communications in Statistics-Theory and Methods, 41(23), 4225-4239. DOI: https://doi.org/10.1080/03610926.2011.568154

Box, G. E. P., and Wilson, K. B. (1951). On the experimental attainment of optimum conditions. Journal of the Royal Statistical Society: Series B (Methodological), 13(1), 1- 45. DOI: https://doi.org/10.1111/j.2517-6161.1951.tb00067.x

Chen, X. P., Guo, B., Liu, M. Q., and Wang, X. L. (2017). Robustness of orthogonal-array based composite designs to missing data. Journal of Statistical Planning and Inference, 194, 15-24. DOI: https://doi.org/10.1016/j.jspi.2017.10.004

Georgiou, S. D., Stylianou, S., and Aggarwal, M. (2014). A class of composite designs for response surface methodology. Computational Statistics & Data Analysis, 71, 1124-1133. DOI: https://doi.org/10.1016/j.csda.2013.03.010

Ghosh, S. (1979). On robustness of designs against incomplete data. Sankhya, Ser. B 40, 204 -208.

Ghosh, S. (1982). Robustness of BIB designs against non-availability of data. J Stat Plan Infer., 6, 29-32. DOI: https://doi.org/10.1016/0378-3758(82)90053-2

Ghosh, S., Rao, S. B., and Singhi, N. M. (1983). On a robust property of PBIB designs, J. Statist. Plann. Inf., 8, 355-364. DOI: https://doi.org/10.1016/0378-3758(83)90051-4

Hedayat, A., and John, P. (1974). Resistant and susceptible BIB designs. Ann Stat., 1, 148-158. DOI: https://doi.org/10.1214/aos/1176342620

Lamidi, S., Olaleye, N., Bankole, Y., Obalola, A., Aribike, E., and Adigun, I. (2022). Applications of Response Surface Methodology (RSM) in Product Design, Development, and Process Optimization. Research Advances and Applications, http://dx.doi.org/10.5772/intechopen.106763 DOI: https://doi.org/10.5772/intechopen.106763

MacEachern, S. N., Notz W. I., Whittinghill, D. C., and Zhu, Y. (1995). Robustness to the unavailability of data in the linear model, with applications. J. Statist. Plann. Inf., 48, 207-213. DOI: https://doi.org/10.1016/0378-3758(95)00002-Q

Marina, S. (2013). Dealing with missing data: Key assumptions and methods for applied analysis, Technical Report 4, Boston University School of Public Health.

Mead, R., and Pike, D. J. (1975). A review of response surface methodology from a biometric viewpoint. Biometrics, 31, 803851. DOI: https://doi.org/10.2307/2529809

Nwabueze, T. U. (2010). Basic steps in adapting response surface methodology as mathematical modelling for bioprocess optimization in the food systems. International Journal of Food Science and Technology, 45, 1768-1776. DOI: https://doi.org/10.1111/j.1365-2621.2010.02256.x

Oladugba, A. and Okeke, E. 2019. Robustness of Space-Filling Orthogonal Array Based Composite Design to Missing. Observation. Abstract Booklet Royal statistical Society, Belfast, United Kingdom, Sept. 2019. Pp324

Patchanok, S. (2015). Robust response surface designs against missing observations. A Ph. D dissertation, Montana State University, Bozeman, Montana.

Rashid, F., Akbar, A., and Arshad, H. M. (2022). Effects of missing observations on predictive capability of augmented Box-Behnken designs. Communications in Statistics - Theory and Methods,51(20), 7225-7242. DOI: https://doi.org/10.1080/03610926.2021.1872633

Rashid, F., Akbar, A., and Zafar, Z. (2019). Some new third order designs robust to one missing observation. Communications in Statistics - Theory and Methods, 48(24), 6054-6062. DOI: https://doi.org/10.1080/03610926.2018.1528362

Rashid, F., Akram, M., Akbar, A., and Javed, A. (2017). Some New Augmented Fractional -Behnken Designs. Communications in Statistics-Theory and Methods, 46(4), 2007-2012. DOI: https://doi.org/10.1080/03610926.2015.1032423

Rebollo-Hernanz, M., Caas, S., Taladrid, D., Segovia, A., Bartolom, B., Aguilera, Y., and Martn-Cabrejas, M. A. (2021). Extraction of phenolic compounds from cocoa shell: Modeling using response surface methodology and artificial neural networks. Sep. Purif. Technol., 270, 118779. DOI: https://doi.org/10.1016/j.seppur.2021.118779

Safari, M., Abdi, R., Adl, M., and Kafashan, J. (2018). Optimization of biogas productivity in lab-scale by response surface methodology. Renewable Energy, 118, 368375. DOI: https://doi.org/10.1016/j.renene.2017.11.025

Tanco, M., del Castillo, E., and Viles, E. (2013). Robustness of three-level response surface designs against missing data. IIE Transactions, 45(5), 544 - 553. DOI: https://doi.org/10.1080/0740817X.2012.712240

Yolmeh M, Jafari S. M. (2017), Applications of response surface methodology in the food Industry processes. Food Bioprocess Technology, 10, 413-433. DOI: https://doi.org/10.1007/s11947-016-1855-2

Zhou, Y. D., and Xu, H. (2016), Composite designs based on orthogonal arrays and definitive screening designs. Journal of the American Statistical Association, 112(520), 1675-1683. DOI: https://doi.org/10.1080/01621459.2016.1228535

Published
2025-04-30
How to Cite
Asogwa, O. C., & Otekunrin, O. A. (2025). ON THE DEVELOPMENT OF MINIMAX LOSS AUGMENTED BOX-BEHNKEN DESIGN ROBUST TO TWO MISSING OBSERVATIONS. FUDMA JOURNAL OF SCIENCES, 9(4), 295 - 299. https://doi.org/10.33003/fjs-2025-0904-3356