Robustness of sequential third-order response surface design to missing observations

References

• Gardiner DA, Grandage AHE, Hader RJ. (1956). Some third order rotatable designs. Institute of Statistics Mimeo Series No. 149, Raleigh, NorthC.
   Google Scholar
• Hemavathi M, Varghese E, Shekhar S, et al. Sequential asymmetric third order rotatable designs (SATORDs). J Appl Stat. 2020. DOI:10.1080/02664763.2020.1864817.
   PubMed Web of Science ®Google Scholar
• Box GEP, Hunter JS. Multifactor experimental designs for exploring response surfaces. Ann Math Stat. 1957;28(1):195–241.
   Google Scholar
• Hemavathi M, Shekhar S, Varghese E, et al. Theoretical developments in response surface designs: an informative review and further thoughts. Commun Stat Theory Meth. 2021. DOI:10.1080/03610926.2021.1944213.
   Web of Science ®Google Scholar
• Draper NR. Missing values in response surface designs. Technometrics. 1961b;3(3):389–398.
   Web of Science ®Google Scholar
• McKee B, Kshirsagar AM. Effect of missing plots in some response surface designs. Commun Stat – Theory Methods. 1982;11(4):1525–1549.
   Google Scholar
• Box GEP, Draper NR. Robust designs. Biometrika. 1975;62(1):347–352.
   Google Scholar
• Herzberg AM, Andrews DF. Some considerations in the optimal design of experiments in non-optimal situations. J R Stat Society: B Methodol. 1976;38(3):284–289.
   Google Scholar
• Andrews DR, Herzberg A. The robustness and optimality of response surface designs. J Stat Plan Inference. 1979;3(3):249–258.
   Web of Science ®Google Scholar
• Akhtar M, Prescott P. Response surface designs robust to missing observations. Commun Stat – Simul Comput. 1986;15(2):345–363.
   Web of Science ®Google Scholar
• MacEachern SN, Notz WI, Whittinghill DC, et al. Robustness to the unavailability of data in the linear model, with applications. J Stat Plan Inference. 1995;48(2):207–213.
   Web of Science ®Google Scholar
• Whittinghill DC. A note on the robustness of Box-Behnken designs to the unavailability of data. Metrika. 1998;48(1):49–52.
   Web of Science ®Google Scholar
• Chukwu AU, Yakubu Y, Bamiduro TA, et al. Robustness of split-plot central composite designs in the presence of a single missing observation. Pac J Sci Technol. 2013;14(12):194–211.
   Google Scholar
• Akram M. (2002). Central composite designs robust to three missing observations [Ph.D. Thesis]. Bahawalpur: Islamia University.
   Google Scholar
• Das RN. Robust second order rotatable designs, part-I (RSORD). Calcutta Stat Assoc Bull. 1997;47:199–214.
   Google Scholar
• Das RN. Robust second order rotatable designs, part-II (RSORD). Calcutta Stat Assoc Bull. 1999;47:67–78.
   Google Scholar
• Morgenthaler S, Schumacher MM. Robust analysis of a response surface design. Chemom Intell Lab Syst. 1999;47(1):127–141.
   Web of Science ®Google Scholar
• Parsad R, Srivastava R, Batra PK. (2004). Designs for fitting response surfaces in agricultural experiments. Project Report, IASRI, New Delhi. I.A.S.R.I./P.R.-04/2004.
   Google Scholar
• Ahmad T, Gilmour SG. Robustness of subset response surface designs to missing observations. J Stat Plan Inference. 2010;140(1):92–103.
   Web of Science ®Google Scholar
• Morris MD. A class of three-level experimental designs for response surface modeling. Technometrics. 2000;42(2):111–121.
   Web of Science ®Google Scholar
• Alrweili H, Georgiou S, Stylianou S. Robustness of response surface designs to missing data. Qual Reliab Eng Int. 2019;35(5):1288–1296.
   Web of Science ®Google Scholar
• Rashid F, Akbar A, Arshad HM. Effects of missing observations on predictive capability of augmented Box-Behnken designs. Commun Stat Theory Methods. 2021. DOI:10.1080/03610926.2021.1872633
   Web of Science ®Google Scholar
• Rashid F, Akbar A, Zafar Z. Some new third order designs robust to one missing observation. Commun Stat Theory Methods. 2019;48(24):6054–6062.
   Web of Science ®Google Scholar
• Tanco M, Castillo E, Viles E. Robustness of three-level response surface designs against missing data. IIE Trans. 2013;45(5):544–553.
   Web of Science ®Google Scholar
• Ghosh S. On robustness of designs against incomplete data. Sankhya, Series B. 1979;40(3):204–208.
   Google Scholar
• Myers RH, Montgomery DC. Response surface methodology. 2nd ed. New York: Wiley-Inter science; 2002.
   Google Scholar
• Yakubu Y, Chukwu AU, Adebayo BT, et al. Effects of missing observations on predictive capability of central composite designs. Int J Comput Sci Appl. 2014;4(6):1–18.
   Google Scholar
• Smucker BJ, Jensen W, Wu Z, et al. Robustness of classical and optimal designs to missing observations. Comput Stat Data Anal. 2017;113:251–260.
   Web of Science ®Google Scholar
• Da Silva MA, Gilmour SG, Trinca LA. Factorial and response surface designs robust to missing observations. Comput Stat Data Anal. 2016;113:261–272.
   Web of Science ®Google Scholar
• Oh JH, Park SH, Kwon SS. Graphical evaluation of robust parameter designs based on extended scaled prediction variance and extended spherical average prediction variance. Commun Stat – Theory Methods. 2018;47(14):3523–3531.
   Web of Science ®Google Scholar
• Draper NR. Third order rotatable designs in three dimensions. Ann Math Stat. 1960a;31(4):865–874.
   Google Scholar
• Draper NR. A third order rotatable designs in four dimensions. Ann Math Stat. 1960b;31(4):875–877.
   Google Scholar
• Draper NR. Third order rotatable designs in three dimensions, some specific designs. Ann Math Stat. 1961a;32(3):910–913.
   Google Scholar
• Draper NR. Third order rotatable designs in three factors, analysis. Technometrics. 1962;4(2):219–234.
   Web of Science ®Google Scholar
• Das MN, Narasimham VL. Construction of rotatable designs through balanced incomplete block designs. Ann Math Stat. 1962;33(4):1421–1439.
   Google Scholar
• Herzberg AM. Two third order rotatable designs in four dimensions. Ann Math Stat. 1964;35(1):445–446.
   Google Scholar
• Arshad MH, Akhtar M, Gilmour SG. Augmented Box-Behnken designs for fitting third-order response surfaces. Commun Stat – Theory Methods. 2012;41(23):4225–4239.
   Web of Science ®Google Scholar
• Rashid F, Akram M, Akbar A, et al. Some new augmented fractional Box–Behnken designs. Commun Stat – Theory Methods. 2017;46(4):2007–2012.
   Web of Science ®Google Scholar
• Cornelious NO, Cruyff MN. A sequential third order rotatable design of eighty points in four dimensions with an hypothetical case study. Asian J Probab Stat. 2019;4(4):1–9.
   Google Scholar
• Huda S. Some third-order rotatable designs in three dimensions. Ann Inst Stat Math. 1982;34(2):365–371.
   Web of Science ®Google Scholar
• Huda S. Two third-order rotatable designs in four dimensions. J Stat Plan Inference. 1983;8(2):241–243.
   Web of Science ®Google Scholar
• Koske JK, Mutiso JM, Mutai CK. Construction of third order rotatable design through balanced incomplete block design. Far East J Appl Math. 2011a;58:39–47.
   Google Scholar
• Koske JK, Kosgei MK, Mutiso JM. A new third order rotatable design in five dimensions through balanced incomplete block designs. J Agric Sci Technol. 2011b;13:157–163.
   Google Scholar