On D-efficiency of Reduced Models for Central Composite Experimental Designs within a Split-plot Structure

International Journal of Mathematical Modelling & Computations

مقاله 4، دوره 11، 3 (SUMMER) - شماره پیاپی 43، آذر 2021   

نوع مقاله: Full Length Article

شناسه دیجیتال (DOI): 10.30495/ijm2c.2021.684818

نویسندگان

Yisa Yakubu^{* 1}؛ Angela Unna Chukwu²؛ Sule Shehu Ahmed³

¹Department of Statistics, Federal University of Technology, Minna, Niger State, Nigeria

²Department of Statistics, University of Ibadan, Nigeria

³Department of Mathematics and Statistics, School of Natural Sciences, Niger State Polytechnic, Zungeru, Nigeria.

چکیده

Choosing a response surface design to fit certain kinds of models is a difficult task. Extensive research comprising a collection of efficient second-order response surface designs from which a researcher may choose to best fit his/her needs has been conducted, which are based solely on a widely-accepted assumption of a completely randomized error structure of statistically-designed experiments. However, this assumption is not feasible in industrial experiments, which are often split-plot in nature and for which randomization of some factors have to be restricted due to certain constraints. The performance of such experimental designs depends strongly on the relative magnitude (d) of the whole-plot and sub-plot error variances. This work focuses on reduced second-order models having one, two, or all of their quadratic and/or interaction terms removed from the full models of some chosen candidate split-plot central composite designs (CCDs). It investigates the effects of model reduction on efficiency of these designs by computing the relative D-efficiencies for the formulated reduced models with respect to their corresponding full designs and assessing the efficiency losses under specific values of d. The study revealed a significant loss of D-efficiency in these designs, which depend strongly on the removed term(s) and increases, across all values of d, as the number of whole-plot factors increases.

کلیدواژه‌ها

Relative D-Efficiency loss؛ Split-plot design؛ Design optimality criteria؛ Reduced Models