Abstract:
The technique of fitting a response surface is one widely used especially in the chemical
industry to aid in the statistical analysis of experimental work in which the yield of a
product depends in some unknown fashion on one or more controllable variables. The
world is facing depletion of resources and search for alternative measures is inevitable
in all human endeavor. Since the resources are scarce, we need to produce maximally
by utilizing design of experiments like in this study. In the current study, optimal
economical second order rotatable designs SORDs in four and five dimensions were
constructed. The objectives of the study were; to construct economical SORDs in four,
and five dimensions, evaluate the alphabetic optimality criteria for the designs, and
determine the A- and E- efficiencies for the designs. The sets of points for a sequential
rotatable arrangement in four and five dimensions formed rotatable arrangements if
their excess functions were zero. All the variables determined were real and positive
and this confirmed the existence of a rotatable arrangement. The designs were
considered to be SORDs after satisfying both the moment and non-singularity
conditions. The moments which formed the elements of the moment matrix were
determined by taking the parameter system of interest to be that of a second order
model. The moment matrices formed the basis for determination of the optimality
criteria for every design considered. The determinant criterion (D-), Average variance
criterion (A-), Eigen value criterion (E-) and the trace criterion (T-). Were considered.
For each criterion the design with the least value will be optimal to the specific criteria
under consideration. The study yielded; 32, 40, 48a, and 48b points SORDs in four
dimensions and; 52, 74,100a, and 100b points SORDs in five dimensions respectively.
From the Table 2 the design G 2 (40 points SORD in four dimensions) is A-, D-, T- and
E-optimal. The design G 6 (74 points SORD in five dimensions) is A-, D- and-optimal
and designs G 7 was found to be E-optimal. The analysis of efficiencies facilitated the
choice of the most desirable design from the other designs under consideration. In
conclusion, the more homogenous the design is, the more optimal it became, and thus
the designs obtained provides very essential tools for use in various fields such as in
medicine, agriculture and industry. The study recommends evaluation of robustness of
missing data for these designs and all other designs to enable researchers make
informed decisions whenever missing information is anticipated.
