Construction of a Thirty-Three-Point Second-Order Rotatable Design in Three Dimensions Using Trigonometric Functions
Kilesi Tikani *
Department of Mathematics and Physical Sciences, Maasai Mara University, Narok, Kenya.
Cornelious Nyankundi
Department of Mathematics and Physical Sciences, Maasai Mara University, Narok, Kenya.
Joseph Ouno
Department of Mathematics and Physical Sciences, Maasai Mara University, Narok, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Response surface methodology (RSM) is a collection of mathematical and statistical tools intended for analysing experiments in which a response is influenced by one or more controllable variables. The construction of second-order rotatable designs (SORDs) frequently requires substantial resources, making such designs inefficient and expensive to implement. Consequently, it is important to use an appropriate design that allocates a relatively small number of design points to the elements of interest in the response. The objective of this study was to develop a rotatable design in three dimensions using trigonometric functions. The specific objectives were to construct a modified second-order rotatable design in three dimensions, assess the performance of the constructed SORD using D-, A-, E-, T-, and G-optimality criteria, and examine its relative efficiencies. The reduced SORD was constructed by selecting part of a suitable set of existing design points while keeping the other set constant. The resulting points were subjected to the moment and non-singularity conditions required for second-order rotatability. The alphabetic optimality criteria (A-, D-, E-, T-, and G-) were evaluated using the full parameter system of interest. An optimality criterion is a scalar measure that summarises the quality of a design and is maximised or minimised according to the criterion under consideration.
Keywords: Second-order rotatable design, optimality criteria, response surface methodology