# Construction of a Five-Level V-Dimensional Modified Third Order Rotatable Designs using a Pair of Pairwise Balanced Designs

### Abstract

*Rotatable designs are devised for use of response surfaces. Rotatability is evidently a greatly popular property for Response Surface Methodology (RSM). RSM is a group of statistical and mathematical techniques valuable for developing, improving and optimizing models and processes. Experimentation of any kind usually requires resources of which they may be limited due to either in availability or high cost of acquisition. To reduce on costs of an experiment one has to make a better preference of the experimental design prior to the experiment itself. An appropriate design that would provide relatively smaller number of the design points of the response at particular points of significance is essential. The aim of this study was to construct modified third order rotatable designs (MTORDs) by use of Pairwise Balanced designs in order to address the problem of the design points. The objective of the study was to construct a five-level v-dimensional modified TORD by using PBD. The five-level v-dimensional modified third order rotatable designs is constructed by use of a suitably chosen pair of Pairwise Balanced Designs by repeating the set of the design points generated from each of the designs a constant number of times. These points were combined together with a number of central points without any additional set of points. In this study, some modified third order rotatable design constructed through pairwise balanced designs were obtained. In conclusion, the modified TORD constructed using PBD yield relatively smaller numeral of the design points as compared to the corresponding existing designs. Other studies that could possibly lead to designs having fewer numeral design points than what is obtained from the present study could be explored. The study recommends further studies on latest methods of construction of modified higher order rotatable designs and applications on this area.*

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*African Journal of Education,Science and Technology*,

*5*(3), Pg 190-200. Retrieved from http://ajest.info/index.php/ajest/article/view/406