CONSTRUCTION OF MODIFIED THIRD ORDER ROTATABLE DESIGNS THROUGH PAIRWISE BALANCED DESIGNS

Abstract

Rotatable designs are designed 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 technique valuable for developing, improving and optimizing models and process. Experimentation of any kind usually requires resources of which they may be limited due to either in availability or high cost of acquiring. To reduce on expenses of an experiment one has to make a better preference of the experimental design prior to the experiment. An appropriate design that would provide relatively less number of the design points of the response at particular points of significance is essential. The aim of this study was to construct a modified third order rotatable designs (MTORD) by use of Pairwise Balanced designs in order to address the above problem. The objectives of the study were to construct a three-level and five-level v-dimensional modified third order rotatable Designs (TORD) using Pairwise Balanced Designs (PBD). The threelevel and five-level v-dimensional modified order three rotatable designs were constructed by use of a suitably chosen pair off Pairwise Balanced Designs by repeating the set of the design points generated from every one of the designs a constant numeral 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 fewer numeral of the design points as compared to the corresponding existing designs in the literature. Other studies that could possibly lead to designs with fewer numeral design points than what is obtained in 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.