A new third order rotatable design in five dimensions Through balanced incomplete block designs

Abstract

Response surface methodology (RSM) is a collection of statistical and mathematical techniques useful for developing, improving and optimising processes. To cut on costs, an experimenter has to make a choice of the experimental design prior to experimentation. The most extensive applications of RSM are in the particular situations where several input variables potentially influence some performance measure or quality characteristic of the process. The field of RSM consists of the experimental strategy for exploring the space of the process or independent variables and empirical statistical modeling to develop an appropriate relationship between the yield and the process variables and optimisation methods for finding the values of the process variables that produce desirable values of the response. The fitting of the response surface can be complex and tedious if done haphazardly. The use of rotatable designs has been suggested. These designs ensure equal precision on the response estimates. The advent of high speed computers, the realisation of the importance and need to choose and adopt an experimental design that is best according to some well defined statistical criterion, led to the development of a subject like optimality of designs. In view of the massive research effort in improving the statistical tools for investigation of response surfaces, it would be hoped that experimenters would be increasingly using the sophisticated developed statistical tools, which is not the case in general terms. Experiments of this kind could be widely applicable in human medicine, veterinary medicine, agriculture and in general, product research-innovation development for optimum resource utilisation based industrialisation process in line with the Kenya Vision 2030. In this paper, a third order rotatable design in five dimensions from a third order rotatable design in lower dimensions is constructed through balanced incomplete block designs (BIBDS). The result of the experiment in lower dimensional design need not be discarded. RSM will be appropriate to the study of phenomena that are presently not well understood to permit the mechanistic approach where the mechanistic approach is itself used when the mechanisms of some scientific phenomena are understood sufficiently well.