The design and analysis of 2^{k − p} × s prototype experiments

Prototype testing and experimentation play a key role in the development of new products. It is common practice to build a single prototype product and then test it at specified operating conditions. It is often beneficial, however, to make several variants of a prototype according to a fractional factorial design. The information obtained can be important in comparing design options and improving product performance and quality. In such experiments the response of interest is often not a single number but a performance curve over the test conditions. In this article we develop a general method for the design and analysis of prototype experiments that combines orthogonal polynomials with two-level fractional factorials. The proposed method is simple to use and has wide applicability. We explain our ideas by reference to an experiment reported by Taguchi on carbon monoxide exhaust of combustion engines. We then apply them to an experiment on a prototype fluid-flow controller.