Sequential and optimal experimental design. An example of application to the synthesis of metal alloys

Abstract
In this article we shall define and illustrate how to further optimize experimental design methodology through a real example from the field of chemistry. This depends on two principles: the first principle is to provide the experimenter with several optimal experimental designs (based on mathematically defined criteria), rather than the traditional single design. In this way several objectives can be simultaneously reconciled. The second principle, underlying the data analysis stage, is the correct use of statistical tests (in regression as well as variance analysis), particularly to check on their validity after using them. This is the methodology we shall briefly attempt to illustrate here.