DsDs-optimal experimental plans for robust parameter design

A methodology based upon the DsDs-optimality criterion is proposed to establish experimental plans for robust parameter design (RPD) studies. This criterion, justified by the fact that in most actual situations only a subset of the model parameters is relevant to solve the optimization problem implied in RPD, allows obtaining experimental plans in situations where classical Taguchi's crossed or Box's combined designs are not adequate. A procedure to obtain DsDs-optimal continuous designs in RPD studies with quantitative variables is developed, and the structure of these optimum designs for studies with 2 or 3 control factors and 1–3 noise factors is analyzed. A set of directly applicable exact experimental plans with a moderate number of runs is also proposed for these situations. The methodology is finally applied to obtain an experimental plan for a more complex actual problem in a spot welding process.