Efficient alternatives to Taguchi's crossed arrays for robust parameter design

In his idea of robust parameter design, Taguchi proposes modeling the controllable factors of interest in a process along with the uncontrollable or noise factors with the goal of finding settings of the control factors that are robust to noise variability. Taguchi methodology has generated both extraordinary interest due to numerous successful applications, and much debate due to some limitations such as experimental designs with an excessive number of runs. Consequently, practitioners of response surface methodology have suggested the use of combined array designs to overcome the limitations of Taguchi's approach. An example of a combined array design that has been successfully applied as an alternative to Taguchi's designs is the composite mixed resolution (CMR) design. Most CMR designs are, in terms of design size, superior to or competitive with the corresponding Taguchi's design. However, for those cases where the number of runs required by the CMR designs is greater or equal to Taguchi's designs, it is desirable to have available an alternative experimental design.; The purpose of this research is to find alternative combined arrays designs for the cases involving six to twelve variables where CMR designs are not smaller than Taguchi's designs. The original contributions of this research are the following: (1) The development of mathematical expressions to evaluate the efficiencies of combined array designs. (2) The development of design generators to obtain modified small composite designs. (3) The development of combined arrays designs with the same size as CMR designs and with higher or comparable efficiency to estimate the effects of the control and noise factors. (4) The development of combined array designs smaller than CMR designs and with the same efficiency.