An application of the quality engineering approach reconsidered

Robust design methods allow one to make products or processes less sensitive to variations. The objective is to set the parameters of a system so that it functions well over a wide operative range while subjected to fluctuating uncontrollable factors. Conventional tightening of input tolerances is costly and it is not the only way to reduce variations in a process. Taguchi's parameter design method consists in performing a design of experiment in which control and noise variables are set at fixed levels. Taguchi has developed cross product designs for experimentation that consist of two arrays, one for the noise factors and one for the control factors. Control factors are process or product variables that can be easily controlled. Noise factors can be controlled in the laboratory but cannot be controlled during production. The noise factor levels are varied according to an orthogonal outer array to simulate the variations of the process. The control array is used to select the design points where the process variance is to be estimated. The signal-to-noise (S/N) ratio proposed by Taguchi is designed to be used as a response to reduce dispersions. Cross-product arrays however, often require a very substantial number of runs. Moreover, fixing the level of the hard-to-control factors during the experimentation process is often costly. Robust design experiments are therefore frequently run in a split-plot way. That is, the levels of the hard-to-control factors are moved much less frequently than the levels of the control factors. In this paper, the cost-effectiveness of Taguchi's direct cross-product arrays is compared to that of mixed resolution combined arrays.