Robust Parameter Design Reducing Variation

The aim of the parameter design is to establish a combination of levels of the design factors which leads to a minimum in the variability around a mean, minimum or maximum value in the response. The idea behind the parameter design is to find a set of analytical conditions which are both functional i.e. they fulfil the objective) and robust i.e. they are not sensitive to noise factors), as far as possible. 

Taguchi classified robust designs according to the main objective when measuring the response in three basic types nominal-is-besf (minimal variability around a target value), larger-the-better (minimal variability for a maximum in the response) and smaller-the-bettef (minimal variability for a minimum in the response). 

in the nominal-is-besf case, the signal-to-noise (s/n) ratio is defined, for each run of the design matrix, as 

For the larger-the-betteE and smaller-the-bettef cases, the respective expressions for the s/n ratios are given below. In all cases, y,- are the observed responses and n,- the number of replicates for each run. 

According to these definitions, in the smaller-the-betteE case, the s/n ratio increases as the mean and variability decrease. Similarly, in the darger-the-better case, the s/n ratio increases as the mean increases and variability decreases. 

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