Also see Taguchi Designs.
The Taguchi Signal to Noise ratios are a set of grouped responses that consider both the variation of replicated measurements and the proximity of the average response to a specified target value. Taguchi defined over 70 such Signal to Noise Ratios, three of which are most common: Smaller is better, Larger is better, and Nominal is better.
SN-S, Smaller is Better
S/N ratio = -10 log [SUM(yi2)/n]
Target value for response = 0
Goal: Minimize SUM(y2); Maximize S/N ratio
SN-L, Larger is Better
S/N ratio = -10 log [SUM(1/yi2)/n]
Maximize response; Equivalent to minimize 1/y
Goal: Minimize SUM(1/y2); Maximize S/N ratio
Nominal is Best
S/N ratio = 10 log [SUM(ybar2)/s2]
Goal: As variability of response decreases relative to the average response, S/N ratio increases; Maximize S/N ratio
A simple criticism of the Signal to Noise ratios is that they are confusing and potentially misleading. A more detailed criticism of the ratios is that they confuse variation of the response with the average response in a single metric, which tends to obscure information. This is particularly dangerous in cases where the variation changes as a function of the average response. A preferred approach is to consider the average and variance of the response as separate metrics (or responses), each to be maximized, minimized or targeted as necessary (Note: Usually a minimized variance is desirable).
More detailed analysis of the Signal to Noise ratios may be found in these references:
Box, (1988). Signal-to-Noise ratios, performance criteria & transformations Technometrics, 30, 1-40.
Pignatiello & Ramberg (1985). Discussion of off-line quality control, parameter design & the Taguchi method by Kackar. JQT, 17, 198-206.
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