Taguchi Ratios

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(y_i²)/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/y_i²)/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(y_bar²)/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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