Q: What is the Taguchi SN ratio?

The Signal-to-Noise (SN) ratio is an index of quality stability (robustness) proposed by Genichi Taguchi. Nominal-the-best (target value): SN = 10·log(μ²/σ²); Larger-the-better: SN = −10·log(Σ1/y²/n); Smaller-the-better: SN = −10·log(Σy²/n). The level combination maximizing the SN ratio is taken as the optimal condition. Because SN ratios account for both mean and variance simultaneously, they are widely used as optimization objectives beyond Cpk.

Q: How do you interpret the ANOVA F-ratio?

F-ratio = MS_effect / MS_error, where MS (mean square) = SS (sum of squares) / df (degrees of freedom). A larger F-ratio indicates a larger effect relative to error variance, indicating a significant factor. When p-value < 0.05, the factor is statistically significant at the 5% significance level. However, in designed experiments with few replicates, F-tests have low power, and engineering judgment is also required.

Question 1

What is the difference between a full factorial and a fractional factorial design?

Accepted Answer

A Full Factorial design tests all combinations of factor levels. With k factors at 2 levels, 2^k runs are required, allowing all main effects and interactions to be estimated. A Fractional Factorial design reduces the number of runs by testing only a subset of combinations. Interaction information becomes confounded (aliased) with main effects, reducing reliability but improving efficiency. Taguchi orthogonal arrays are one form of fractional factorial design.

Question 2

How do you interpret interaction effects?

Accepted Answer

An interaction means 'the effect of factor A changes depending on the level of factor B.' In an Interaction Plot, two parallel lines indicate a small interaction, while crossing or non-parallel lines indicate a large (significant) interaction. When the F-test p-value for the interaction term in ANOVA is <0.05, it is statistically significant. When interactions are significant, optimal conditions cannot be determined from main effects alone.

Question 3

What is the Taguchi SN ratio?

Accepted Answer

The Signal-to-Noise (SN) ratio is an index of quality stability (robustness) proposed by Genichi Taguchi. Nominal-the-best (target value): SN = 10·log(μ²/σ²); Larger-the-better: SN = −10·log(Σ1/y²/n); Smaller-the-better: SN = −10·log(Σy²/n). The level combination maximizing the SN ratio is taken as the optimal condition. Because SN ratios account for both mean and variance simultaneously, they are widely used as optimization objectives beyond Cpk.

Question 4

How do you interpret the ANOVA F-ratio?

Accepted Answer

F-ratio = MS_effect / MS_error, where MS (mean square) = SS (sum of squares) / df (degrees of freedom). A larger F-ratio indicates a larger effect relative to error variance, indicating a significant factor. When p-value < 0.05, the factor is statistically significant at the 5% significance level. However, in designed experiments with few replicates, F-tests have low power, and engineering judgment is also required.

Design of Experiments — Factorial & Taguchi L9 DOE Tool

Main Effect & Interaction Calculation