Page 417 - Six Sigma Demystified

Part 3 S i x S i g m a To o l S 397

• Larger is better. Used when the target value for the response is infinity. The
signal-to-noise ratio is calculated as

2
S/N ratio = –10 log [Σ(1/y /n)]
i
• Nominal is better. Used to minimize the variability of the response. The
signal-to-noise ratio is calculated as

2
2
S/N ratio = 10 log [Σ( y )/s ]
Interpretation

Variance Stabilization
The transformed response should be checked for constant variance using the
equality-of-variance test. If the transformed response passes the tests for constant
variance, then the ANOVA for the transformed response is acceptable for use.
In the preceding example, Bartlett’s test for equality of variance is not
rejected for the transformed response, so the regression analysis is redone using
the transformed response.

Calculated Parameters
Generally, calculated parameters will be analyzed using the same techniques
discussed elsewhere in this book.
A simple criticism of signal-to-noise ratios is that they are confusing. 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 signal-to-noise ratios may be found in Box (1988)
and Pignatiello and Ramberg (1985).

u Chart

U charts are one of a set of control charts specifically designed for attributes
data. The U chart monitors the percent of samples having the condition, rela-
tive to either a fixed or varying sample size, when each sample can have more