Page 416 - Six Sigma Demystified

396 Six SigMa DemystifieD

Data range: Select column of log (averages) as x axis (first column in Data
Range); select column of log (standard deviations) as y axis (second column in
Data Range)
Results: Obtain the slope from the plot; round up or down to closest slope in
Table T.20

Calculated Parameters
Simple calculated responses occur frequently when a response is measured and
then converted to a response with more general interest. For example, the labor
required to assemble a piece of furniture may be measured in labor hours and
then converted to labor cost because that more directly relates to profitability.
Measurement equipment may output a resistance that can be converted to a
more meaningful temperature response.
We also can convert multiple responses to a single response. A simple exam-
ple is the calculation of density based on measured displaced volume and mass.
We may similarly calculate utilization based on usage and availability (such as
“bed days” in health care).
Finally, we may calculate statistics based on the grouping of repeated runs to
better understand how a factor influences the process variation. Taguchi’s sig-
nal-to-noise ratios are one example of this.
Classical experiments often investigated the effects of a parameter on the
mean response. Taguchi popularized investigating parameter effects on the varia-
tion of the response using signal-to-noise ratios. Estimating the effects on varia-
tion is often useful for designing processes that are robust to parameter variation

or in some cases to reduce common-cause variation.
Estimation of the variance requires grouping of responses based on multiple
observations at each condition, such as with replication or repeat runs (during
the running of the experiment) or after insignificant terms have been discarded.
Taguchi’s signal-to-noise ratio is a grouped response that considers both the
variation of replicated measurements and the proximity of the average response
to a specified target value. Taguchi defined over 70 signal-to-noise ratios, 3 of
which are most common:
• Smaller is better. Used when the target value for the response is zero. The
signal-to-noise ratio is calculated as

2
S/N ratio = –10 log [Σ(y )/n]
i