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Robustness
Taguchi has emphasized the importance of robust designs. A
robust product or process is one that is less sensitive to variation
of the inputs. That way the inputs can continue to vary but less of
this variation is transmitted to the output. This minimizes the
need to tighten tolerances. Robustness is achieved by careful
selection of targets for the inputs. See Section 3.4.
In VarTran, robust designs are achieved by finding the set of
targets minimizing the defect rate, maximizing Cpk, or
maximizing the distance inside specification. This minimizes the
transmitted variation while driving the average to its ideal value.
Root Mean Square
Error (Root MSE)
The root MSE is:
Root MSE = (µ − Target ) 2 + σ 2
where µ is the average and σ is the standard deviation. It has the
same units as the average and standard deviation.
The root MSE is always greater than or equal to zero. It can only
be zero if the average is on target and the standard deviation is
zero. Minimizing the root MSE drives the average to target with
minimum variation. Minimizing the root MSE is equivalent to
minimizing the Taguchi Loss.
Sigma Level
Measure of quality that directly relates to the defect rate. Six
Sigma corresponds to 3.4 defects per million. Three sigma to
0.13% defective or 1300 defects per million. See Section 5.2.
Six Sigma Quality
Six sigma quality requires that for each measurable characteristic
such as fill volume, seal strength and so on, the defect rate to be
no more than 3.4 defects per million. In a table of the normal
curve, the value 3.4 defects per million is found at 4.5 standard
deviations. Six sigma quality requires that the process average be
kept at least 4.5σ from the nearest specification limit. See
Section 5.2.
This is accomplished if:
•
Cpk >= 1.5
•
Cp >= 2 and Cc <= 0.25
•
The Interval for Values based on +/-4.5 SD is within
the specification limits.
Glossary
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