Page 60 - Six Sigma Advanced Tools for Black Belts and Master Black Belts

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The IDOV Roadmap 45
3. Understand and verify the capability of the measurement system.
4. Identify KPIVs and KPOVs for each CTQ.
5. Establish the relationship between KPIVs and KPOVs.
The main deliverable is the transfer function between the KPIVs and KPOVs which
must be of adequate predictive power so that the associated design risk can be quan-
tified with high level of confidence. We will present some important concepts and
tools in Part D of this book. An excellent reference on this topic is the book by Wu and
Hamada. 4

4.2.3 Optimize
In the optimize phase, armed with the transfer functions for major CTQs, appropriate
tolerances will be established using Monte Carlo simulation. To carry out the intended
simulation, assumptions of input distributions for the KPIVs are needed so that the
KPOVs can be simulated using the transfer functions. For example, suppose that the
KPOV (Y) of a CTQ can be represented by the function
Y = a 0 + a 1 X 1 + a 2 X 2 + a 3 X 1 X 2 ,

where the X i are the KPIVs. To assess the response, the input distributions of the X i
are assumed and a large number of the response of the KPOV can then be simulated.
This can easily be done in software such as MINITAB or even Excel. The capability
measures with respect to the specification developed in the identify phase can then
be assessed. Monte Carlo simulation also provides a convenient means to perform
sensitivity analysis by changing the parameters of the input distributions and the
distributional assumptions. The process can be repeated to optimize the inputs and
obtain realistic tolerance.
Usually the number of replications -- the number of random variables generated
each time for a particular KPIV -- is very large, say, 10 000. Correspondingly, the num-
ber of responses is also very large. It is thus not advisable to try fitting a distribution
to the data as “all models are wrong”. Conclusions should be drawn directly from the
empirical distribution or the histogram of the response. The resolution of the results
can easily be improved by increasing the number of replications.
Another major task during this phase is to estimate the reliability of the product by
carrying out some accelerated tests which involve testing the product under higher
stress levels than those under which it will usually operate. The key to success is
to identify the correct stressor or way to shorten the lifetime of the product so that
failure data for the same failure mode as those under usual operating conditions can be
obtained within reasonable test duration. The best place to start looking for the correct
way of stressing the product is the design FMEA table drafted in the identify phase
as it lists major failure modes and how failures are triggered. Field data of previous
generations of the product must also be examined in order to understand how the
product fails, to identify critical failure modes and to set realistic reliability targets.
A detailed treatment of this topic is beyond the scope of this chapter, and readers
5
may refer to Tobias and Trindade for an excellent treatment of the subject. Here, we
present the essential ideas by assuming that the failure time follows an exponential
distribution with mean time to failure θ (or failure rate λ = 1/θ).