Hi Charles,

        I've been thinking about your question since you posted it and think I
have an answer.  Since your distribution is no longer Normal, you can't use Cp
and Cpk values.  (Note, this doesn't include control chart calculations that
follow the Central Limit Theorem.)  You should still be able to estimate a
percent nonconformance.

"The Quality Toolbox" by Nancy R. Tague gives this information:

"If the process is not normal, you cannot calculate a capability index or
performance index.  There are three options:
1)  Transform the data.  For example, a skewed distribution can be transformed
into a normal distribution using natural logarithms.
2)  If you know the process' distribution (binomial, Poisson, and so on),
directly calculate from that distribution the values that correspond to a
given Cpk and compare to your data.
3)  Do not calculate a capability index.  Instead, calculate directly the
percentage of the process that is outside specifications."

        Other things to think about:
        Your initial process capability (before return and adjustment) should
be straightforward and probably has more meaning.  This gives you an estimate
of percent nonconforming to specification that your customer saw.
        Now, if you put this adjustment step within your standard process
flow, I can see why you would want to calculate a new Cpk.  If you adjusted
each power supply, it should form a Normal Distribution.

        My stats book gives two approaches to aid in the interpretation of
standard deviation.  One is called "The Empirical Rule" and applies to
mound-shaped distributions.  This would include the Normal and your
truncated-normal distribution.  Approximately 68% of measurements fall within
+/-1 standard deviation, 95% within +/- 2 standard deviations, and 99.7%
within +/-3 standard deviations.
        The second is called "Chebyshev's Rule" and applies to any sample of
measurements, regardless of the distribution shape.  It says generally, at
least 1-1/(k^2) of the measurements will fall within k standard deviations of
the mean.  Within +/- 2 standard deviations, at least 75%.  Within +/- 3
standard deviations, 89%.

        For BiModal Distributions, separate the data and run calculations
independently for Cpk.

Hope this helps,

Glenn

Charles Law <[log in to unmask]> Wrote:
|
|      Hi,
|
|      I believe that all of you must have some ideas on the term "Normal
|      Distribution".
|      What I am now facing is a population from batch of power supply output
|      voltage.  Since some power supplies had failed in meeting the customer
|      specification at their initial measurement, output were then adjusted
|      by tuning the trim-pot in the power supplies.  After that, I measured
|      the output voltage of all the power supplies then drew the
|      distribution graph.  You can see that the distribution is now clipped
|      at both ends.  Does anyone knows how this kind of distribution called?
|      And, if I cannot use the formula for a normal distribution to
|      calculate the cpk , what can I use to measure the process capability
|      under this condition?
|      Besides, does anyone know something about "Bimodal Distribution" and
|      how is it defined?
|      Comments are welcome.
|
|      Best Regards,
|      Charles

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