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Minitab can provide a capability analysis based on distribution fitting or using the Johnson Transformation.
This is an oversimplified explanation, but the basic theory is to calculate the area under the fitted curve, select a point equivalent to the same area under a Normal curve from the median to 3 StdDev, and use those numbers to calculate Cpk. Depending on how badly the distribution is skewed, the "3 StdDev" value for the lower half versus the upper half can differ dramatically.
If you try to duplicate this method on your own, please visit the Minitab website for the specific method.
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