Box-Cox transformation on Minitab

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• #30911

GONZALEZ
Participant

Hello,I have been using Box-Cox transformation in Minitab for normalizing data being used for calculating CPK. However, I noticed that some times Box-Cox transformation doesn’t achieve normality, therefore I would like to know if it’s valid to estimate CPK on this particular case using box-cox transformation or If I should use some other technique.If anyone has any information about what Minitab is doing behind stages would be great,Best regards,

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#81149

Erik L
Participant

Miguel,
The real issue, before determining a Cpk calculation, is to make the determination that the process that is producing the data is stable.  Once you have that you have your short-term estimate of variability to feed into the calculation.  Stability around the estimate of variability should be your primary concern.
In regards to Box-Cox, the appropriate transform can be chosen from anywhere within the 95% CI.  If you let Minitab choose the optimal lamda it might not really be the right one for the data.  Take a look at the total range that you can use for a transform and see if there is one that makes more practical sense.  For instance, if 0 is within the 95% CI one would typically use that as justification to use the log transform (assuming time series data).
Regards,
Erik

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#81150

MMBB
Participant

Eric is right about the stability. That is why the AIAG SPC reference manual recommends creating control charts before caclulating & assessing the capability indices. MINITAB offers that capability via their capability sixpack – control charts, normal probability plot, and metrics.
Eric is also right about your ability to use any transformation within the 95% confidence interval presented by the Box-Cox transformation technique. The advice is to use a value that is easy to explain, for example, a lambda value of 2 represents a “square” transformation – that is, x’ = x^2. (this means the transformed value, x’, equals x^2, which means the square of x).
Lambda = 1 means x’ = x    [no transform]Lambda = 0.5 means x’ = SQRT(x)    [square root transform]Lambda = 0 means x’ = ln(x)    [a natural log transform]Lambda = -0.5 means x’ = 1/SQRT(x)    [inverse square transform]Lambda = -1 means x’ = 1/x   [inverse transform]Lambda = -2 means x’ = 1/(x^2)    [inverse square transform]   you get the idea . . .
Now, to your question of what to do if the Box-Cox transformation doesn’t provide normality . . .
Well, technically you have two choices:
1. Use MINITAB’s Weibull Capability Sixpack to see if the Weibull distribution can provide a decent fit to your data. If yes, life is good.
2. Use “nonparametric” emperical percentiles to calculate capability indices. Instead of using 3*sigma or 6*sigma in the denominators, use the difference between the median and the 99.87th percentile (the equivalent of 3*sigma) or the difference between the 99.87th percentile and the 0.13rd percentile (the equivalent of 6*sigma). The problem here is that it will takea VERY large sample size to be able to calculate these percentiles accurately. Maybe 10,000 or more – to be honest I really don’t know the sample size needed – maybe someone out there does.
MINITAB, as shipped, doesn’t calculate nonparametric percentiles, but you can download a macro that does from their website (go to Support, then the Macro Catalog).
Beyond these three techniques (Box-Cox, Weibull, Empirical), some say that a mild deviation from normality shouldn’t affect the capability indices too much. How much is some and too much, I don’t know.
Can anyone give a reference to an article that clears this up?

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#81151

Wingjohn Lau
Member

Miguel,
The article “Six Sigma Special Topics: Z-Shifts, Statistics & Non-Standard Data Analysis” from GE’s R&D center will help you in this topic. Get the article here http://www.crd.ge.com/cooltechnologies/pdf/2001crd120.pdf
Wing

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#81231

rams
Participant