# Data Analysis - Johnson Transformation/Weibull Distribution/Capability Analysis

#### optomist1

##### A Sea of Statistics
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Good Point Bev,

a run chart and a box plot shows and confirms what you have stated...a runchart goes a long way...

Marty

#### Stephen Cook

##### Registered
I have a set of seal strength data (30 bags, 4 seals per bag as a subgroup for each bag) within a specification range of 0.5 to 2.5 and actual values of 1.3 to 1.7. The probability plot shows the data are not normally distributed. The Johnson transformation in Minitab transforms the data to acheive a p-value greater than 0.05 which is acceptable to me. When I perform a Six-Pack analysis of the data, I get a capability histogram (LSL: -3.61, USL:2.83) with normal probability plot (AD:0.487, P:0.208). I am concerned about the negative numbers on the capability histogram after applying the Johnson Transformation. Should I be concerned? I am wondering whether the best approach is to find a non-normal distribution that best fits the data. When I consider Weibull and Largest Extreme Value Distributions, neither is able to meet the 0.05 significance without removing the extreme outliers in the data set. I am not certain how to best approach analyses of these data and I am looking for help.
I am having exactly the same problem. Ppk 1.40, P < .05. Did Johnson Transformation of both spec limits and data.
Now, how does one calculate the new resulting Ppk? The transformed data has negative values, so Minitab, Six Pack, results in error, can not compute Box Cox with negative values.

Can anyone tell me how to get Minitab to calculate Ppk value using negative numbers, transformed from Johnson Transformation?
or
A better way all together?
See attached data set.

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#### bobdoering

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I am a little puzzled about what you are trying to do. Some distributions do not allow negative numbers, some do.

But, I have attached a simple curve fitting exercise. The Johnson Family Distribution is an extremely good fit at a p value of .95 (where 1.00 is a perfect fit). The normal distribution has a p value of .19, so it is a terrible model for your data. Therefore, using the model that most closely represents your data, your capability is .95. Not surprising, when you are so close to the upper specification. Remember, the model that most closely represents your data is the one that gives the most reliable conclusions. That is the point of all statistical analyses.

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#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Of course now I have to make the obligatory statement that Cp/Ppk calculations are hokey-pokey math (or Jabberwocky) that do not provide any more real insight into the process that a simple run chart will (without math) and that they even obfuscate and mislead the user about the process.

#### Miner

##### Forum Moderator
Staff member
Always check to verify that you have a stable process before attempting to fit a distribution or to transform your data. Your process is not stable, so any transformation is highly suspect. Get the process stabilized first.

#### bobdoering

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Always check to verify that you have a stable process before attempting to fit a distribution or to transform your data. Your process is not stable, so any transformation is highly suspect. Get the process stabilized first.
Many physical phenomena are not stable. For example, ultimate force failures are rarely stable, where yield are more stable. Not seeing your process, it is difficult to tell if you have measurement or process variation as the primary variation of your total variation equation. The jumps are disturbing as far as stability. I did not do the run chart because I was not sure if the data was from a pile of parts, or reported in time ordered sequence (always the best sampling!)

That said, your variation is tiny compared to the identified specification. If there was a way to adjust the process down, instability would likely be a non-issue (noise, out of CNX).

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