Comparing process parameters on non-normal batches

#1
Hello,

I'm currently working with data from three consecutive batches. I want to calculate and compare Cp and Cpk for every batch. Only first batch follows a normal distribution (passes AD test), while the others, don't. Box-Cox transformation yields good results for those two batches.

Q1: Should I transform all three batches? Or just leave the normal-distributed batch and transform the non-normal? Again my objetive is to calculate Cp/Cpk so I don't know if I can "compare" values if I transform only 2 batches...

Q2: I'm transforming my data with optimal λ as calculated by Minitab, which is λ = 4 for 2nd batch and λ =3 for third one. Can I transform (and compare) using different λ? Or should I use same λ for all batches?

We also calculate Ppk (and other long term process parameters) using Excel as required per client. If my understanding is correct, I should use on Excel the already transformed data for this parameters, right? If then - can Minitab provide me with the transformed dataset? I'm assuming that calculating Cp Cpk with transformed data and Ppk with non-transformed would be a huge red flag.

I've tried to find information on the internet but couldn't really solve this issues. I'm attaching my data just in case it is useful (upper bound is 2.5, no lower bound).

Thank you so much for your time.
 
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#3
Thank you for your answer. I've been trying to attach but I can't figure out how... There is only a button for inserting link, images and media/spoiler/code... I've tried dragging across the screen and dropping the file but doesn't seem to work either
 

Miner

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#4
Thank you for your answer. I've been trying to attach but I can't figure out how... There is only a button for inserting link, images and media/spoiler/code... I've tried dragging across the screen and dropping the file but doesn't seem to work either
I believe you have to have a minimum of 5 posts before you are able to attach a file.

@Eric Gasper Are you able to assist here?
 

Miner

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#7
I looked at this data and have a few questions for you.
  1. What are these batches and what type of process generated them
  2. How was the data collected? Randomly, time sequence, physical position within the batch?
  3. Is the testing process controlled? Can environment affect test results?
 
#8
I looked at this data and have a few questions for you.
  1. What are these batches and what type of process generated them
  2. How was the data collected? Randomly, time sequence, physical position within the batch?
  3. Is the testing process controlled? Can environment affect test results?
  1. Pharmaceutical product manufactured in batches. Those are moisture content values (in the final product) after the process is completed
  2. There was a physical position filter previous to the data adquisition and then, after filtering, data was selected randomly. Main objective was to get a complete, representative dataset from the batches
  3. It is controlled. Ideally, environment should not affect interbatch

Thank you for your time!
 

Miner

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#9
Looking at your data, I do not believe that the process is generating non normal data. The data appears to be inherently normal, but with a few outliers (batch 3) and a subset of data that is distinctly different (i.e., mixture in batch 2). Note the bottom two graphs. The bottom left is batch 2. The bottom right is the same data, but with the circled subset removed. Batch 2 now shows normal.

Given your explanation (and guessing at your process), you might be looking at incomplete mixing or drying that makes these batches non homogeneous.

1643833874206.png
 

Miner

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#10
Another suggestion: If you can order the data either in time order sequence or to correspond to the physical position, you could either plot the data on an I-MR control chart or by location. It would help you diagnose the source of this subset and outlier.
 
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