Stats tip: Help! My Ppk is larger than my Cpk

Matt SavageI often get asked SPC application questions such as: Can Ppk be larger than Cpk? Can Cpk be larger than Cp? Do you recommend CPM, Cpk, Ppk or something else? I prefer to answer these process capability questions with simple one-word answers, but that doesn’t usually satisfy the quality zealot’s curiosity. So here’s the long and the short of one of the questions.

In short, Yes, Ppk can be larger than Cpk. If you are doubtful, or consider yourself a quality zealot, grab a cup of joe, and read on.

Cpk is an index that is designed to communicate the state of quality of what you are measuring. Cpk uses three pieces of information to calculate the index:

  1. The mean or average of the data that was collected.
  2. The upper and/or lower specification. Some refer to a specification as a tolerance, so use this if you are more comfortable.
  3. The standard deviation of the data that was collected

This third piece of information, the standard deviation, is often the source of confusion. Cpk calculations use the standard deviation that is represented by the “within subgroup variation” while Ppk calculations use the standard deviation that is represented by the “within AND between subgroup variation.”

Naturally, you would think that the variation represented by within and between the subgroups would be larger. And in most cases, it is. But it is simply not the case in every single capability study. The variation represented by within and between the subgroups is NOT larger 100% of the time. Full stop. So if your Ppk happens to be larger than Cpk, accept it as unlikely, but possible.

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