Taz & Darius,
I had forgotten about Cr & Cpm (or maybe I never knew) so I had to look those up. After looking the various indices, here is my humble opinion.
Cp: has been made pretty much obsolete by Cpk, so it isn't very useful
Cr: is just 1/Cp, so it suffers the same shortcomings as Cp
Cpk: has shortcomings listed in the first post in this thread, but it is much better than Cp because it includes an effect due to centering. Basically, I think it focuses too much on reducing variation and too little on centering.
Cpm: I like this one. The equation is more complicated than Cpk, but it adds more of a penalty for being off-center. If I had seen this originally, I might not have tried my own.
Warning, the next part is a little more theoretical and more speculative, so proceed at your own risk!
And now my candidate - call it Cpt (t for Taguchi).
1) Find the taguchi cost for each piece:
cost(i) = [x(i) - target]^2 / (tolerance)^2
2) Average these costs.
ave. cost = sum(cost(i)) / n
3) Take 1 over this number (since people like big numbers for good processes)
Cpt = 1/ (ave. cost)
With a few more math tricks, this can be adjusted to give the same value as Cpk for a centered process. I've tried it with some different sorts of data and it seems to give a logical and useful value - a value that is IMHO more logical and useful than that given by Cpk. And there is no mention of normal distributions and there is no need to estimate the standard deviation!
Tim F
I had forgotten about Cr & Cpm (or maybe I never knew) so I had to look those up. After looking the various indices, here is my humble opinion.
Cp: has been made pretty much obsolete by Cpk, so it isn't very useful
Cr: is just 1/Cp, so it suffers the same shortcomings as Cp
Cpk: has shortcomings listed in the first post in this thread, but it is much better than Cp because it includes an effect due to centering. Basically, I think it focuses too much on reducing variation and too little on centering.
Cpm: I like this one. The equation is more complicated than Cpk, but it adds more of a penalty for being off-center. If I had seen this originally, I might not have tried my own.
Warning, the next part is a little more theoretical and more speculative, so proceed at your own risk!
And now my candidate - call it Cpt (t for Taguchi).
1) Find the taguchi cost for each piece:
cost(i) = [x(i) - target]^2 / (tolerance)^2
2) Average these costs.
ave. cost = sum(cost(i)) / n
3) Take 1 over this number (since people like big numbers for good processes)
Cpt = 1/ (ave. cost)
With a few more math tricks, this can be adjusted to give the same value as Cpk for a centered process. I've tried it with some different sorts of data and it seems to give a logical and useful value - a value that is IMHO more logical and useful than that given by Cpk. And there is no mention of normal distributions and there is no need to estimate the standard deviation!
Tim F



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