Repost: How to argue Cpm over Cpk (Process Capability Indices)

Is this any good?

http://www.isixsigma.com/offsite.asp?A=Fr&Url=http://www.qualityadvisor.com/library/capability/capability_index_dilemma.htm

Al

Al,

Yes, I think that article was great. It was one of which I used for my arguement presentation, but it doesn't discuss how Cpm can "warn" that your process is still in control, but could be threatening one of the specifications. Perhaps a cross between Cpk & Cpm can do the trick?

Cpm(hybrid) = min{

(USL-mean) / 3*sqrt[sigma^2+(mean-OPT)^2]

(mean-LSL) / 3*sqrt[sigma^2+(mean-OPT)^2]}

Hi¡

I would recommned following thing: in case of Tolerances like Upper tolerance = 0 or Lower tolerance = 0 use Cpm instead of Cpk.

I tell you why with an example:

Process with target value 3.5, Upper tolerance: +0.01, Lower tolerance: -0.00

First batch od production: Mean=3.505,3*Sigma=0.005 -> Cpk=1

Second batch od production: Mean=3.502,3*Sigma=0.002 -> Cpk=1

Try to plot both graphs, Cpk is the same for them but Cpm is different,Cpm can show how is the batch related to extremes

Their are issues you can run into when accomplishing capablity studies for non-normal data distribution. Your data will be truncated to one side with (LSL 1, OPT 2, USL 10). Bell curves generally work well with-in a bilateral tolerance and not well in a unilateral tolerance.

Best practice for variable data is (n-30), the gates to go thru for non-normal data are (I-MR Chart to check for stablity), (Anderson Darling Test to check for normality of data set), then a I would recommend a (Box Cox Transformation of the data set) to get a optimal lambda for capablity analuiysis for a valid CPK value.

Good afternoon Will.reeves.

I beiliev that if you win the battle with your boss, your company will lose the quality war.

Heres why.

The CPK is less than 1 because you are not centered in the tolerance, and your process standard deviation is too high for your OPT of 2. With your mean at 2.162, subtracting three std dev's (3*.4796= 1.4386) gives you a mean minus 3 sigma value of .7234, one half a std deviation below the LSL of 1.0.

You need to either move the OPT (recenter the process) or reduce the std deviation to about .33 in order to get that cpk up to 1.0 min.

Playing sleight of hand by offerring Cpm as a surrogate for Cpk is like saying no one will be hurt, my car has seatbelts, but then noone buckling up as you drive without brakes to a wall.

Over time, that process will produce material outside the LSL of 1 , and your protestations of CPM is "Blah Blah Blah" will be engraved on a tombstone somewhere.

To be perfectly frank, cpK 1.0 is just compliant, 1.33 is better, it gives you an extra std deviation of "bumper room"; I think that you would need a std deviation of about .15 at your current OPT and mean to get there.

I apologize I don't have my tables handy.

Do NOT SUccumb to the charms of Cpm while Cpk is below 1.0.

BAD THings will happen.

milo

Milo,

Indeed, that will end the debate. In an effort to claim Cpm as a better capability indicator I found Cpk would still be better (even if the target is not centered). Thanks for the help.

-Will

That is great news. Learning has occurred and the process is better understood. Customers are protected.

A great way to end the week.

milo