Process Capability - Understanding what Process Capability Indices mean

T

ttuyoc

#1
Hello All,

I have a hard time understanding what the process capability indices mean? I hear > 1.33 is ideal but what exactly does that number mean? What if your Cpk is 1.5, 2.0, 3? I understand that process capability measures how well your process performs in relation to the specification limits, but the indices confuse me.

Can someone shed some light on this?
 
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Solinas

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#2
It's basically a comparison of the spread of the spec limits, compared with the spread of your process.

Let's assume your process is a normal distribution, well centered with respect to the spec limits. Your process Cpk is the ratio of the spec spread to the process spread. Divide spec spread by process spread.

A Cpk of 1 means that the spreads are the same. That would be good, but not great. What happens if your process shifts? You start making more stuff out of spec.

A Cpk bigger than 1 means your spec spread is bigger than your product spread. That's the good situation - your process makes stuff within the spec range. If your process shifts around some, you're still in spec. The bigger the Cpk number, the more elbow room you have.

A Cpk less than 1 means your spec spread is LESS than your product spread - and you're making stuff out of spec.

So - a Cpk is pretty much just a ratio:
Spec
--------
Process

In a fraction, if the top and bottom are equal, you get 1 when you divide.
If the top is bigger than the bottom, you get a number greater than 1 (like 6 divided by 2)
If the bottom is bigger than the top, you get a number between 0 and 1 (like 2 divided by 6).

There are, of course, important considerations as far as normality of the data distribution, the centering of the distribution, etc. but I hope this clarifies the basic idea.

Solinas
 

Statistical Steven

Statistician
Leader
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#3
Another way to look at it is that 3*CpkL is the Z score for the probability of out of specification on the low side of the specification. 3*CpkU is the Z score for the probability of out of specification on the high side of the specification. You can then use this information to get PPM and other summary statistics on your process.

Remember that Cpk, Cp, Pp, PpK, Cpm or any other process capability index is a snap shot in time and does not reflect future performance of the process.
 

bobdoering

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#4
Another way to look at it is that 3*CpkL is the Z score for the probability of out of specification on the low side of the specification. 3*CpkU is the Z score for the probability of out of specification on the high side of the specification.
And the key point is that the difference between Cp and Cpk is the attempt by Cpk to determine how "centered" the process is to the specification. If centering is not applicable, then the utility of Cpk is severely diminished (to put it nicely.)
 

Statistical Steven

Statistician
Leader
Super Moderator
#5
And the key point is that the difference between Cp and Cpk is the attempt by Cpk to determine how "centered" the process is to the specification. If centering is not applicable, then the utility of Cpk is severely diminished (to put it nicely.)
You put it very nicely :)

Actually, the best index is the ratio of Cp to Cpk. Closer to one the more centered a process.
 
F

f1guru

#7
just been reading this thread and i am totally new to doing these studies, i used a chart someone on here had recommended and entered my study of 45 parts the tolerance was 16.000 +0.006 and -0.005 mm the company who did the machining of the components managed to hit 15.999 to 15.997 for all components and the cpk was 26 or something!!!! what am i doing wrong as all dimensions were right thru the top of bell curve and in an ideal world these parts could not be better it also said process was not capable please help!!!:(
Can someone point me in right direction for an excel spreadsheet i can use for diameters and perpendicularity
 
F

f1guru

#8
if anyone can help i have studies for perpendicularity and diameters to do but not sure what excel spreadsheet i should use???
 

bobdoering

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#9
if anyone can help i have studies for perpendicularity and diameters to do but not sure what excel spreadsheet i should use???
Start with the diameters - they are the easiest.

What you need is the time-ordered sequence data for starters. It will give you some idea as to whether the gaging has enough resolution, and whether the variation is primarily from tool wear.

Also, what was the size of the lot evaluated, and will it be the typical ongoing size of the lot - or will the lot get larger? Was the process a ground diameter? What did they use to measure the diameter? 11 microns tolerance gets you pretty close to needing a laser mic or good air gage. Do they have a Gage R&R?
 
J

Joelbear5

#10
A Cpk less than 1 means your spec spread is LESS than your product spread - and you're making stuff out of spec.
Solinas
I know this was supposed to be a general overview of Cpk and Cp, but I wanted to point out that even when your Cpk is less than 1 (which means one or both of your upper/lower control limits are outside of the specification limit) that your data values may still be within the specification limits (i.e. - all of your parts still meet engineering conformance).
 
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