Cpk = 1.33 if control limits are +/- 3 sigma - True?

A

Annette

A statement has been made in our company that if the control limits are set to +/- 3 sigma and the data is in control then the Cpk is 1.33. Is this correct?
 

Tim Folkerts

Trusted Information Resource
Two comments. First, Cpk is determined by spec limits, not control limits. You are certainly free to set the spec limits to +/- 3 sigma, but it is a somewhat backwards approach. You would basically be saying you want the part to be a good as you are able to make it, rather than good enough to meet some desired level based on the use of the part.

Secondly, by definition, Cpk = Z(min)/3. In your case, Z(min) = Z(upper) = Z(lower) = 3, so your Cpk = 3/3 = 1.0

You need to have the spec limits at +/- 4 sigma to be at Cpk=1.33


Tim F
 
A

Annette

Thanks for your input. This is the thinking behind this. If the control limits are set to +/- 3 sigma and all data is within the control limits then the Cpk meets 1.33. They want to be able to look at the control chart only instead of looking at the Cp and Cpk on the other screens.
 

Steve Prevette

Deming Disciple
Leader
Super Moderator
Annette said:
Thanks for your input. This is the thinking behind this. If the control limits are set to +/- 3 sigma and all data is within the control limits then the Cpk meets 1.33. They want to be able to look at the control chart only instead of looking at the Cp and Cpk on the other screens.

I am going to chime in with Tim on this one. There is absolutely no logic that supports your Cpk is any given value only knowing what the control chart results are. Now, if you tell me that currently the specification works out to be at 4 standard deviations from the average, then yes, as long as you stay "in control" (and there are other criteria for "in control" rather then ONLY points within the control limits) then you would indeed be at a 1.33.

This is an advantage of charting and analyzing using Excel - if this was an Excel chart, you could have the Cp and Cpk calculated on the datasheet, and then automatically link to that cell and put the Cp and Cpk values on the chart (using the concatenate command helps to put a data block on nicely). For example, on the attached chart they wanted to know the FY and CY to date rates.
 

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A

aliasJohnQ

Question for you: If the customer wants a 1.55 cpk, yet we are struggling to provide a 1.33 on just 30 parts, what can I do to increase my cpk? My parts are within the tolerance of +-.001 already. If I widen out the tolerance, I get a better number, but the customer doesn't want that. What's next?
 

Stijloor

Leader
Super Moderator
Question for you: If the customer wants a 1.55 cpk, yet we are struggling to provide a 1.33 on just 30 parts, what can I do to increase my cpk? My parts are within the tolerance of +-.001 already. If I widen out the tolerance, I get a better number, but the customer doesn't want that. What's next?

Reduce the variation in the process. Standard Deviation comes down, Cpk goes up.

Allow me to point out that Customers are way too obsessed :mg: with capability indices.

Stijloor.
 

Jim Wynne

Leader
Admin
Question for you: If the customer wants a 1.55 cpk, yet we are struggling to provide a 1.33 on just 30 parts, what can I do to increase my cpk? My parts are within the tolerance of +-.001 already. If I widen out the tolerance, I get a better number, but the customer doesn't want that. What's next?

There is a persistent and firmly entrenched myth about 30 pieces being some kind of magical quantity, and that you can measure them without regard to chronological considerations or knowing whether they're representative of a mature running process, and develop a meaningful Cpk number. Not possible, unless you're extremely lucky.

There are three ways to increase the Cpk result, one of which--lying--is often resorted to when customers are unreasonable. I don't endorse this approach, of course, so you're left with the other two: expand the tolerance band or improve the process. This is assumes, of course, that there is no voodoo math involved.

With tolerances of ±.001", you also need to make sure your measurement system is capable. If you're eating up half of the tolerance with measurement error, you're never going to get where you need to be.
 
A

aliasJohnQ

Thanks to all. I agree lies created by some of the quality people out there is not right, and if you can't change the tolerance, make the part better. We are struggling with using all of the tolerance now, but maybe a gun to the head of the operator might do the trick.........................BOOM!
I guess that didn't work.........Another volunteer please!
 
A

aliasJohnQ

Sorry for those who take offense. I was brought up with Monty Python, so anything can happen!
 
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