CCp : Composite Cp. A new star born (?!)

[cyberspider]

I don't know , how silly this is but first prove it wrong please.

Basis :
1. Cp desirable is 1.33 (i.e. 1.33 x 3 = 3.99 means roughly 4 sigma process). More Cp means you have wider tolerance which you should address or else it can not be that high. Or you are not revisiting your tolerance limits.
2. Root Mean Square deviation

Consider this let's say you want to have a composite measure of Cp for more than one variable say, x1, x2 and so on.... and you have calculated Cp for each of the variable say, Cpx1, Cpx2, Cpx3 and so on....

now applying same principle as we apply to standard deviation we have.

Composite Cp (CCp) = Square Root of { Sum [ (Cpx - 1.33)^2 ] / n }
n = no. of variables...
1.33 = Here it is in place of X bar.

Hey man ! same formula as standard deviation.

Lower CCp means lower deviation (Good) and higher CCp means check your tolerance limits which you might have kept wide open for "ISO" purpose. or you are a proud owner of highly capable process. As you like it.

Same concept could be extended to Cpk.

I may be totally wrong also. But think about telling your boss CCp when asked about health of process and getting a pat (or slap ??). Try at your own risk.

Can anyone try extending the concept ??

 

[Marc]

Anyone have any comment(s) / input on this one?

 

[cncmarine]

please clarify "desirable" cp?

 

[Dave Dunn]

Based on the formula you give, and assuming I'm doing my calculations correctly:

Composite Cp (CCp) = Square Root of { Sum [ (Cpx - 1.33)^2 ] / n }

Let's assume you want to composite 3 dimensions with the following Cp's
1.33
1.00
10.00

1.33-1.33=0
1.00-1.33=-.33
10.00-1.33=8.67

squared:
0^2=0
-.33^2=.1089
8.67^2=75.1689

summed: 0+.1089+75.1689=75.2778
divided by number of variables=25.0926
square root=5.0093=CCp

A couple things show up as problems to me while doing the calculations.

First, note that in the case of a 1.00 Cp, the negative value received after subtracting the 1.33, when squared returns a positive value of .1089. This is the same result that you would get if you input a Cp of 1.66, so in effect the calculation for any input Cp less than your target 1.33 returns an incorrect value.

Secondly, the result of 5.0093 shows that the 10.00 Cp completely obscures the fact that you have one dimension barely meeting the 1.33 Cp requirement, and one that isn't close to being capable. Combining dimensional capabilities into one calculated value like this doesn't give an accurate picture of the problems in a part or process. An analogy could be a car with an engine that produces 300 horsepower, stopping distance of 50 feet, and can pull 1.5 g in cornering, but doesn't have seats. Factor everything together into one value and you can say that, yes, overall it's an absolutely spectacular car, but that value does not indicate that the car has a fundamental flaw.

Regarding Cp and Cpk, higher results don't indicate that you need to address your tolerances. It simply means that your process has the capability of producing parts within the tolerances required for the dimension. High Cp and Cpk is good.

Quite the opposite is true. If you have a low Cp or Cpk, you need to address your process and improve it so that it will capably produce within the specifications. If that can't be improved, then you need to discuss with your customer whether they're willing to deviate the tolerances.

 

[Tim Folkerts]

I was starting to write a response, but then I remembered this thread:
Does anyone know the conception of "Plant Cpk average"?

You might check there.

In my own opinion, your score over-empasizes 1.33 as an ideal and over-emphasizes big numbers in the composite. I can think of one or two ways to improve those characteristics, but check the other thread first.

Tim F

 

[cyberspider]

Tim,

Checked the thread. I sincerely thank every one who have taken interest on this thread. I agree that it over emphasis on 1.33 but that is for reference sake.

However, let's say we are operating a process with different parameters, sum of variance (i.e. total of sqare of standard deviations) may give fairly good approximation of the performance.

I mean Total Variance = Sum of (Variances). Your opin please.

Any way, this is an idea on deriving some composite measure of the system performance. And I am not upto anything to prove but this may induce some more idea and concept. You see, "An idea may change your world".

By the way, can any one suggest some alternate to our good old "Cp
family" (Cp,Cpk,Cpu,Cpl)? . Hopefully the alternate should have capability to get composited.

Thanks,

 

[Statistical Steven]

Years ago I worked on the idea of a composite Cpk and Cp index. The basic approach is to convert each factor's Cp or Cpk to PPMs. Average PPMs (weighted if you want to give more weight to 1 factor) and convert back to Cp or Cpk.

The problem with Cp is that it does not use the mean or target to determine if you are centered. So for that index we had to assume a centered process, and called it "Best Case Cp"

I always stressed that Cp is the best possible capability, while Cpk gives the current state of the process. It is actually the ratio of the two that tells you the most. That is, if the ratio is 1 you are as capable as the possible without additional management intervention (read that resources).

Thanks

 

[qualitygoddess - 2010]

By the way, can any one suggest some alternate to our good old "Cp
family" (Cp,Cpk,Cpu,Cpl)? . Hopefully the alternate should have capability to get composited.

Thanks,

Just a dumb question, but is Cpmk part of the good old family? This calculation does take into account the target value. I know I found reference to it in a statistics book by Ryan.

 

[Darius]

Just a dumb question, but is Cpmk part of the good old family? .

Cpm and Cpmk are 2nd. generation index, and IMHO they are from 1994-1996 aprox, Cp and Cpk are from 80th's (but not sure).