# Can I calculate Cpk from Cp and Cr?

D

#### dragonmaster

Not being real good with math, I would like to know if I can calculate CPK form just having CP and CR available.

M

#### Martin

If you send me your e-mail address I can send you an excel file of a capability study. This calculates your Cp and Cpk value in a sec. You just fill in the values (X) and the program calculates the Cp, Cpk, if it's capable and a lot more.

Greetings,
Martin

D

#### Don Winton

Capability Ratio = Tolerance Width/process capability; however i can't make it work out right.

I thought capability ration was Cr = 100/Cp?

Regards,

dWizard

J

#### James Cupello

I would like to respond to dragonmasters original question.

As Don Winton notes: Cp is just the inverse of Cr. Cp is known as process capability. It is simply the ratio of two numbers: A and B.

The numerator in the ratio (number A) is simply the difference between the upper spec and lower spec limits. Obviously I am assuming a two-sided spec limit.

Referring to Sam's post, a +/- spec limit of 0.005 is equivalent to
0.005 - (- 0.005)

or a value of 0.01 for the numerator, not "0."

The denominator (number B) is 6 times the short term estimate of sigma. Lets not get into long-term and short-term estimates of sigma, even though the difference is important. For dragonmasters simple question lets keep it simple.

So we have A/B = 0.01/(6*sigma)= Cp.

Cr = (6*sigma)/0.01

In either case, the answer is not zero.

Cpk is another matter. Cp is a capability index since it measures a processes potential for performance. It is the best one could expect if the process were centered directly between the upper and lower spec limits.

Cpk assumes the process is not centered. In such a case you must calculate two values for Cpk, and use the lesser of the two resulting values.

First we measure Cpk relative to the upper spec limit (USL). Then we measure Cpk relative to the lower spec limit (LSL). The smaller of the two values is the Cpk for the process. The two equations are:

Cpk = (USL - Xbar)/ 3*sigma

Cpk = (Xbar - LSL)/ 3*sigma

Pick the smaller.

If you want to read everything there is to know about measuring process capability suggest Davis R. Bothe's MEASURING PROCESS CAPABILITY, McGraw-Hill, ISBN 0070066523. It runs about \$100, so I hope you really want to know this stuff.

Cheers.

------------------

S

#### Sam

I found this little "quicky" formula in Juran's hdbk.
Capability Ratio = Tolerance Width/process capability; however i can't make it work out right.
I don't understand the Cp - Cr concept;most tolerances I work with are bilateral,such as +/- 0.005, in which case the Cp always comes out "0", unless I'm using the wrong formula.

S

#### Sam

Don, you are correct, but Juran also has the other equation listed in his book.

James, you sre correct. After seeing your response I realized my error; my thoughts were fixated on tolerance rather than USL and LSL. he equation states in the Numerator "USL - LSL", when using tolerance it should be the algebraic sum.

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