Can anyone please tell me if there is a way to determine what tolerance is required on a specific dimension to acheive a 1.33 Cpk? Is there a cut and dry method to say, for example: P1 = 4.5 Newtons; to hold 1.33 you will need a tolerance of ____? Or, based on the Cpk result of 0.684 you need x amount more tolerance to achieve Cpk 1.33, based on the sample data. Is there a quick calculation to determine this?

EX. P1 = 4.5 Newtons ± .4 Newtons

What will I have to hold to maintain a 1.33 Cpk?

Tolerance = ± 4 sigma

if USL - Mean < Mean - LSL

Cpk = (USL - Mean)/(3*Sigma) => USL = Mean - Cpk *3*Sigma
and if Cpk=1.33 then USL = Mean - 4 * Sigma

if USL - Mean > Mean - LSL

Cpk = (Mean - LSL)/(3*Sigma) => LSL = Mean + Cpk *3*Sigma
and if Cpk=1.33 then LSL = Mean + 4 * Sigma

So (Mean - Cpk *3*Sigma, Mean + Cpk *3*Sigma)

But still, Cpk depends on the sample size so the calculus get harder and depends on wich estiamate do you like: the maximum or the minimum or not less than a fixed Cpk value and the current Cpk.


:ko:

Here is a simple Cpk worksheet that calculates the Cpk and gives you the estimated tolerance needed to meet a given Cpk.

I hope it will help.

Dave

Dave, nice worksheet, but the calculus of the standard deviation is total variation estimate, desto ppk not Cpk.
:caution:

I thought Cpk was based on the tolerance anyway, hence you need a tolerance to determine Cpk as it is the ratio of the 3 sigma spread to the mean - USL/LSL spread.

However the point about designers actually considering process capability when they dream up a tolerance is absolutely vital. I often think that if they just considered this many of us would be out of work. So much 'poor' quality is designed in through unknown process capability.

Here is a simple Cpk worksheet that calculates the Cpk and gives you the estimated tolerance needed to meet a given Cpk.

I hope it will help.

Dave
Thanks for the spreadsheet. This will help me very much.

I thought Cpk was based on the tolerance anyway, hence you need a tolerance to determine Cpk as it is the ratio of the 3 sigma spread to the mean - USL/LSL spread.

:bigwave: How have you been M?

You are right as usual of course but what we are talking about here is a "reverse capability" used to estimate the tolerance needed to meet a given Cpk in production. The method used is only an estimate and does no more than give you a "ballpark" for quoting a job. I guess you could say this is one of those "tools" we often use that is not strictly accurate. The "Gurus" would frown and the "experts" would lower their eyes but it really works wonders when sales or the customer asks "well, what DO you need?"

Nice to see you again.

Dave

:bigwave: How have you been M?

You are right as usual of course but what we are talking about here is a "reverse capability" used to estimate the tolerance needed to meet a given Cpk in production. The method used is only an estimate and does no more than give you a "ballpark" for quoting a job. I guess you could say this is one of those "tools" we often use that is not strictly accurate. The "Gurus" would frown and the "experts" would lower their eyes but it really works wonders when sales or the customer asks "well, what DO you need?"

Nice to see you again.

Dave

Absolutly. Very good "common sense" tool.

Hey gang. . .

Am I missing something here?? :confused:

Why are you talking about Cpk for setting a tolerance when Cp is the real measure of the processes capability irregardless of the centering. Centering is an adjustment. You can also look at Cr which is the inverse of Cp.

Cp = (Blue Print Tol. / 6-Sigma), The higher the better.

Cr = (6 Sigma / Blue Print Tol.) = % of Blue Print tolerance, The lower the better.


IMHO, I think you would be better off looking at Cp as the basis. If you want to look at it another way, take your 6-sigma spread (From your process capability study), and multiply it by 1.33. Now you will be challenged to hold the process on target to maintain it. Shoot for 1.67. Ford didn't pick it by chance. That will give you room for natural variation and process movement over the long haul.

FYI

At 95% Confidence with a minimum Cpk of 1.33 means Cpk(50 sample)= 1.67363
At 95% Confidence with a maximum Cpk of 1.33 means Cpk(50 Sample)=1.09463
At 95% Confidence the not less than Cpk of 1.33 means Cpk(50 Sample) =1.60779
At 90% Confidence with a minimum Cpk of 1.33 means Cpk(50 Sample) =1.60779
At 90% Confidence with a maximum Cpk of 1.33 means Cpk(50 Sample) =1.12801
At 90% Confidence the not less than Cpk of 1.33 means Cpk(50 Sample)= 1.53799
:smokin:

FYI

At 95% Confidence with a minimum Cpk of 1.33 means Cpk(50 sample)= 1.67363
At 95% Confidence with a maximum Cpk of 1.33 means Cpk(50 Sample)=1.09463
At 95% Confidence the not less than Cpk of 1.33 means Cpk(50 Sample) =1.60779
At 90% Confidence with a minimum Cpk of 1.33 means Cpk(50 Sample) =1.60779
At 90% Confidence with a maximum Cpk of 1.33 means Cpk(50 Sample) =1.12801
At 90% Confidence the not less than Cpk of 1.33 means Cpk(50 Sample)= 1.53799
:smokin:
Could you explain please. I'm not that statistically literate, but I don't understand this at all :confused:

Bill

:caution: Size does matter, a sample size of 50 means a lot of possible variation on the capability index.

A value of Cpk of 1.33 obtained with 50 points at a degree of confidence (ie. 95%) could be 1.096 to 1.564 at the next 50 points and still be the same (no change in the Cpk).




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