Tolerancing based on Cpk Data - Spreadsheet Attached

[gianni]

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?

[Proud Liberal]

Tolerance = ± 4 sigma

[Darius]

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.

[D.Scott]

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

[Darius]

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

[M Greenaway]

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.

[gianni]

Originally Posted by D.Scott

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.

[D.Scott]

Originally Posted by M Greenaway

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.

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