Calculation/math to find 1.33 Cpk

J

jager

#1
Is there a formula that will give me what tolerance I need to obtain 1.33 Cpk? For example, if my spec is .250 +/- .005 and the Cpk comes out at 1.15 and I need to be at 1.33, what tolerance do I need to obtain 1.33? Do I need +/- .006, or +.006/-.005, or +/-.007, or ???
I can go into our SPC software and put in different tolerances until the Cpk comes up 1.33, but I would like to know the math behind that. Is there a formula? Can anyone help me out? Thank you
 
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Kales Veggie

People: The Vital Few
#2
= tolerance range * 1.33 / 1.15 (increasing your tolerance range)

By careful by arbitrarily increasing your tolerance range. Your tolerance must be based on what the application needs. Not the manipulation to get a good CpK.
 
J

jager

#3
We are to give a customer the tolerance needed to get to 1.33 and would like to know if there is a formula, rather than just trial and error in our SPC software to find it. Thank you for your reply.
 

CarolX

Super Moderator
Super Moderator
#5
We are to give a customer the tolerance needed to get to 1.33 and would like to know if there is a formula, rather than just trial and error in our SPC software to find it. Thank you for your reply.
jager - I feel your pain - I just went though a similar exercise.

There are a number of spread sheets in excel available on this site - but you will need to plug in your data and then adjust the tolerances to achieve your 1.33.

And a little :topic:

from Kales Veggie

By careful by arbitrarily increasing your tolerance range. Your tolerance must be based on what the application needs. Not the manipulation to get a good CpK.
Many times - application needs are unknown and an abitrary number is thrown at the feature.

As I just went thru this with a customer - I was asked to provide a "shop capability" study of different features and had to report back what tolerance they should use to achieve 3S, 4S, and 6S. :frust::frust:.

I call this moving the bar higher so all can pass.
 
J

jager

#6
Thank you. We were asking for the formula so we could report back quickly to a customer without going through the trouble of plugging different tolerances into the SPC software until we got to 1.33. If we had the mathmatical formula, we could just use a calculator and get the tolerance quickly. If you know of any other places that would have this, I would appreciate the info. Thanks again.
 

Jim Wynne

Staff member
Admin
#7
Thank you. We were asking for the formula so we could report back quickly to a customer without going through the trouble of plugging different tolerances into the SPC software until we got to 1.33. If we had the mathmatical formula, we could just use a calculator and get the tolerance quickly. If you know of any other places that would have this, I would appreciate the info. Thanks again.
I don't have time to test this myself, but there's an online calculator here that might help.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#9
do you know your process standard deviation?

since the formula for Cp (or Pp) = tolerance / 6SD, if your process is centered about the target the tolerance = 6SD*1.33

if your process isn't centered, then just manipulate the formula for the side of the target that the average lies on.
 
J

jager

#10
Thanks, how about for Cpk? We can manipulate our upper or lower spec limit in the software and creep up on the 1.33 Cpk that we want.
 
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