Xbar - R Control Chart taking into account the Probability Limit

[jp519]

How do you construct the Xbar - R control charts taking into account the probability limit (alpha = 0.002)?
All help is appreciated.

 

[Stijloor]

How do you construct the Xbar - R control charts taking into account the probability limit (alpha = 0.002)?
All help is appreciated.

Can someone help this new Member?

Thank you very much.

Stijloor.

 

[reynald]

Can someone help this new Member?

Thank you very much.

Stijloor.

Well here is my take on this:

for Xbar R, control limits are given as:
Limits = Xbar +/- A2*Rbar

now A2 is actually equal to 3/[d2*sqrt],
where:
-- d2 is a constant that can be taken from SPC tables,
-- n is your subgroup size
-- 3 is the Z from normal distribution set such that alpha level is very small

There is where alpha level comes in. At alpha = 0.002 or (0.001 at each tail), Z is equal to 3.09025.
Factor that into the equation yields:

Limits = Xbar +/- 3.09025*Rbar/[d2*sqrt]

Note: based on discussion from
Statistical quality control By M. Jeya Chandra 8.3.1.1

Regards,
Reynald

 

[Bev D]

hmmm. mathematically correct, but technically a bad answer as SPC is not intended to be some 'exact' probability test, nor is it based on teh Normal distribution...

Reynald answered the OP's exact question, (I think - unless the OP just wanted to know which menu items to select and where to enter the alpha data in minitab...

However, this really begs the question: WHY would the OP want to chagne the limit from the 'standard' time tested and proven limits??

 

[diav615]

Like the OP, I would like the answer to this problem.

@ Bev - Is there a way to use Minitab to select the alpha value using the menus?

 

[reynald]

However, this really begs the question: WHY would the OP want to chagne the limit from the 'standard' time tested and proven limits??

I totally agree with this, it's just that I encountered this problem in the academe (as a student) that's why im familiar in the approach. As a pratitioner now though I don't use this because I believe that simplicity is one of the selling points of control charting.

Like the OP, I would like the answer to this problem.

@ Bev - Is there a way to use Minitab to select the alpha value using the menus?

As for this, go to usual control charting menus:
STAT>>CONTROL CHARTS>VARIABLES>>Xbar-R
Then go to "XBAR-R OPTIONS" button:
A.) On the estimate tab-->Select Rbar
B.) On the S-Limits tab, you will see
"Display control limits at this multiples of standard deviation"--> input 3.09
C.) On the test tab, select 1 point > K standard deviations from center line
-->set K = 3.09

Then hit on "ok", then "ok"

 

[diav615]

As for this, go to usual control charting menus:
STAT>>CONTROL CHARTS>VARIABLES>>Xbar-R
Then go to "XBAR-R OPTIONS" button:
A.) On the estimate tab-->Select Rbar
B.) On the S-Limits tab, you will see
"Display control limits at this multiples of standard deviation"--> input 3.09
C.) On the test tab, select 1 point > K standard deviations from center line
-->set K = 3.09

Then hit on "ok", then "ok"

Hi Reynald,

This worked! Many thanks for your help!

 

[Bev D]

Hi Reynald,

This worked! Many thanks for your help!

just because you can doesn't mean you should.

WHY do you want to alter the 'alpha' level? are you a student who is being forced to do this (hopefully only so you see how the math works OR how futile doing it really is). I will repeat: anyone who wants to alter the alpha level doesn't understand SPC and certainly isn't using the approach appropriately. They are only fooling themsleves.

 

[jp519]

Its mainly to see how the math works...
Thanks for all the help!