What is the correct formula for calculating part variation (PV)?

[Robert O'Brien]

I have conflicting references on the formula for calculating part variation (PV) on a gage R&R study. The formula given in the CQE handbook is as follows:

PV = grand average range/d2

Grand average is obviously the average range among all appraisers and d2 (which I’m slightly confused by) is from the constants for control charts table. Is this correct?

My second conflicting resource is as follows:

PV = grand average range x K3

I’m not sure where K3 comes from. I’m guessing it is obtained from the MSA manual, which unfortunately I do not have.

Can anyone provide me some insight on the correct formula for calculating PV?

Best regards,
Rob O'Brien

 

[Atul Khandekar]

Not conflicting really...

K3 = 1/(d2*) and PV=Rp*K3.

PV-stdev is estimated from range of just one subgroup - Range (Rp) of one subgroup containing part averages. Part avearge for each part is calculated from all readings by all appraisers for that part.

The factor d2* is used in place of the standard control chart factor d2. The d2* is a kind of corrected factor when you want to estimate stdev from relatively few subgroups. If you search the forums, you will find some discussion and references about the d2_Star (d2*) factor.

As with d2, the values of d2* depend on the subgroup size (no of parts, in this case):

SG Size 5 -> d2* = 2.48124
SG Size 6 -> d2* = 2.67253
SG Size 7 -> d2* = 2.82981
SG Size 8 -> d2* = 2.96288
SG Size 9 -> d2* = 3.07794
SG Size 10 -> d2* = 3.17905
and so on... These values are tabulated in the MSA manual. You can also find these in the book "Quality Control & Industrial Statistics" by AJ Duncan.

Hope this helps.

 

[Robert O'Brien]

Thank you

Hello Atul,

I never thanked you for your response, for that I apologize. It was very helpful and beneficial to my understanding.

Thank you and regards,
Rob

 

[Atul Khandekar]

Rob, glad to know it helped...and no need to apologize please..

Rgds,
-Atul.