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# Help with Table of Constants and Formulas for Control Charts

S

When using the Appendix E from the AIAG SPC Manual, the subgroup size starts at 2 and continues from there.

Our processes produce discreet quantities and it is challenging (at best) to enter data for a 2-piece subgroup. What should I use for A2 (factors for control limts), d2 (divisors for estimate of standard deviation) and D4 (factors for control limits) when faced with a subgroup size of one ?

Thanks!

A

Re: Table of Constants and Formulas for Control Charts -

Use an Individuals - moving range chart (I-mR) for individual observations.

For the I-mR chart, you can calculate the upper control limit for mR: UCLmR = D4*mR-bar, where D4 = 3.267

And the limits for the individuals are: X-bar +/- 3* (mR-bar/d2), where d2 = 1.128 for n=2

Cheers,

Last edited by a moderator:
S

Re: Table of Constants and Formulas for Control Charts -

How do I calculate control limits with the I-mR chart?

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Adam has the formula in his post, but I will try to make it clearer:

First calcualte the average of the individual points. this is the Center line for the value chart.

Next calculate the moving ranges:
• range of value 1 to value 2
• range of value 2 to value 3
• etc.
you will have 1 less moving ranges than you have values...

Next calculate the average of the moving ranges.

Now the control limits for the value chart:
LCL= Center Line - 2.66*Average Moving Range
UCL= Center Line + 2.66*Average Moving Range
(2.66 is 3/1.1218, this is the "A2" value. 1.128 is the d2 value for n=2; because the moving range is calculated by using two sequential individual values)

the control limits for the Moving Range chart is
Center Line = Average Moving Range
UCL_MR = 3.267*Average Moving Range
(3.267 is the value for D4 for n=2)

Does that help?

S

Bev,

Your response has been helpful. Allow me to plug some numbers into what you've provided in hopes that this will turn on some additional lights for me. I am using SPC software and have the ability to freeze control limits. With subgroups greater than or equal to 2, I used the formulas dictated for the table that's the subject of this thread. The single-piece subgroup size had me scratching my head.

Being that I'm using SPC, however, I already have averages for both individual points (Avg X) as well as the moving ranges (Avg R). They follow in this example:
Avg X: 0.688490
Avg R: 0.000127

Using your calculations, I get the following for UCL and LCL for the value chart:
LCL: 0.68815218
UCL: 0.68882782

My UCL_MR equals: 0.000414909

Please review and confirm my math.