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Help with Table of Constants and Formulas for Control Charts



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 [1]?



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


Last edited by a moderator:


Re: Table of Constants and Formulas for Control Charts -


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

Thank you for your response.

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?



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.

Thanks for your help.

Best regards,


Quite Involved in Discussions
shadowjade, your calculation looks ok if the moving range is calculated OK. I have a question..

Does your data points are the most outside of control limits but your range chart looks OK?, the small number you have as moving range makes me think on an automated sampling system and short period of time between samples.
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