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## SPC for big subgroups

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Guest user Created:   Jan 26, 2021 Last commented:   Jan 27, 2021

# SPC for big subgroups

Hello. I have been working with SPC Xbar-R charts, for measurements samples sizes from 1 to 7 .

Now I have a situation that I am not sure how to handle: In a new process we got, there is a measurement machine that performs thickness measurements from one sample and the result we got (from 30K-10K measurements) are Average, Max, Min.

I was asked to use SPC to keep track of the process performance using this three data. I am a little bit confused since the sample from I got the three statistics (Avg, max and Min) is really big so I cannot apply the typical SPC ideas.

First, I tried to use this three data for a Xbar-R chart, but it is clearly wrong since the sample I am using (3 data) comes from a bigger sample (10K-30K). I was thinking to use Xbar-S chart, but I am afraid it will be the same problem.

Thank you very much in advance.

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Fırat İnceli Jan 27, 2021

You can use an X-R card. You can use the number of subsamples from 1 to 5 when using this card. For example, if your sub-sample number is 3, you can fill the card with a total of 3X25 = 75 values, or if your sub-sample number is 5, 5X25 = 125 values in total. As you know, d2 constant changes according to the number of subsamples. For this, you can use the SPC rev 2 blue manuals published by AIAG.   Normally, many companies use excel for this card. As you know, excel calculates itself with formulas. The X-S card can also be used. For this, the number of subgroup samples should be more than 5.

For the X-R card, I have specified the formulas used below:

X mean= (X1+X2...........X25)/25

R= X max-X min

R mean= (R1+R2........R25)/25

S(standard deviation)= R mean/d2

The d2 constant changes according to the number of subsamples. For example, if the subgroup number is 3 then the d2 constant is 1,69. If the subgroup number is 5 then the d2 constant is 2,33, as you can see on this screenshot: https://i.imgur.com/iCmdZvN.png

Cp (Product Capability)=  ( Upper Speciation Limit-Lower Specification Limit)/6xSCpk= (Upper Specification Limit-X mean)/3xS or (X mean-Lower Specification Limit)/3xS

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