# Standard Deviation Selection on Control Charts - Minitab "pooled deviation"

S

#### stm08007

Hello,

I know there are tons of articles related to this, but I'm still having trouble understanding..

I want to know why the standard deviations given on the capability charts (within and overall) are very different than the standard deviations that should be used for control limit purposes..

To be more specific-
I used the data from below (I apparently cant post links since I dont have 10 posts-- do a google search for the following):
The Estimated Standard Deviation and Control Charts | BPI Consulting

This outlines 3 different ways to determine the STD to use for control limits.. When I input this data and use the control chart option in minitab, I see minitab uses "pooled deviation" as their default. However, if I do capability analysis on the same data, the "within" and "overall" standard deviations they spit out are different than all 3 of the STD options given in the link above (pooled, average of subgroup ranges, average of subgroup variations).

Any input would be much appreciated!

#### Miner

##### Forum Moderator
Staff member
I was able to duplicate the 1st and 3rd results from the data you referenced and was also able to duplicate those results using the Within StDev from the capability analysis. The Overall StDev uses a completely different method, not covered in your referenced article. That method is the same one you probably learned in high school where you calculate the overall standard deviation without regard for subgrouping. This approach should never be used in the context of a control chart.

S

#### stm08007

interesting.. so you are saying, for control chart purposes, if using the capability analysis, you should always use the "within" to calculate your control limits?

Can you briefly explain why that is so? (I believe I've seen the overall used in the past)

Also (and this I hope I can formulate properly)- to use the formula
sigma-Xbar= sigma/sq.rt., what would I use for the sigma? This is if I want to get the standard deviation of the sample average

This is in my stats book to easily calculate control limits... With the data in the link you used, would sigma be the "overall" standard deviation, and then I divide by square root 30?

Not sure why this is confusing me so much!

#### Miner

##### Forum Moderator
Staff member
Start with reading Donald Wheeler's The Right and Wrong Ways of Computing Limits.

The key takeaways are:
• Control limits are always based on "Within subgroup" variation
• Short term capability (Within, Cp/Cpk) is also based on "Within subgroup " variation
• Long term performance (Overall, Pp/Ppk) is based on the overall variation (high school formula)

Be cautious when using 3rd party software as some violate these rules. Minitab does use the correct approach, but provides multiple options for special cases. These options can allow novices to unwittingly use the wrong approach when they stray from the default settings.

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