# If I know x-bar, spec limits, and Cpk, can I calculate the control limits?

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#### brgman63

If I know x-bar, spec limits, and Cpk, can I calculate the control limits?

#### Chennaiite

##### Never-say-die
Trusted Information Resource
If I know x-bar, spec limits, and Cpk, can I calculate the control limits?
What are your objectives ? Why do you want to do it ?

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#### Duke Okes

Yes you can, but you'll have to back the std deviation out of the Cpk calculation.

#### Bev D

##### Heretical Statistician
Super Moderator
you also need to know the subgroup size and if it's rational.
but as stated earlier - why would you want to do that?
what good are the control limits if you don't have the subgroup data in time series??
why not just calculate the 'old fashioned' (correct) way from the time series subgrouped data?
doing it in the way you propose is frought with potential error and I dont' see any value in it?

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#### statdoug

As Bev stated, this approach is frought with hazards. I am assuming that you no longer have the data. Without knowing the way the data was gathered, it is difficult to know what sigma(hat), if that was what the Cpk was calculated from, represents.

The formula is simple, |xbar - closest spec. limit|/(3xCpk) yields the original sigma(hat) value.

Divide this by the square root of the sample size you plan to use, and use Xbar +/- 3 * this value.
(note we divided by 3 in the first formula, then multiply by three in the second. Obviously we could leave "3" out completely, but conceptually it is helpful.)

Because of the unknowns involved, without details of how the data was gathered, and how the original sigma value was calculated, these limits should only be viewed as very preliminary. As soon as you have enough data to see how the process is running under the sampling plan that you are using, you should abandon these limits and get ones that are calculated correctly in order to determine what the process is really doing.

Bear in mind, that, without the original data, you can not be sure whether the range was in control in the original data, whether OOC ranges were eliminated or not, how many subgroups were used, and alot of other potential problems. Proceed at your own risk.

#### Jim Wynne

If I know x-bar, spec limits, and Cpk, can I calculate the control limits?
Welcome to the Cove. Where did the Cpk number come from?

#### Bev D

##### Heretical Statistician
Super Moderator
good question! (of course)
there are several critical issues with Cpk:
• is it long term or short term formula?
• which standard deviation was used? within subgroup or total?
• What was the sample plan for Cpk? one lot, 30 consecutive parts, 30 random parts from across multipel lots, multiple subgroups, etc.
• was the process stable when Cpk was calculated?

the control limits are based on an estimate of the between subgroup variation from the within subgroup variation...its not quite as straight forward as the formula statdoug provided - it could be right or it could be wrong depending on which standard deviation was used for the Cpk value.

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#### statdoug

it could be right or it could be wrong depending on which standard deviation was used for the Cpk value.
If the "standard" standard deviation was used wouldn't the term have been Ppk rather than Cpk?