# How I calculate Standard Deviation

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• #50090

Brew
Participant

How do I calculate the standard deviation when the USL and the LSL are known ? I would like To see an example if someone has one and is willing to share. This is a new experience for me.

Thanks for any help,
Brew

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#172014

B Kumar
Participant

Hello,
In this case, do you have sigma level. If you know the Sigma level, you can calculate sigma value as below.
Sigma Value = (USL – LSL)/ Sigma Level.
If your data is continuous data
Sigma Value  = (UCL – Mean)/3;
or Sigma Value = (Mean – LCL)/3
UCL and LCL are Upper and lower Control limits.
Suppose, if your data is Attribute data, then
Sigma Value = NORMSINV [ (1 – DPO) +1.5 ]
DPO = Number of defects / Total opportunities for eror.
So, generally USL – LSL = Sigma Level * Sigma Value.
By
Ravi B

0
#172017

sandrine berthet
Member

Not enough
You have to know the Cp to use the equation and to figure the sd

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#172022

aiman farid
Participant

You can’t calculate the standard deviation when only the USL and the LSL are known. As the USL and the LSL are specification spread.

To calculate standard deviation you need real data or the UCL and the LCL as actual  process spread.

Or, when you know the relationship between both (process and specification spread)

The USL and the LSL + capability index Cp (no shift) or Cpk (shifted)

The USL and the LSL + Sigma level (number of standard deviations lying between the mean and the nearest specification limit)
Aiman Farid

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#172154

Bill Fowlkes
Participant

Ravi, this is so wrong.  If it was true that sigma = (mean – LSL)/3, or better sigma = (USL – LSL)/6, then all Cp would equal 1 and everyone would have the same defect rates.  Of course that is not true.
If fact, the USL and LSL should be related to customer requirements, and the sigma to manufacturing varaibility.  So, the correct answer is that you CAN NOT calculate the standard deviation from the spec limits.  Those are two very different things.

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