# Questions regarding Cpk Calculation - Should we be using LSL/USL or LCL/UCL?

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#### ejmoska

Hello,

just a small question to which i can't seem to find an answer:

For Cpk calculation, we have:
Target 0%
UCL 2%
LCL -2%
USL 4%
LSL -4%

when calculating Cpk, should we be using LSL/USL or LCL/UCL?

also, if we have out of spec values somewhere within results, should they be left there to display "true" Cpk or moved to another metric, like FPY?

What if the out-of-spec data, jumps to i.e -99%, -30% or 20% this greatly affects mean value, and Cpk no longer shows accurate data. So far we are removing such values which greatly affect mean, but is this really the correct way to go?

Last edited by a moderator:

#### AMIT BALLAL

Super Moderator
For calculating Cpk, LSL/USL should be used.

Did you use control chart to check presence of any special cause prior to calculating process capability? Is your process in control, but out of specification?

Can you share the SPC report, so that the question can be answered properly?

Thanks,
Amit

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#### Bev D

##### Heretical Statistician
Super Moderator
Can you also explain how you are applying the calculation? Are you recalculating every lot, week, month? What is the actual sample size you are using?
Why are you calculating Cpk? Is a Customer requiring it or are you doing it because you think it's the 'right thing' to do?

Cpk is potentially very misleading number if not done properly...

#### Steve Prevette

##### Deming Disciple
Super Moderator
It should be pointed out that you use BOTH the specification limits and the SPC control limits in the Cpk calculation. This is assuming that the SPC chart shows the process is stable. You are basically comparing the spread of the observed variation against the allowed variation, and accounting for if the observed data are "off-center" from the center of the allowed variation (spec).

If your statement "What if the out-of-spec data, jumps to i.e -99%, -30% or 20%" is true, likely the process is not stable, and Cpk does indeed become meaningless. If such "jumps" are actually part of the stable process, then your Cpk is indeed poor. Keep in mind you don't recalculate the mean / UCL / LCL on a whim.

#### Bev D

##### Heretical Statistician
Super Moderator
one caution: the Control limits can be used for comparing the process variation to the specification limits IF the control chart is an I, MR chart for individual data points. We cannot use the control limits from Xbar charts for averages, we would have to calculate the spread of the individual values separately....

we still should still assess stability using a (appropriate) control chart.

#### Steve Prevette

##### Deming Disciple
Super Moderator
one caution: the Control limits can be used for comparing the process variation to the specification limits IF the control chart is an I, MR chart for individual data points. We cannot use the control limits from Xbar charts for averages, we would have to calculate the spread of the individual values separately....

we still should still assess stability using a (appropriate) control chart.

True. Though one could take X-bar Range charts and convert to what would be the individual standard deviation.