# The Relationship Between Cp/Cpk and Sigma Level

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- This topic has 9 replies, 6 voices, and was last updated 1 week, 3 days ago by ashish1883.

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- November 21, 2020 at 1:32 pm #250984

ahamumtazParticipant@ahamumtaz**Include @ahamumtaz in your post and this person will**

be notified via email.What if I got Cp/Cpk value is less than zero. but when I calculate level sigma, I got 3.5, is it possible?

and what the relation between Cp/Cpk and Level sigma?

0November 21, 2020 at 4:48 pm #250986

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.Cpk = minimum (USL-mean, mean – LSL)/(3*std)

Therefore, in order for Cpk to be negative your mean will have to either be less than the LSL or greater than the USL.

Sigma = minimum (USL-mean, mean – LSL)/std

Therefore, if the mean is greater than USL then (USL – mean) will be the smaller value and it will be negative which means Sigma will be negative.

If the mean is less than the LSL then the minimum value will be (mean – LSL) which will also be negative which means your Sigma will be negative once again.

Thus, the results that give you a negative Cpk cannot result in a positive Sigma

1November 22, 2020 at 8:05 pm #250988Thanks for explaining this. It was very useful. https://solarpanelcostprice.com.au/3kw-solar-power-system/

0November 25, 2020 at 10:54 am #251029

Chris SeiderParticipant@cseider**Include @cseider in your post and this person will**

be notified via email.Look at the total ppm defective. Translate between Cpk and sigma level…for that one side of the curve.

0November 26, 2020 at 9:48 am #251045

MBBinWIParticipant@MBBinWI**Include @MBBinWI in your post and this person will**

be notified via email.@ahamumtaz – You should go back and research the definitions of Cp, Cpk and Sigma that were provided to you. You should find some verbiage that states something like: Cp is “potential” capability, whereas Cpk is “actual” or “observed” capability. The difference being the location of the distribution in relation to the target and upper/lower boundaries of acceptance. You cannot have a negative Cp, since that definition does not include the location issue (using absolute values). If you use Cp as your measure for Sigma, then you could have the scenario you describe – but this would be wrong.

0November 30, 2020 at 8:39 am #251107

Robert TiptonParticipant@[email protected]**Include @[email protected] in your post and this person will**

be notified via email.Hello –

If you have a negative CPk, it means you have at least 50% Failures, assuming the formula is correct.

The lower the negative CPk, the more Percent failures.

As an Example; Negative 1 CPk would be about 99.7% Failures, to the Specification

Then look at the CP Value. If CP is positive, you probably only need to adjust the mean (X-Bar), to center the process.

It is possible to have a negative CPk, with a positive sigma (Std. Dev.) as the Std. Dev. will always be a positive number.

The CPk value is the Real Calculated Value

The CP Value is a Theoretical Value, Assuming the Process is perfectly centered around the Nominal Dimension.

Hope this helps

0November 30, 2020 at 8:40 am #251108

Robert TiptonParticipant@[email protected]**Include @[email protected] in your post and this person will**

be notified via email.Sigma is the Standard Deviation, not the formula you indicated

0November 30, 2020 at 10:38 am #251109

Robert ButlerParticipant@rbutler**Include @rbutler in your post and this person will**

be notified via email.@[email protected] – One of my pet gripes is the fact that when the folks were developing their terminology for six sigma the took the word “sigma” and applied it to the calculation indicated in my first post. That formula is the formula for the sigma level which has nothing to do with the sigma of standard deviation fame. Unfortunately, a number of programs and a lot of verbiage, both posted and published in the professional journals, insist on shortening the term “sigma level” to just “sigma.”

With regard to this confusion – on the less than worrisome end are posts like our exchange – what can really get interesting is when someone makes a statement about sigma being negative (what they mean is the sigma level is negative) and when someone else, who knows that sigma (as in standard deviation) is the square root of the variance, jumps in and calls the first poster an idiot for trying to claim a negative value for a square root….and so it goes

1December 1, 2020 at 7:46 pm #251149

MBBinWIParticipant@MBBinWI**Include @MBBinWI in your post and this person will**

be notified via email.@rbutler – well said!

0February 21, 2021 at 5:50 pm #252520

ashish1883Participant@ashish1883**Include @ashish1883 in your post and this person will**

be notified via email.If you go by the formulas, Cp cannot be negative , Cpk can be negative when mean is lower than lower spec or higher than upper spec . In that case, Sigma level is also negative. example, for a torque spec limit of 16 to 20 N on a bolt,

Z = ( USL- x bar ) / s

for mean of 23, and usl of 20, std dev of 3,

Z = ( 20-23)/3 = -1

cpku = ( usl – x bar ) / 3s = -3 / 3 ( 3 ) = – 0.33

cpkl = ( x bar – lsl ) / 3s = ( 23-20) / 3 ( 3 ) = 0.33

Cp = ( usl – lsl ) 6s = ( 20 – 16 ) / 6 ( 3 ) = 4/18 = 0.2

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