Relation between sigma level and Cpk
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 This topic has 8 replies, 7 voices, and was last updated 19 years, 11 months ago by Randall Floyd.

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December 14, 2001 at 3:14 am #28380
Hi,
I want to ask whether this is right or not.
Cpk = min ( USLtarget/3*sigma , TargetLSL/3*sigma) as per def.
Sigma level = No.of std. Deviations one can fit in between target and close Specifications limit
= min( USLtarget/Sigma , TargetLSL/sigma)
from the above two equations we can say that
Sigma Level = 3* Cpk
Can anybody tell me whther this is right
thanks in advance
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0December 14, 2001 at 5:02 am #70545Sridhar,The sigma value for process data is just the calculated zvalue between the process mean and the nearest spec limit, or {(xbarLSL)/SD, (USLxbar)/SD}min. Cpk is typically calculated as: {(xbarLSL)/3SD, (USLxbar)/3SD}min, or 1/3 the zvalue. Therefore, given Cpk=1/3(zvalue) or 1/3(sigma value), then 3Cpk=sigma value. Your derivation seems reasonable. For any estimates of ppm using this relationship will require the individuals data to distribute normally.Ken
0December 14, 2001 at 6:36 am #70546If the target is the center of a two sided spec sigma level = 3 * Cp not 3*Cpk.Only in a one sided spec or off center target does sigma level = 3 * Cpk.
0December 14, 2001 at 7:30 am #70548Hi stan,
If the target is centered then both Cp and Cpk equal is int it right?
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sridhar0December 14, 2001 at 9:43 pm #70566
Jim JohnsonParticipant@JimJohnson Include @JimJohnson in your post and this person will
be notified via email.Based on my experience and what formal information I have your statement is correct. It is important to remember the considerations that Ken points out.
0December 14, 2001 at 10:02 pm #70567Additionally for the Cpk calculation it it wise to have a process that is exibiting control. If that isn’t present then the estimate for the standard deviation could be dramatically impacted.
Regards,Erik0December 14, 2001 at 10:09 pm #70569Stan,Thanks for your input, but if I remember correctly Cp=(USLLSL)/6SDwithin. That calculation does not allow one to readily equate the zvalue to Cp. As we both remember Cp provides an estimate of the ratio between the requirements(tolerance width) and process width. In essence, Cp is the number of histograms bounded at +/3SD that can fit within the specifications. While this is useful information in determining the “potential” sigma value for the process it does not provide information for determining the actual sigma value. To make this estimate you need both the grand average for the process and the computed Cpk. Additionally, SRidhar’s point is well taken. When the process average is centered within the specifications Cp is equivalent to Cpk. Therefore, either could be used to estimate the sigma value, but again the terms in Cp do not allow this calculation to be done… Ken
0December 16, 2001 at 3:54 am #70590
Dr. Shree NanguneriParticipant@Dr.ShreeNanguneri Include @Dr.ShreeNanguneri in your post and this person will
be notified via email.Yes Sigma Level short term is = 3* Cpk.
Dr. Shree0December 17, 2001 at 8:48 pm #70630
Randall FloydParticipant@RandallFloyd Include @RandallFloyd in your post and this person will
be notified via email.This is true only when using Short term data. If the you are using Zlt the conclusions need to be shifted by +1.5.
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