# When to use Cpk or Cp to determine the six sigma value?

Six Sigma – iSixSigma Forums Old Forums General When to use Cpk or Cp to determine the six sigma value?

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• #28520

Kiong
Participant

Hi All,
Assume that a particular process is statistically stable and assuming that the calculated Cp=0.75 and the Cpk = 0.33 what should be the sigma value? Based on six sigma table (with 1.5dev drift), which sigma value should I choose, using Cp or Cpk?
Thks
Kiong

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#71214

John Dubuc
Participant

Looking at the fomulas, if it’s important that the process mean be at a specified level use Cpk if not use Cp.

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#71216

Erik L
Participant

Kiong,
If you review the definition for the calculation of the Sigma Level of a process, “The number of standard deviations that exist between the central tendency of a distribution and the closest of the Upper of Lower Specification limits,”  you should see that the correct formula would be Cpk.  In the best case scenario, CP and Cpk will be equal if it’s perfectly centered relative to the VOC.  Cp is calculated, without regard to the central tendency of the distribution and asks whether a process “could” be capable of meeting the requirements of the customer. Therefore, calcualting from Cp will give quite erroneous numbers for the sigma level of the process.  If the process, that you’ve mentioned is in control, and the Cpk value is too low you might want to look to DOE as a mechanism to identify the input factors that will shift the distribution more towards the nominal value of interest.
Regards,
Erik

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#71218

Sridhar
Member

Hi,
Always use Cpk for six sigma calculation. When your process is at target then both Your Cp and Cpk are same. Cpk is always less than or equal to Cp. Use Cpk for six sigma calculation.
thanks
sridhar

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#71222

Keshri
Participant

Cpk upper and lower both arew required to calculate the sigma value.

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#71243

banerjee
Member

Does not matter which one you use.If you are tackling a centering problem, use Cp.If its a variation issue,use Cpk simply because it tells you what the minimum variation in your process is and how many standard deviations can be fit between the spec limi wich is closest to the mean.The default is howver Cpk most of the times.As long as you know where the center and spread of the process is and you know what to improve, the problem is solved.

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#71299

Dr. Dave Stimley
Participant

Here is how it is done:
You will need the values of CPU and CPL to start.
Then:
1. Compute Zu = 3xCpu and Zl = 3xCpl
2. Find the fraction defective for each of the Z values from a Z table and add them together.
3. Multiply step 2 by 1,000,000 to get equivalent DPMO
4. From the DPMO you may find the sigma from a conversion table or graph.Example:
CPU = 1.33 and CPL = .667 (Note: Cpk is the lessor of CPU or CPL)Then
1. Zu = 3×1.33 = 4 and Zl = 3x.667 = 2
2. Fraction defective for z = 4 = .0000317
Fraction defective for z = 2 = .0228000
Total Defective = .0228317
3. Equivalent DPMO = 1,000,000X.0228317 = 22831.7
4. Sigma for DPMO 22831.7 = 3.50This calculation assumes that you have taken a fairly large sample from a stable process.

Dr. Dave Stimley
Master Black Belt
Scientific Atlanta

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#71317

Rui Cardoso
Member

I’ve seen several times in the automotive industry several KPC caractheristics that the goal is to minimize, like leaks for instance on actuators. In this type of caractheristics the process should run near the low limits, therefore the cpk will be bad, but maintaining a tied variation the cp will be good. In my opinion you should use cpk when your goal is the average of the process and the cp every time your intention is tu run near the upper or lower limits (maximize or minimize the caractheristic). Rui Cardoso – Portugal

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#71339

Ropp
Participant

Cp is only a measurement of your variation with respect to the width of your specification, but does not recognize the location of the specification as boundaries.  Cpk is concerned with both the width and location of the upper and lower specification.  If you are trying to measure Sigma performance, you will use Cpk as others have mentioned in their reply.
Best example I’ve seen yet was related to a field goal kicker.  If you record the placement of the kick each time with respect to the goal posts, how frequently does he kick it between the left and right goal posts – that’s Cpk.  If you notice that he is kicking it 10 yards to the right of the right post every time, consistenly in a range the same width as the goal posts, that is your Cp measurement.  In this example Cp would be very good as he is very precise but not accurate, but Cpk would not as none of the kicks are within the boundaries of the upper and lower spec (left and right goal post) – he is not accurate.
I hope this helps.

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#71344

vin
Member

Has anyone ever used Cpm instead of Cp or CpK? My understanding is that this is an even stricter metric than CpK since the “sigma” used in the calculation is not standard deviation around the process mean. Instead, it calculates the deviation around the nominal target and uses that “deviation”. Minitab provides a value for Cpm when you do a process capability study, assuming you provide a nominal target…

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