# calculating Cpk Cp

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• #29099

Sultan
Member

I will appreciate, if some one will calculate the Cpk and Cp for the following case with explanation.
If process mean is 7standard deviation from Upper control limit and 5 standard deviation from lower limit..
Thanks

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#73694

Cravens
Participant

CpK is the smallest distance between the process average the closest spec limit…divided by 3 sigma.  The closest spec limit is 5 sigma away.  Therefore, CpK = 5/3 = 1.66  (You always round variation and capability numbers down so as not to inflate the confidence level in the data)
Cp is the process spread between the Upper and lower spec limits divided by 6 sigma.  So, (7+5)/6 = 2.00 Cp.

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#73698

Mike Carnell
Participant

Syed,
You can’t get there from here. Need the Specification Limits.
Control limits can be anywhere. There is no relationship between Specs and control limits. It is always nice if they are located fairly close together.

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#73704

Participant

Cp and Cpk Calculation:
Hi Syed,
Try Reference: Juran’s Quality Control Handbook  Ch. 16, P. 19-35
Useful pts – to get you going.
Cp =  (USL – LSL)/6s
To determine whether a process, given its natural short-term variation, has the potential capability to meet established customer requirements or specifications. Cp is a ratio of the tolerance width to the short-term spread of the process. Cp does not consider the center of the process. It estimates the “instantaneous capability” of the process.
Cp = 1: The process barely meets specifications. There is a probability that at least 0.3% defects will be produced and even more if the process is not centered.
Cp > 1: The process output falls within specifications, but, defects might be produced if the process is not centered on the target value.
Cp = 2: Represents the short-term objective for process capability. Since Zst = 3 x Cp, we achieve 6s when Cp = 2.
Cpk

Cp = Cpk = process mean is on traget or process is centred.
Cpk = min (Cpl, Cpu)
Cpk considers process centering. Cpk is a ratio of the distance measured between the process mean and the closest specification limit to half of the total process spread.
Therefore, Cp against specific limits, then
Cpl =  (mean – LSL)/3s
Cpu =  (USL – mean)/3s
Cpk = 0: The process mean falls on one of the specification limits, therefore, 50% of the process output falls beyond the specification limits.
Cpk < -1: The process mean is completely out of the specification limits, therefore, 100% of the process output is out of specification limits.
Therefore, now you can utlises your own process sample mean and then real specification limits both USL and LSL, to calculate your Cp and Cpk.
Hope this helps.

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#73706

Peter Wooding
Participant

Syed
There seems to be some vital information missing from youy question – we need to know where the Upper and Lower Specification limits are. Cp and Cpk are all about where your process means and spreads are in relation to the Spec.
Also Upper and Lower Control Limits are necessarily 6 std devs apart, and the mean is halfway (by definition). If your mean is 7 std devs from the UCL and 5 std devs from the LCL then a) the mean is not halfway and b) the control limits are either 2 or 12 std devs apart. The implication of this is that both your mean and your std dev have changed since the control limits were determined – your process is not in control!
First get your process back in control, then establish your current Mean and Std Dev and calculate the indices using;
Cp = (USL-LSL)/(6 std devs)
Cpk = Minimum of [(USL-Mean) or (Mean-LSL)]/(3 std devs)

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#73728

Sultan
Member

Thanks all of you, who answered my questions.

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