# Attribute Charting - Where does Cp and Cpk come into the equation?

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#### mike101338

Let me start by saying statistics is something fairly new to me. Let me give some background on how we inspect to make sure I am moving in the right direction.

All inspections we perform is on a pass / fail method. We track our bad product as defective, not defects. Run quantities and sample size quanities are variable.

I am using a p chart to track the data. Once graphed I can show stability. I am struggling with how I demonstrate capability. Is this where Cp and Cpk come into the equation? If so, how?

Defining what the USL and LSL is an unknown to me. I am assuming the LSL is 0, as you can not have less than 0 defects. However when I enter this into the Cpk analysis it shows that I am out of spec on the low side. Not possible as 0 defects is perfect, not out of spec. When I enter the USL, I have chosen 3 percent (not the goal, but anything lower at this time would turn people off to SPC). In order for me to attain a Cpk of 1.33 with 3 percent defect I have to attain a sigma level of greater than 4, with a DPM of 30, which is obvoisly not 3 percent. Have I not entered data correctly somewhere or have I made a mistake somewhere else?

Any advice anyone can give me is greatly appreciated.

Mike

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#### ben

Since there are no specification limits for attirbutes, attribute data cannot be used to calculate a Cpk value.

However, you might try calculating the equivalent Cpk.

For example, say your average fraction nonconforming (p-bar) is .00023 or .023%.

Find .00023 on the Z table, which gives you a Z score of 3.50.

Divide 3.50 by 3 for an equivalent Cpk of 1.16.

To hit an equivalent Cpk of 1.33, you will need a maximum defect rate of around 64 per million.

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#### mike101338

Thanks for your advice Ben. Can you tell me where I can find a z table. I have one, but it leaves large gaps in the percentages. If I am going to use this with any regularity then I need a chart with greater detail.
Thanks,
Mike

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#### Bill Ryan - 2007

I messed something up posting the link but if you copy the address and paste it in the search line it works.

Sorry,
Bill

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#### Ravi Khare

Z table

If you have a copy of MS Excel handy, you could get the z score of any value at a fine resolution. There are 3 functions related to Normal Distributions within Excel.

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