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# Computing CP and CPK (Means)

Proper smoking of meat requires maintaining a smoker temperature in the range 200 to 225 degrees Fahrenheit. Suppose the temperature in my smoker currently varies around a mean m = 210 degrees, with standard deviation s = 4 degrees.

1.Compute Cp and Cpk for this process and interpret. (What does each ratio tell you?)
2.Leaving the mean at 210 degrees, what standard deviation is required in order to have my process Cpk = 1.33? What standard deviation is required to have Cpk = 2.0?
3. Suppose the process mean could be centered between the specification limits. Now what standard deviation is required to have Cp = 1.33? What standard deviation is required to have Cp = 2.0? (Note, when the mean is centered between the specification limits, Cp and Cpk are equal.)

#### Solution Preview

Let's summarize the information that we are given:
USL = 225
LSL = 200
m = 210
s = 4

Note the following formulas for Cp and Cpk:

Cp = (USL - LSL)/(6s)
Cpk = min{ (USL- m)/(3s), (m - LSL) /(3s) }

1. We can compute Cp and Cpk using the given information and the formulas.
Cp = (225 - 200) / (6*4) = 1.04
Cpk = min { (225-210)/(3*4) , (210 - 200)/(3*4) } = min {1.25, 0.83 } = 0.83

Cp tells that if we assume our mean to be centered within the ...

#### Solution Summary

The expert computes the CP and CPK means. The expert interprets and processes.

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