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.)

Additional info: You don't assume a 6-sigma efficiency for all queations. You can estimate the process capability (how many sigma) from the values of Cp and Cpk. If the Cp or Cpk is above 2, you say its process capability reached 6 sigma.