Question: You are the manager dealing with a decision to potentially purchase a new machine to cut insoles for the company’s top-of-the line running shoes. You are excited as the company’s goal is no more than 3.4 defects per million and this machine may be the innovation you need.

The insoles cannot be more than + or - .015 of an inch from the required thickness of .250”

You need to determine if you should replace the existing machine which has a Cp value of 1.0

i) If samples from the new machine indicate a mean of .251 with a standard deviation of .006 inch, calculate the Cpk value and determine if the new machine should replace the existing one. If so, why? If not, what standard deviation should the new machine have to satisfy the 3.4 defects per million target.