A company is going to introduce a new cell phone. ABC Cell Services is going to sell the phones and has established specification limits of 5.0 ounces and 5.5 ounces for the weight of the phone. The company currently has determined that its phones currently weigh 5.2 ounces.
a) The company wants to have a Cpk of 2.0 or greater (equivalent to a six sigma process), the mean of the process is currently 5.2 ounces and the standard deviation is 0.04 ounces. Is the company capable of meeting the required process capability? If not, is the problem due to the variability or the mean being of the process not being centered?
b) If the company wants to have a Cpk of 2.0 or greater (equivalent to a six sigma process), what is the maximum value of the standard deviation (σ) so that the Cpk of the process indicates that the company can provide the six sigma process (process capability = 2.0)?
c) Suppose that the company is operating at a standard deviation (σ) of 0.025. What is the range on the mean of the process to maintain a Cpk of 2.0 or greater?
d) Suppose that the company can maintain an average weight of 5.2 ounces and a standard deviation (σ) of 0.05 ounces. The company does not believe it can improve on these values. The company wants to see if ABC would be willing to adjust its spec limits rather them keep them at 5.0 and 5.5 if necessary to meet the minimum Cpk of 2.0. What should the company tell ABC that it would need to adjust the spec limits to in order to ensure a Cpk of 2.0 or greater?