5. (22 points)

Smith Manufacturing is currently considering using one of three suppliers. For a specific part, Smiths upper specification limit (USL) is 13.8 centimeters (cm) and its lower specification limit (LSL) is 10.8 centimeters (cm).

a) The first supplier, ABC, can adjust its mean but cannot reduce its standard deviation. Its standard deviation is 0.3 cm. What is the range (lower and upper limits) for the mean of the process if ABC wants its process capability index (C_pk) to satisfy at least Smiths minimum acceptable value of 1.33?

b) The second supplier, DEF, cannot adjust the mean of its process which is currently 11.8 cm. However it can improve its standard deviation if necessary. What is the maximum standard deviation () allowed if DEF wants its process capability index (C_pk) to be at least the minimum acceptable value of 1.33?

c) The third supplier, GEF, has a process whose standard deviation is 0.35 cm and the mean of its process is 12.0. Can this supplier meet the customers specification requirements at this time if the customers process capability is 1.33? If it cannot, explain if it is due to a drifting of the mean or too much variability.