Smith Manufacturing, a parts reseller, is currently considering using one of several suppliers.For a specific part, Smith's upper specification limit (USL) is 12.6 centimeters (cm) and its lower specification limit (LSL) is 9.9 centimeters (cm).Smith wants both the process capability ratio and process capability index to be at least 1.10 at the minimum.

a) The first supplier, WEBLE, can adjust its standard deviation but cannot shift the mean of its process. The mean of WEBLE's process is 11.5 cm and the standard deviation is 0.5 cm.What is the maximum standard deviation () of this process if the company wants to ensure that it can maintain a minimum acceptable C_pk?

b) The second supplier, FASTENER, is currently operating with a mean of 11.3 and a standard deviation of 0.38 cm.Can the company meet the customer's specification requirements at this time?If it cannot, explain if it is due to a drifting of the mean or too much variability.

c) The third supplier, BUB, has a process whose standard deviation is 0.36 cm but the mean of its process is not known.BUB says it cannot or will not be able to change the standard deviation of its process.What is the range (the upper and lower limits) on the mean of the process to maintain a C_pk of 1.1 or greater?