# Blackburn Engineering, a parts reseller in Nashville, is current

Blackburn Engineering, a parts reseller in Nashville, is currently considering using one of three suppliers. For a specific part, Blackburn’s upper specification limit (USL) is 8.8 centimeters (cm) and its lower specification limit (LSL) is 6.5 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 (Cpk) to satisfy at least Blackburn’s minimum acceptable value of 1.33?
b) The second supplier, DEF, cannot adjust the mean of its process which is currently 7.5 cm. However it can improve its standard deviation if necessary. What is the maximum standard deviation (σ) allowed if DEF wants its process capability index (Cpk) to be at least the minimum acceptable value of 1.33?
c) The third supplier, GEF has a process whose standard deviation is 0.6 cm and the mean of its process is 7.3 cm. Answer the following:
• Can this supplier meet the minimum Cpk of 1.33? Explain
• If the supplier cannot meet the minimum Cpk, explain if it is due to a drifting of the mean or too much variability or both.

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