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# Range, Standard Deviation, Process Capacity Index

Hart Manufacturing is considering using one of three suppliers. For a specific part, Hart'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, MAT, 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 MAT wants its process capacity index to satisfy at least Hart's minimum acceptable value of 1.33?

B. The second supplier, CAT, cannot justify 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 allowed if CAT wants its process capability to be at least the minimum acceptable value of 1.33?

C. The third supplier, BAT, has a process whose standard deviation is 0.6 cm and the mean of its process is 7.3 cm. Can this supplier meet the minimum requirement (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.

#### Solution Preview

1. Range=Cp*6ơ=1.33*6*0.3=2.394 cm

2. (x bar-LSL)/(3ơ)=1.33
(7.5-6.5)/(3 ơ)=1.33
Ơ=0.25 cm
Or ...

#### Solution Summary

Range, standard deviation and process capacity indexes are examined.

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