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Question 10.9: A process has a mean of 9.20 grams and a standard deviation ......

A process has a mean of 9.20 grams and a standard deviation of .30 gram. The lower specification limit is 7.50 grams and the upper specification limit is 10.50 grams. Compute C_{pk}.

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1. Compute the index for the lower specification:

\frac{\text{Process mean}-\text{Lower specification}}{3\sigma}={\frac{9.20-7.50}{3(.30)}}={\frac{1.70}{.90}}=1.89

2. Compute the index for the upper specification:

\frac{\text{Upper specification}-\text{Process mean}}{3\sigma}={\frac{10.50-9.20}{3(.30)}}={\frac{1.30}{.90}}=1.44

The smaller of the two indexes is 1.44, so this is the C_{pk}. Because the C_{pk} is more than 1.33, the process is capable.

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