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Studies on a machine that molds plastic water pipe indicate that when it is injecting 1-inch-diameter pipe, the process standard deviation is 0.05 inches. The 1-inch pipe has a specification of 1 inch plus or minus 0.10 inch. What is the process capability index ( Cpk) if the long-run process mean is 1 inch?

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Answer:

0.67

Explanation:

Given the following :

Process standard deviation(sd) = 0.05

Mean (m) = 1

specification of 1 inch plus or minus 0.10 inch

Upper specification limit(USL) = 1 + 0.1 = 1.1

Lower specification limit (LSL) = 1 - 0.1 =. 0.9

Cpk = min [[(m - USL) / 3(sd)], [(m - LSL) / 3(sd)]]

Cpk = min [[(1 - 1.1)/3(0.05)], [(1-0.9)/3(0.05)]]

Cpk = min[ -0.1/0.15], [ 0.1 / 0.15]

Cpk = min(-0.67, 0.67)

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