Discussion
Cylindrical pins of diameter \(15^{\pm 0.020}\) mm are being produced on a machine. Statistical quality control tests show a mean of 14.995 mm and standard deviation of 0.004 mm. The process capability index Cp is
Answer: B
The process capability index is 1.667.
Cp compares the specified tolerance band with the natural process spread of six standard deviations:
\[ \begin{aligned} C_{p} &= \frac{USL - LSL}{6\sigma} = \frac{15.020 - 14.980}{6 \times 0.004} \\ &= \frac{0.040}{0.024} = 1.667 \end{aligned} \]
Cp ignores where the mean sits. The off-centre mean of 14.995 matters only for Cpk, which would be (14.995 - 14.980)/(3 × 0.004) = 1.25. 0.833 uses only half the tolerance, and 3.333 divides by 3σ instead of 6σ.
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