A key joint in a precision machining process has a lower specification limit of a width of 0.99 mm and an upper specification limit of 1.01 mm. The standard deviation is 0.005 mm and the mean is 1 mm. What is the process capability index for the precision machining process

the process capability index for the precision machining process is 0.667

Explanation:

Given the data in the question;

Lower Specification Limits LSL = 0.99 mm

Upper Specification Limits USL = 1.01 mm.

The standard deviation σ = 0.005 mm

mean μ = 1 mm

capability index Cpk = ?

Cpk = min( USL - μ / 3σ, μ - LSL / 3σ )

we substitute

Cpk = min( 1.01 mm - 1 mm / 3(0.005 mm ), 1 - 0.99 mm / 3(0.005 mm) )

Cpk = min( 0.01 mm / 0.015 mm, 0.01 mm / 0.015 mm )

Cpk = min( 0.6666, 0.6666 )

∴ Cpk = 0.6666 ≈ 0.667

Therefore, the process capability index for the precision machining process is 0.667

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