Studies on a machine that forges cylinder barrels for Volkswagen aftermarket performance engines indicate that when it is forging 103 mm diameter cylinders, the process standard deviation is 0.20 mm. The cylinders have a specification of 103 mm plus 0.75 mm or minus 1.25 mm. What is the minimum process capability index (Cpk)? a. 1.25 b. 1 c. 0.75 d. 0.67 e. 2.08

a. 1.25

Explanation:

Calculation for the minimum process capability index (Cpk)

First step is to calculate the USL which is Upper Specification limit

Upper Specification limit=103+0.75

Upper Specification limit= 103.75

Second Step is to calculate the LSL which is Lower Specification limit

Lower Specification limit = 103-1.75

Lower Specification limit= 101.25

Last step is to calculate the minimum process capability index (Cpk) using this formula

Minimum Process capability index= [(M-LSL)/3sd; (USL-M)/3sd]

Where,

Actual Mean = M=103

Standard deviation= sd= 0.2

Hence,

Minimum Process capability index= 1.25

Therefore the minimum process capability index (Cpk) will be 1.25

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