The Elon Company manufactures parts for an aircraft company using three computer

Question

The Elon Company manufactures parts for an aircraft company using three computerized numerical controlled (CNC) turning centers. The company has to decide which machines are capable of producing a specific part with design specifications of 0.0970 inch ± 0.015 inch. The machines have the following parameters: Machine 1 (mean= 0.0995, s = 0.004); Machine 2 (mean = 0.1002, s = 0.009); Machine 3 (mean = 0.095, s = 0.005). Determine which machines (if any) are capable of producing the products within the design specifications.

Explanation / Answer

Solution:

Upper Specification = 0.112
Lower Specification = 0.082

Machine 1:
Cpk = Min[(0.112-0.0995)/(3*0.004), (0.0995-0.082)/(3*0.004)] = Min[1.46, 1.04] = 1.04 Since both Cp < 1 and Cpk 1, the process is capable.

Machine 2:
Cpk = Min[(0.112-0.1002)/(3*0.009), (0.1002-0.082)/(3*0.009)] = Min[0.67, 0.44] = 0.44
Since both Cp < 1 and Cpk < 1, the process is not capable.

Machine 3:
Cpk = Min[(0.112-0.095)/(3*0.005), (0.095-0.082)/(3*0.005)] = Min[0.87, 1.13] = 0.87
Since Cp 1 but Cpk < 1, the process is not capable.

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