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C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 5 ± 0.05 inches. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 5.000 inches with a standard deviation of 0.050 inches.
Calculate the Cpk for this machine. (Round your answer to 3 decimal places.)

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ProfLincoln

Answer:

0.333

Explanation:

Cpk = Cpl or CPU ( the lower is taken as the cpk)

Where Cpl = (USL - Mean)/ 3 × standard deviation

CPU = (mean - LSL)/3 × standard deviation

 Where

The process mean = 5

Tolerance = 0.05

Sample mean = 5.000 inches

Standard deviation (sd) = 0.050 inches

Upper standard  limit (USL) = 5 + 0.05 = 5.05

Lower standard limit (LSL) = 5 - 0.05 = 4.95

Cpl = (USL - Mean)/ 3 × standard deviation

= (5.05 - 5)/ 3 × 0.05

= 0.05/0.15

Cpl = 0.333

Cpk = Cpl = 0.333

Tundexi

The Process capability index (Cpk) for this machine is 0.333.

Given Information

The process mean = 5

Tolerance = 0.05

Sample mean = 5.000 inches

Standard deviation (SD) = 0.050 inches  

Upper standard limit (USL) = 5 + 0.05

Upper standard limit (USL) = 5.05

Lower standard limit (LSL) = 5 - 0.05

Lower standard limit (LSL) = 4.95

  • The Formula for Cpl is [(Mean - LSL) / (3 * SD)]

Cpl = (5 - 4.95) / (3 * 0.05)

Cpl = 0.05/0.15

Cpl = 0.333

  • The Formula for Cpu is [(USL - Mean) / (3 * SD)]

Cpu = (5.05 - 5) /  (3 * 0.05)

Cpu = 0.05 / 0.15

Cpu = 0.333

Process capability index (Cpk) = Minimum of (Cpl, Cpu)

Process capability index (Cpk) = Minimum of (0.333, 0333)

Process capability index (Cpk) = 0.333

Therefore, the Process capability index (Cpk) for this machine is 0.333.

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