Question

C-Spec, Inc. is attempting to determine whether an existing machine is 3 sigma capable of milling an engine part that has a key specification of 3 ± 0.05 inches. After a trial run on this machine, C-Spec has found that the machine has a sample mean of 3.001 inches with a standard deviation of 0.030 inch.

a). Calculate the Cpk for this machine. (Round your answer to 3 decimal places)

b). What would be the defect rate if the machine is used in production? (Round your answer to 2 decimal places)

Answer 1

UPPER SPECIFICATION = 3.05
LOWER SPECIFICATION = 2.95
PROCESS MEAN = 3.001
STANDARD DEVIATION = 0.03

Cpk = MINIMUM((UPPER SPECIFICATION - MEAN) / 3 * STANDARD DEVIATION), (MEAN - LOWER SPECIFICATION) / 3 * STANDARD DEVIATION)

Cpk = MINIMUM((3.05 - 3.001) / 3 * 0.03), (3.001 - 2.95) / 3 * 0.03)
Cpk = MINIMUM(0.5444, 0.5667)
Cpk = 0.544

No, the process is not even 2 sigma capable. For 3 sigma capaicbility, we need at least a Cpk of 1

2.PROBABILITY OF BEING UNDER 2.95:
Z-LSL = (LOWER SPECIFICATION - MEAN) / STANDARD DEVIATION = (2.95 - 3.001) / 0.03 = -1.69999999999999 = PROBABILITY = NORMSDIST(Z-LSL) = NORMSDIST(-1.69999999999999) = 0.044565

PROBABILITY OF BEING OVER 3.05:
Z-USL = (UPPER SPECIFICATION - MEAN) / STANDARD DEVIATION = (3.05 - 3.001) / 0.03 = 1.63333333333333 = PROBABILITY = 1 - NORMSDIST(Z-USL) = 1 - NORMSDIST(1.63333333333333) = 0.0512

PROBABILITY = PROBABILITY OF BEING UNDER LSL + PROBABILITY OF BEING OVER USL = 0.044565 + 0.0512 = 0.095765 OR 9.57%

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