Question

A company produces pipes with a nominal outside diameter of 1.000 inch +/- 0.005 inch. The process has a standard deviation of 0.001 inch. Calculate and evaluate the Cpk for:

a. A sample with an average diameter of 0.997 inch.

b. A sample with an average diameter of 0.998 inch.

c. A sample with an average diameter of 1.001 inch.

Answer 1

1. UPPER SPECIFICATION = 1.005
LOWER SPECIFICATION = 0.995
PROCESS MEAN = 0.997
STANDARD DEVIATION = 0.001

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

Cpk = MINIMUM((1.005 - 0.997) / 3 * 0.001), (0.997 - 0.995) / 3 * 0.001)
Cpk = MINIMUM(2.666667, 0.666667)
Cpk = 0.67

2. UPPER SPECIFICATION = 1.005
LOWER SPECIFICATION = 0.995
PROCESS MEAN = 0.998
STANDARD DEVIATION = 0.001

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

Cpk = MINIMUM((1.005 - 0.998) / 3 * 0.001), (0.998 - 0.995) / 3 * 0.001)
Cpk = MINIMUM(2.333333, 1)
Cpk = 1

3. UPPER SPECIFICATION = 1.005
LOWER SPECIFICATION = 0.995
PROCESS MEAN = 1.001
STANDARD DEVIATION = 0.001

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

Cpk = MINIMUM((1.005 - 1.001) / 3 * 0.001), (1.001 - 0.995) / 3 * 0.001)
Cpk = MINIMUM(1.333333, 2)
Cpk = 1.33