Question

Compare the processes described in the following table. What is the Cpk of the process that will generate the fewest defects? Tolerance Process Мean St.Dev. 198 +- 48 A 198 18.7 49 +- 17 B 49 5.7 1151+- 337 C 1151 112.6 861 87.3 861+/- 258 D

Answer 1

Formula:

Cpk = MIN(UPPER LIMIT - MEAN / 3 * STANDARD DEVIATION, MEAN - LOWER LIMIT / 3 * STANDARD DEVIATION)

PROCESS A

Cpk = MIN(246 - 198 / 3 * 18.7, 198 - 150 / 3 * 18.7)
Cpk = MIN(0.8556, 0.8556)
Cpk = 0.8556

PROCESS B

Cpk = MIN(66 - 49 / 3 * 5.7, 49 - 32 / 3 * 5.7)
Cpk = MIN(0.9942, 0.9942)
Cpk = 0.9942

PROCESS C

Cpk = MIN(1488 - 1151 / 3 * 112.6, 1151 - 814 / 3 * 112.6)
Cpk = MIN(0.9976, 0.9976)
Cpk = 0.9976

PROCESS D

Cpk = MIN(1119 - 861 / 3 * 87.3, 861 - 603 / 3 * 87.3)
Cpk = MIN(0.9851, 0.9851)
Cpk = 0.9851

Fewest defects will be generated by the most capable processes out of all the processes. Using the data, we can say that process C is the most capable out of the 4.