The specification limits for a product are 8 cm and 10 cm.A process that produces the product has a mean of 9.5 cm and a standard deviation of 0.2 cm.What is the process capability,Cpk?
A)3.33
B)1.67
C)0.83
D)2.50

Question

Quizplus · Accepted Answer

First, calculate the process capability index, Cp:

Cp = (Upper specification limit - Lower specification limit) / (6 x standard deviation)

Cp = (10 - 8) / (6 x 0.2) = 16.67

However, Cp does not take into account the process mean. To calculate the process capability index that accounts for the process mean, Cpk, use the following formula:

Cpk = min[(Upper specification limit - Mean) / (3 x standard deviation), (Mean - Lower specification limit) / (3 x standard deviation)]

Cpk = min[(10 - 9.5) / (3 x 0.2), (9.5 - 8) / (3 x 0.2)] 
Cpk = min[2.5, 0.83] 
Cpk = 0.83

Therefore, the answer is C) 0.83.

The Specification Limits for a Product Are 8 Cm and 10