The specifications for a product are 6 mm $\pm$0.1 mm.The process is known to operate at a mean of 6.05 mm with a standard deviation of 0.01 mm.What is the Cpk for this process?
A)3.33
B)1.67
C)5.00
D)2.50

Question

Quizplus · Accepted Answer

Cpk calculates the capability of a process to meet specifications based on the mean and standard deviation of the process. 
The formula for Cpk is: 
Cpk = min[(USL-mean)/3sigma, (mean-LSL)/3sigma]

Here, 
USL = F1F1F1S1 + F1F1F100.1 = 6.1 mm 
LSL = F1F1F1S1 - F1F1F100.1 = 5.9 mm 
mean = 6.05 mm 
sigma = 0.01 mm

Plugging these values into the Cpk formula: 
Cpk = min[(6.1-6.05)/(3*0.01), (6.05-5.9)/(3*0.01)]
Cpk = min[1.67, 1.67]

Therefore, the Cpk for this process is 1.67 (option B).

The Specifications for a Product Are 6 Mm ±\pm± 01 MmThe Process Is Known to Operate at a Mean of Mm.The

The Specifications for a Product Are 6 Mm $\pm$ 01 MmThe Process Is Known to Operate at a Mean of Mm.The