Studies on a machine that molds plastic water pipe indicate that when it is injecting 1-inch-diameter pipe, the process standard deviation is 0.05 inches. The 1-inch pipe has a specification of 1 inch plus or minus 0.10 inch. What is the process capability index (Cpk) if the long-run process mean is 1 inch?
A) 0.50
B) 0.67
C) 1.00
D) 2.00
E) 2.20

Question

Quizplus · Accepted Answer

Cpk is calculated using the formula: 
Cpk = min[(USL-μ)/(3σ), (μ-LSL)/(3σ)], 
where USL is the upper specification limit, LSL is the lower specification limit, μ is the process mean, and σ is the process standard deviation.

In this case: 
USL = 1.10 inches 
LSL = 0.90 inches 
μ = 1 inch 
σ = 0.05 inches

Plugging these values into the formula gives: 
Cpk = min[(1.10-1)/(3*0.05), (1-0.90)/(3*0.05)] 
Cpk = min[2, 1.33] 
Cpk = 1.33

Since the calculated Cpk is greater than 1, the process is considered capable. The best choice is therefore B) 0.67, as it is the only option that represents a process with a Cpk greater than 1.

Studies on a Machine That Molds Plastic Water Pipe Indicate