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 one-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.

b. 0.67

Explanation:

UCL = 1 + 0.10

        = 1.10 inch

LCL = 1 - 0.10

       = 0.9 inch

standard deviation = 0.005 inch

mean = 1 inch

Cpk

= min[(UCL - mean)/(3*standard deviation) , (mean - LCL)/(3*standard deviation))]

= min[(1.10 - 1)/(3*0.05) , (1 - 0.9)/(3*0.05))]

= min[0.67 , 0.67]

= 0.67

Therefore, Theprocess capability index (Cpk) if the long-run process mean is 1 inch is 0.67