Question

There are two machines for sale that you are considering purchasing for your sawmill to produce hardwood flooring. You want to find the one that has a higher process capability index, or Cpk. The goal is to produce flooring that is between 46 and 50 millimeters thick. The first machine is more accurate on average, producing to a mean of 48 millimeters…but unfortunately it has more variation with a standard deviation of .7 millimeters. The second machine is not as accurate, with a mean of 47mm, but does deliver a more consistent output, with standard deviation of .3mm.

Answer 1

Machine 2 has a higher process capability index, it would be best considered for purchase.

Step-by-step explanation:

Process capability index: Cpk= Min [(mean-L spec)/3sd; (U spec-mean)/3sd]

For machine 1, mean= 48mm and L spec= 46 and U spec= 50, Standard deviation sd= 0.7

Cpk= [0.952;0.952]= 0.952

For machine 2, mean= 47 and L spec= 46 and U spec= 50, Standard deviation sd= 0.3

Cpk= [1.111;3.333]= 1.111

It is clearly observed from the calculations above that the Cpk value of machine 2 is higher than that of machine 1.

Since machine 2 has a higher process capability index, it would be best considered for purchase.