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 0.3mm.
1. What is the Cpk of machine 1?
2. What is the Cpk of machine 2?
3. If your goal is to be 'capable', what would you do?
4. If (somehow) you could combine the best of both machines (the centering or average of machine 1 coupled with the constancy or standard deviation of machine 2, what would the Cpk be?

Answer 1

Answer:

1. The Cpk of machine 1 would be 0.952

2. The Cpk of machine 2 would be 1.111

3.  I would buy machine 2, because the Cpk value is more than 1.

4. The Cpk would be 2.222

Explanation:

1. In order to calculate the Cpk of machine 1 we would have to use to following formula:

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

According to given data:

In machine 1, mean= 48mm

L spec= 46

U spec= 50

Standard deviation sd= 0.7

Therefore, Cpk of machine 1= [0.952;0.952]= 0.952

1. In order to calculate the Cpk of machine 2 we would have to use to following formula:

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

According to given data:

In machine 2, mean= 47

L spec= 46

U spec= 50

Standard deviation sd= 0.3

Therefore, Cpk of machine 2= [1.111;3.333]= 1.111

3. If my goal is to be capable, I would buy machine 2, because the Cpk value is more than 1.

4. If you combine the best of both machines to calculate the cpk we to make the following calculation:

Combination specification, mean= 48 and L spec= 46 and U spec= 50, Standard deviation sd= 0.3

Therefore, Cpk= [2.222;2.222]= 2.222