Question

The Stryker Baseball Bat Company manufactures wooden and aluminum baseball bats at its plant in New England. Wooden bats produced for the mass market are turned on a lathe, where a piece of wood is shaped into a bat with a handle and barrel. The bat is cut to its specified length and then finished in subsequent processes. A specific style of wooden bat is supposed to have a mean barrel circumference of 9 inches with ±0.5 inches tolerance at its thickest point.

The company is trying to buy a new machine to cut the bats due to a projected increase in sales. There are three different candidate machines that the company is trying to buy at different costs. The following table summarizes the process average, process standard deviation (SD), and purchase cost of each machine. Which machine, if any, should the company purchase (they are trying to buy the cheapest machine that can get the job done)?

Machine	Average	SD	Purchase Cost
1	9.35	0.14	$20,000
2	8.93	0.16	$18,000
3	9.00	0.18	$15,000

1. Determine the Upper Specification Limit.
2. Determine the Lower Specification Limit.
3. Calculate the process capability index of machine 1.
4. Based on process capability index of machine 1, is machine 1 capable?
   1. Yes
   2. No
5. Calculate the process capability index of machine 2.
6. Based on process capability index of machine 2, is machine 2 capable?
   1. Yes
   2. No
7. Calculate the process capability index of machine 3.
8. Based on process capability index of machine 3, is machine 3 capable?
   1. Yes
   2. No
9. Which machine should the company purchase?
   1. Machine 1
   2. Machine 2
   3. Machine 3
   4. None of these

Answer 1

Upper specification limit = 10+0.5= 10.5

Lower specification limit = 10-0.5= 9.5

Process capability index is the capability of the process relative to the upper and lower specification limits and is calculated as follows:

We have process capability limits as follows:

For machine A: Process capability index is min{2.39,.39}=0.39

As process capability index is less than 1, it implies that the machine A is not capable.

For machine B: Process capability index is min{1.05,1.33} = 1.05

As the process capability index is 1.05, that is, less than 1, it implies that the machine B is capable.

For machine C: Process capability index is min{1.05,.98}=0.98

As the process capabillity index is .98, that is, less than 1, it implies that the machine C is not capable.

Therefore the machine that the company should purchase is Machine B as it is the only machine which has process capability index above the cutoff of 1.