The Stryker Baseball Bat Company manufactures wooden and aluminum baseball bats

ID: 343619 • Letter: T

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 specied length and then nished in subsequent processes. A specic style of wooden bat is supposed to have a mean barrel circumference of 10 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..............10.36........0.12...........$20,000 ...2..............9.94........0.14...........$18,000 ...3..............10.03........0.16...........$15,000 Determine the Upper Specification Limit. Determine the Lower Specification Limit. Calculate the process capability index of machine 1. Based on process capability index of machine 1, is machine 1 capable? Yes No Calculate the process capability index of machine 2. Based on process capability index of machine 2, is machine 2 capable? Yes No Calculate the process capability index of machine 3. Based on process capability index of machine 3, is machine 3 capable? Yes No Which machine should the company purchase? Machine 1 Machine 2 Machine 3 None of them

Explanation / Answer

Target value = 10

Tolerances = ±0.5

Lower specification level (LSL) = 10 – 0.5 = 9.5

Upper specification level (USL) = 10 + 0.5 = 10.5

Process mean = µ

Standard deviation of the process =

Process capability = Cp = (USL – LSL)/6

Lower Process capability index = Cpkl = (µ – LSL)/3

Upper Process capability index = Cpku = (USL – µ)/3

Process capability index = Minimum [(USL – µ)/3, (µ – LSL)/3] = Min (Cpku, Cpkl)

Target Circumference

Tolerances ( +/- )

0.5

Upper Specification limit

10.5

Lower Specification limit

9.5

Machine

Average (µ)

10.36

9.94

10.03

SD ()

0.12

0.14

0.16

Cost ($)

20000

18000

15000

Process Capability

1.39

1.19

1.04

Upper Process Capability Index

(10.5-10.39)/(3*0.12)

= 0.39

1.33

0.98

Lower Process Capability Index

(10.39-9.5)/(3*0.12)

= 2.39

1.05

1.10

Process Capability Index

Min (0.39, 2.39)

= 0.39

1.05

0.98

If the process capability index is less than 1, the process is not capable.

If the process capability index is equal to 1, the process is marginally capable.

If the process capability index is more than 1, the process is capable.

Thus, Machine 2 is capable to produce within the tolerance limit.