Problem:
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. Once bats are cut to length, it is difficult to rework them into a different style, so it is important to catch defects before this step. As such, bats are inspected at this stage of the process. A specific style of wooden bat has a mean barrel circumference of 9 inches at its thickest point with a standard deviation of 0.06 inch. (The process variability is assumed to be normally distributed.)
Required:
A mean control chart for this process using 3\sigma limits and a sample size of 10 bats shows an upper control limit and lower control limit of:
a) UCL = 9.12; LCL = 8.88
b) UCL = 9.18; LCL = 8.82
c) UCL = 9.04; LCL = 8.96
d) UCL = 9.06; LCL = 8.94
Solve the problem and show all work.