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 0.6 inch. (The process variability is assumed to be normally distributed.)
a. Construct a mean control chart for this process for 3σ limits and a sample size of 10 bats.
b. Three samples are taken, and they have average bat diameters of 9.05 inches, 9.10 inches, and 9.08 inches. Is the process in control?
c. What effect will increasing the sample size to 20 bats have on the control charts? Will the conclusions reached in part (b) change for this sample size?