1. An automatic lathe produces rollers for roller bearings, and statistical process control charts are used to monitor the process. The central line of the chart for the sample means is set at 8.50 and for the range at 0.31 mm. The process is in control, as established by samples of size 5. The upper and lower specifications for the diameter of the rollers are (8.50 + 0.25) and (8.50 - 0.25) mm, respectively.

a. Calculate the control limits for the mean and range charts.

b. If the standard deviation of the process distribution is estimated to be 0.13 mm, is the process capable of meeting specifications? Assume four-sigma performance is desired.

c. If the process is not capable, what percent of the output will fall outside the specification limits? (Hint: Use the normal distribution.)