Refer to Exercise 11.12

(p. 668), where the desired circuit path widths were .5 to .85 micron. The manufacturer sampled four CPU chips six times a day (every 90 minutes from 8:00 A.M. until 4:30 P.M.) for five consecutive days.The path widths were measured and used to construct the MINITAB R-chart shown on page 680.

a. Calculate the chart's upper and lower control limits.

b. What does the R-chart suggest about the presence of special causes of variation during the time when the data were collected?

c. Should the control limit(s) be used to monitor future process output? Explain.

d. How many different R values are plotted on the control chart? Notice how most of the R values fall along three horizontal lines. What could cause such a pattern?