Referring to Problem 14, if necessary delete any outof-control points and construct the appropriate x- and R-charts. Now, suppose the process stays in control for the next six weeks (subgroups 18 through 23). The subgroup means and ranges for subgroups 33 to 38 are as follows:

a. Plot the ranges on the R-chart. Is there evidence based on the range chart that the process has gone out of control? Discuss.

b. Plot the subgroup means on the x-chart. Is there evidence to suggest that the process has gone out of control with respect to the process mean? Discuss.

Problem 14

The Kaiser Corporation makes aluminum at various locations around the country. One of the key factors in being profitable is keeping the machinery running. One particularly troublesome machine is a roller that flattens the sheets to the appropriate thickness. This machine tends to break down for various reasons. Consequently, the maintenance manager has decided to develop a process control chart. Over a period of 10 weeks, 20 subgroups consisting of 5 downtime measures (in minutes) were collected (one measurement at the end of each of the two shifts). The subgroup means and ranges are shown as follows and are contained in the file called Kaiser.

a. Explain why the x- and R-charts would be appropriate in this case.

b. Find the centerline value for the x-chart.

c. Calculate the centerline value for the R-chart.

d. Compute the upper and lower control limits for the R-chart, and construct the chart with appropriate labels.

e. Compute the upper and lower control limits for the x-chart, and construct the chart with appropriate labels.

f. Examine the charts constructed in parts d and e and determine whether the process was in control during the period for which the control charts were developed. Explain.