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 - 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 -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.

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Subgroup I(น.8 85.9 78.6 72.8 102.6 84.8 67.0 Mean Subgroup 9.6 4.3 8.6 10.6 2 3.5 0.8 Range Subgroup 9. 79.5 .9 47.6 106.7 80.7 81.0 Mean Subgroup 5.2 14.2 14.1 149 2.7 3.3 15.4 Range Subgroup 57.0 98.9 87.9 64.9 016 83.9 Mean Subgroup 5.5 13.8 16.6 Range 9.6 11.5