A precision parts manufacturer produces bolts for use in military aircraft. Ideally, the bolts should be 37 centimeters in length. The company sampled four consecutively produced bolts each hour on the hour for 25 consecutive hours and measured them using a computerized precision instrument. The data are presented in the table below.

a. What process is the manufacturer interested in monitoring?
b. Construct an xÌ…-chart from the data.
c. Does the chart suggest that special causes of variation are present? Justify your answer.
d. Provide an example of a special cause of variation that could potentially affect this process. Do the same for a common cause of variation.
e. Should the control limits be used to monitor future process output? Explain.

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Bolt Lengths (centimeters) Hour 37.03 36.96 37.16 37.20 36.81 37.08 37.04 37.11 37.06 36.97 36.90 36.85 36.99 37.02 36.91 37.01 36.99 36.98 36.90 36.87 37.07 36.88 36.98 37.01 36.98 37.10 36.89 3 4 37.13 37.07 37.01 37.17 36.91 36.88 36.96 36.94 36.91 37.03 36.99 37.00 37.12 37.01 37.11 37.03 8. 10 11 37.10 12 13 14 15 37.06 36.91 36.98 37.22 37.07 37.04 36.98 36.90 37.12 37.10 36.89 36.90 36.99 37.03 37.04 37.01 36.99 37.08 37.03 16 36.95 17 18 19 20 21 22 36.97 37.11 36.88 36.90 37.01 37.09 36.94 37.04 36.99 37.15 36.96 36.95 37.14 36.98 37.01 37.09 37.05 36.93 37.10 36.91 36.94 37.00 36.96 37.12 36.95 36.90 37.01 23 24 25 37.00 36.99 37.10 37.02 37.07 37.03 37.04 37.02 36.90