Specifications require the nickel content of manufactured stainless steel hydraulic valves to be 13% by weight. To monitor the production process, four valves were selected from the production line each hour over an 8-hour period and the percentage nickel content was measured for each, with the results recorded in the next table.

a. Construct a control chart for the mean nickel content of the hydraulic valves.

b. Establish control limits for the mean using Table 19 of Appendix B.

c. Establish control limits for the mean using the standard deviation of the overall sample. Compare to the limits obtained in part b.

d. Do all observed sample means lie within the control limits? What are the consequences of this?

e. Find a 99% tolerance interval for 99% of the nickel contents in the hydraulic valves. Assume that the distribution of nickel contents is approximately normal.

f. Construct a control chart with control limits for the variability in the nickel contents of the hydraulic valves. Interpret your results.

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PCTNICKEL Hour Nickel Content 13.1 12.8 12.7 12.9 2 12.5 13.0 13.6 13.1 12.9 12.9 13.2 13.3 4 12.4 13.0 12.1 12.6 5 12.8 11.9 12.7 12.4 13.0 13.6 13.2 12.9 13.5 13.5 13.1 12.7 8 12.6 13.9 13.3 12.8 3. 670O 1.