Minting Quarters Specifications for a quarter require that it be 8.33% nickel and 91.67% copper; it must weigh 5.670 g and have a diameter of 24.26 mm and a thickness of 1.75 mm; and it must have 119 reeds on the edge. A quarter is considered to be defective if it deviates substantially from those specifications. A production process is monitored, defects are recorded and the accompanying control chart is obtained. Does this process appear to be within statistical control? If not, identify any out-of-control criteria that are satisfied. Is the manufacturing process deteriorating?
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Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available in Data Set 44 “Weights of Minted Quarters” in Appendix B.

Quarters: xbar Chart Treat the 5 measurements from each day as a sample and construct an xbar chart. What does the result suggest?

Identify three specific criteria for determining when a process is out of statistical control.

Notation The control chart for Exercise 1 shows a value of p_bar = 0.0975. What does that value denote, and how is it obtained? What do UCL and LCL indicate?

Control Limits In constructing a control chart for the proportions of defective dimes, it is found that the lower control limit is -0.00325. How should that value be adjusted?

Control Charts for p. In Exercises 5–12, use the given process data to construct a control chart for p. In each case, use the three out-of-control criteria listed near the beginning of this section and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply.

Euro Coins Consider a process of minting coins with a value of one euro. Listed below are the numbers of defective coins in successive batches of 10,000 coins randomly selected on consecutive days of production.

32 21 25 19 35 34 27 30 26 33

Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available in Data Set 44 “Weights of Minted Quarters” in Appendix B.

Find the values of LCL and UCL for an xbar chart.

In Exercises 5–8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.

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Is the process variation within statistical control? Why or why not?

In Exercises 5–8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.

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Is the process mean within statistical control? Why or why not?