14-2 Control Charts for Attributes 717 2. Notation The control chart for Exercise 1 shows a value of p = 0.0975. What does that value denote, and how is it obtained? What do UCL and LCL indicate? 3. 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? 4. Euro Coins After constructing a control chart for the proportions of defective one-euro coins, it is concluded that the process is within statistical control. Does it follow that almost all of the coins meet the desired specifications? Explain. 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. 5. 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 6. Euro Coins Repeat Exercise 5, assuming that the size of each batch is 100 instead of 10,000. Compare the control chart to the one found for Exercise 5. Comment on the general quality of the manufacturing process described in Exercise 5 compared to the manufacturing process described in this exercise. 7. Aspirin Tablets Bottles of aspirin tablets typically have labels indicating that each tablet contains 325 mg of aspirin, but the actual amounts can vary between 315 mg and 335 mg. A tablet is defective if it has less than 315 mg of aspirin or more than 335 mg of aspirin. Listed below are numbers of defects found in batches of 1000 tablets. 16 18 13 9 10 8 6 5 5 3 8. Defibrillators At least one corporation was sued for manufacturing defective heart defibrillators. Listed below are the numbers of defective defibrillators in successive batches of 1000. Construct a control chart for the proportion p of defective defibrillators and determine whether the process is within statistical control. If not, identify which of the three out-of-control criteria apply. 8 5 6 4 9 3 12 7 8 5 22 4 9 10 11 8 7 6 8 5 9. Voting Rate In each of recent and consecutive years of national elections held every two years, 1000 people of voting age in the United States were randomly selected and the number who voted was determined, with the results listed below. Comment on the voting behavior of the population. 549 725 560 780 576 660 516 638 453 688 475 644 486 644 425 654 10. Car Batteries Defective car batteries are a nuisance because they can strand and inconvenience drivers, and drivers could be put in danger. A car battery is considered to be defective if it fails before its warranty expires. Defects are identified when the batteries are returned under the warranty program. The Powerco Battery corporation manufactures car batteries in batches of 250, and the numbers of defects are listed below for each of 12 consecutive batches. Does the manufacturing process require correction? 3 4 2 5 3 6 8 9 12 14 17 20 11. Motor Oil Motor oil is commonly provided in cans labeled as containing 1 quart of the oil. It is common for a car to require 6 quarts of motor oil. If cans are underfilled or overfilled, engine damage can occur. Consider a can to be defective if it contains less than 0.95 qt or more than 1.05 qt. Listed below are numbers of defects in batches of 100 cans randomly selected on 15 different days of production. What action should be taken? 9 6 12 14 8 7 11 11 7 8 9 12 10 5 8
RkJQdWJsaXNoZXIy NjM5ODQ=