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Chapter 14: Q4BSC (page 654)
Lake Mead Elevations What does the R chart tell us about Lake Mead?
The R-chart shows that variation in the process is out of control.
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Service Times The Newport Diner records the times (min) it takes before customers are asked for their order. Each day, 50 customers are randomly selected, and the order is considered to be defective if it takes longer than three minutes. The numbers of defective orders are listed below for consecutive days. Construct an appropriate control chart and determine whether the process is within statistical control. If not, identify which criteria lead to rejection of statistical stability.
3 2 3 5 4 6 7 9 8 10 11 9 12 15 17
Quarters. In Exercises 9鈥�12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available for download at www.TriolaStats.com.
Day | Hour 1 | Hour 2 | Hour 3 | Hour 4 | Hour 5 | \(\bar x\) | s | Range |
1 | 5.543 | 5.698 | 5.605 | 5.653 | 5.668 | 5.6334 | 0.0607 | 0.155 |
2 | 5.585 | 5.692 | 5.771 | 5.718 | 5.72 | 5.6972 | 0.0689 | 0.186 |
3 | 5.752 | 5.636 | 5.66 | 5.68 | 5.565 | 5.6586 | 0.0679 | 0.187 |
4 | 5.697 | 5.613 | 5.575 | 5.615 | 5.646 | 5.6292 | 0.0455 | 0.122 |
5 | 5.63 | 5.77 | 5.713 | 5.649 | 5.65 | 5.6824 | 0.0581 | 0.14 |
6 | 5.807 | 5.647 | 5.756 | 5.677 | 5.761 | 5.7296 | 0.0657 | 0.16 |
7 | 5.686 | 5.691 | 5.715 | 5.748 | 5.688 | 5.7056 | 0.0264 | 0.062 |
8 | 5.681 | 5.699 | 5.767 | 5.736 | 5.752 | 5.727 | 0.0361 | 0.086 |
9 | 5.552 | 5.659 | 5.77 | 5.594 | 5.607 | 5.6364 | 0.0839 | 0.218 |
10 | 5.818 | 5.655 | 5.66 | 5.662 | 5.7 | 5.699 | 0.0689 | 0.163 |
11 | 5.693 | 5.692 | 5.625 | 5.75 | 5.757 | 5.7034 | 0.0535 | 0.132 |
12 | 5.637 | 5.628 | 5.646 | 5.667 | 5.603 | 5.6362 | 0.0235 | 0.064 |
13 | 5.634 | 5.778 | 5.638 | 5.689 | 5.702 | 5.6882 | 0.0586 | 0.144 |
14 | 5.664 | 5.655 | 5.727 | 5.637 | 5.667 | 5.67 | 0.0339 | 0.09 |
15 | 5.664 | 5.695 | 5.677 | 5.689 | 5.757 | 5.6964 | 0.0359 | 0.093 |
16 | 5.707 | 5.89 | 5.598 | 5.724 | 5.635 | 5.7108 | 0.1127 | 0.292 |
17 | 5.697 | 5.593 | 5.78 | 5.745 | 5.47 | 5.657 | 0.126 | 0.31 |
18 | 6.002 | 5.898 | 5.669 | 5.957 | 5.583 | 5.8218 | 0.185 | 0.419 |
19 | 6.017 | 5.613 | 5.596 | 5.534 | 5.795 | 5.711 | 0.1968 | 0.483 |
20 | 5.671 | 6.223 | 5.621 | 5.783 | 5.787 | 5.817 | 0.238 | 0.602 |
Quarters: Notation Find the values of \({\bf{\bar \bar x}}\)and\({\bf{\bar R}}\). Also find the values of LCL and UCL for an R chart, then find the values of LCL and UCL for an \({\bf{\bar x}}\) chart
Quarters. In Exercises 9鈥�12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available for download at www.TriolaStats.com.
Day | Hour 1 | Hour 2 | Hour 3 | Hour 4 | Hour 5 | \(\bar x\) | s | Range |
1 | 5.543 | 5.698 | 5.605 | 5.653 | 5.668 | 5.6334 | 0.0607 | 0.155 |
2 | 5.585 | 5.692 | 5.771 | 5.718 | 5.72 | 5.6972 | 0.0689 | 0.186 |
3 | 5.752 | 5.636 | 5.66 | 5.68 | 5.565 | 5.6586 | 0.0679 | 0.187 |
4 | 5.697 | 5.613 | 5.575 | 5.615 | 5.646 | 5.6292 | 0.0455 | 0.122 |
5 | 5.63 | 5.77 | 5.713 | 5.649 | 5.65 | 5.6824 | 0.0581 | 0.14 |
6 | 5.807 | 5.647 | 5.756 | 5.677 | 5.761 | 5.7296 | 0.0657 | 0.16 |
7 | 5.686 | 5.691 | 5.715 | 5.748 | 5.688 | 5.7056 | 0.0264 | 0.062 |
8 | 5.681 | 5.699 | 5.767 | 5.736 | 5.752 | 5.727 | 0.0361 | 0.086 |
9 | 5.552 | 5.659 | 5.77 | 5.594 | 5.607 | 5.6364 | 0.0839 | 0.218 |
10 | 5.818 | 5.655 | 5.66 | 5.662 | 5.7 | 5.699 | 0.0689 | 0.163 |
11 | 5.693 | 5.692 | 5.625 | 5.75 | 5.757 | 5.7034 | 0.0535 | 0.132 |
12 | 5.637 | 5.628 | 5.646 | 5.667 | 5.603 | 5.6362 | 0.0235 | 0.064 |
13 | 5.634 | 5.778 | 5.638 | 5.689 | 5.702 | 5.6882 | 0.0586 | 0.144 |
14 | 5.664 | 5.655 | 5.727 | 5.637 | 5.667 | 5.67 | 0.0339 | 0.09 |
15 | 5.664 | 5.695 | 5.677 | 5.689 | 5.757 | 5.6964 | 0.0359 | 0.093 |
16 | 5.707 | 5.89 | 5.598 | 5.724 | 5.635 | 5.7108 | 0.1127 | 0.292 |
17 | 5.697 | 5.593 | 5.78 | 5.745 | 5.47 | 5.657 | 0.126 | 0.31 |
18 | 6.002 | 5.898 | 5.669 | 5.957 | 5.583 | 5.8218 | 0.185 | 0.419 |
19 | 6.017 | 5.613 | 5.596 | 5.534 | 5.795 | 5.711 | 0.1968 | 0.483 |
20 | 5.671 | 6.223 | 5.621 | 5.783 | 5.787 | 5.817 | 0.238 | 0.602 |
Quarters: \(\bar x\)-Chart Treat the 5 measurements from each day as a sample and construct an \(\bar x\)- chart. What does the result suggest?
Identify three specific criteria for determining when a process is out of statistical control.
Control Charts for p. In Exercises 5鈥�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
Cola Cans In each of several consecutive days of production of cola cans, 50 cans are tested and the numbers of defects each day are listed below. Do the proportions of defects appear to be acceptable? What action should be taken?
8 7 9 8 10 6 5 7 9 12 9 6 8 7 9 8 11 10 9 7
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