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Although a linear tween can move an object from point A to point B smoothly, it does so at a constant speed; so at the beginning of the tween, the object instantly changes from no speed to the average speed, and at the end of the tween, the object instantly stops Thankfully, you can ease into and ease out of tweens, accelerating at the beginning and decelerating at the end, to make the motion look more natural, as shown in Figure 39-1 The change in speed through a tween is called its easing, and it can be set by the Flash authoring tool as well as animations created in ActionScript..

16-46. Cover cases for a personal computer are manufactured by injection molding. Samples of ve cases are taken from the process periodically, and the number of defects is noted. Twenty- ve samples follow:

Motion XML is composed of a few simple elements in a predictable structure. Although animating in the timeline can provide for some awkwardly precise decimal values, motion XML should be on the whole easy to read and modify.

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(a) Using all the data, nd trial control limits for this U chart for the process. (b) Use the trial control limits from part (a) to identify out-ofcontrol points. If necessary, revise your control limits. (c) Suppose that instead of samples of 5 cases, the sample size was 10. Repeat parts (a) and (b). Explain how this change alters your answers to parts (a) and (b). 16-47. Consider the data in Exercise 16-46. (a) Using all the data, nd trial control limits for a C chart for this process. (b) Use the trial control limits of part (a) to identify out-ofcontrol points. If necessary, revise your control limits. (c) Suppose that instead of samples of 5 cases, the sample was 10 cases. Repeat parts (a) and (b). Explain how this alters your answers to parts (a) and (b). 16-48. Suppose that a process is in control and an X chart is used with a sample size of 4 to monitor the process. Suddenly there is a mean shift of 1.5 . (a) If 3-sigma control limits are in use on the X chart, what is the probability that this shift will remain undetected for three consecutive samples (b) If 2-sigma control limits are in use on the X chart, what is the probability that this shift will remain undetected for three consecutive samples (c) Compare your answers to parts (a) and (b) and explain why they differ. Also, which limits you would recommend using and why 16-49. Consider the control chart for individuals with 3-sigma limits.

FIGURE 39-1

(a) Suppose that a shift in the process mean of magnitude occurs. Verify that the ARL for detecting the shift is ARL 43.9. (b) Find the ARL for detecting a shift of magnitude 2 in the process mean. (c) Find the ARL for detecting a shift of magnitude 3 in the process mean. (d) Compare your answers to parts (a), (b), and (c) and explain why the ARL for detection is decreasing as the magnitude of the shift increases. 16-50. Consider a control chart for individuals, applied to a continuous 24-hour chemical process with observations taken every hour. (a) If the chart has 3-sigma limits, verify that the in-control ARL is ARL 370. How many false alarms would occur each 30-day month, on the average, with this chart (b) Suppose that the chart has 2-sigma limits. Does this reduce the ARL for detecting a shift in the mean of magnitude (Recall that the ARL for detecting this shift with 3-sigma limits is 43.9.) (c) Find the in-control ARL if 2-sigma limits are used on the chart. How many false alarms would occur each month with this chart Is this in-control ARL performance satisfactory Explain your answer. 16-51. The depth of a keyway is an important part quality characteristic. Samples of size n 5 are taken every four hours from the process and 20 samples are summarized as follows: Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 X 139.7 139.8 140.0 140.1 139.8 139.9 139.7 140.2 139.3 140.7 138.4 138.5 137.9 138.5 140.8 140.5 139.4 139.9 137.5 139.2 r 1.1 1.4 1.3 1.6 0.9 1.0 1.4 1.2 1.1 1.0 0.8 0.9 1.2 1.1 1.0 1.3 1.4 1.0 1.5 1.3

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