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(a) Is there any indication that either factor affects the amount of warping Is there any interaction between the factors Use = 0.05. (b) Analyze the residuals from this experiment. (c) Plot the average warping at each level of copper content and compare the levels using Fisher s LSD method. Describe the differences in the effects of the different levels of copper content on warping. If low warping is desirable, what level of copper content would you specify (d) Suppose that temperature cannot be easily controlled in the environment in which the copper plates are to be used. Does this change your answer for part (c) 14-7. Consider a two-factor factorial experiment. Develop a formula for nding a 100 (1 )% con dence interval on the difference between any two means for either a row or column factor. Apply this formula to nd a 95% CI on the difference in mean warping at the levels of copper content 60 and 80% in Exercise 14-6. 14-8. An article in the Journal of Testing and Evaluation (Vol. 16, no. 6, 1988, pp. 508 515) investigated the effects of cyclic loading frequency and environment conditions on fatigue crack growth at a constant 22 MPa stress for a particular

(a) Is there indication that either factor affects crack growth rate Is there any indication of interaction Use 0.05. (b) Analyze the residuals from this experiment. (c) Repeat the analysis in part (a) using ln(y) as the response. Analyze the residuals from this new response variable and comment on the results. 14-9. An article in the IEEE Transactions on Electron Devices (November 1986, p. 1754) describes a study on the effects of two variables polysilicon doping and anneal conditions (time and temperature) on the base current of a bipolar transistor. The data from this experiment follows below Exercise 14-10. (a) Is there any evidence to support the claim that either polysilicon doping level or anneal conditions affect base current Do these variables interact Use 0.05. (b) Graphically analyze the interaction. (c) Analyze the residuals from this experiment. 14-10. Consider the experiment described in Exercise 14-9. Use Fisher s LSD method to isolate the effects of anneal conditions on base current, with 0.05.

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Example 35-8 illustrates pixel snapping. Pixel snapping tells the anti-aliasing code in Flash Player to draw strokes that are close to being on a whole pixel on the pixel boundary rather than blending between the neighboring pixels. The code draws two identical rectangles just slightly off whole pixels. The only difference is that one uses pixel snapping in the line style, and the other does not. When you test the code, you notice that the rst rectangle has smoothed-out lines that show the inaccuracy, whereas the second appears sharp and straight. The effect is shown in Figure 35-5.

Anneal (temperature/time) 900/180 950/60 1000/15 8.30 8.90 7.81 7.75 10.15 10.20 9.38 10.02 10.29 10.30 10.19 10.10

EXAMPLE 35-8

1000/30 11.01 10.58 10.81 10.60

package { import flash.display.Shape; import flash.display.Sprite; public class ch35ex8 extends Sprite { public function ch35ex8() { var nosnap:Shape = new Shape(); addChild(nosnap); nosnap.graphics.lineStyle(0, 0, 1, false); nosnap.graphics.lineTo(100, 0.4); nosnap.graphics.lineTo(100.4, 50); nosnap.graphics.lineTo(0, 50.4); nosnap.graphics.lineTo(0.4, 0) nosnap.x = nosnap.y = 20; var snappy:Shape = new Shape(); addChild(snappy); snappy.graphics.lineStyle(0, 0, 1, true); snappy.graphics.lineTo(100, 0.4); snappy.graphics.lineTo(100.4, 50); snappy.graphics.lineTo(0, 50.4); snappy.graphics.lineTo(0.4, 0); snappy.x = 200; snappy.y = 20; } } }

14-5

Example 35-9 illustrates the scale type parameter. Both rectangles are scaled to four times their original size in the x direction. However, whereas the line thickness in the rst rectangle scales, the line thickness in the second does not. The effect is shown in Figure 35-6. Notice that for the special case of 1-pixel-wide strokes, setting the stroke to hairline thickness has the same effect as setting the scaleMode to LineScaleMode.NONE.

Many experiments involve more than two factors. In this section we introduce the case where there are a levels of factor A, b levels of factor B, c levels of factor C, and so on, arranged in a factorial experiment. In general, there will be abc p n total observations, if there are n replicates of the complete experiment.

Table 14-9 Analysis of Variance Table for the Three-Factor Fixed Effects Model Source of Variation A Sum of Squares SSA SSB SSC 1a 1a 1b 1a Degrees of Freedom a 1 Mean Square MSA MSB MSC

FIGURE 35-5

The task graph is a widely used application model. In the task graph notation, the overall computation is represented as an acyclic directed graph. The nodes of the graph correspond to processes (tasks), and a pair of distinct tasks are connected by a directed edge iff the task at the tail of the directed edge requires as input the results of execution of the task at its head. In the simplest model, a task cannot start executing until all its predecessors have finished

121b

The pixel-snapping parameter urges edges close to a pixel boundary to draw on the pixel rather than anti-aliasing.

121c

EXAMPLE 35-9

121c

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