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(a) Test for differences between salts, application levels, and interactions. Use 0.01. (b) Draw a graph of the interaction between salt and application level. What conclusions can you draw from this graph (c) Analyze the residuals from this experiment. 14-44. An article in the IEEE Transactions on Components, Hybrids, and Manufacturing Technology (Vol. 15, 1992) describes an experiment for investigating a method for aligning optical chips onto circuit boards. The method involves placing solder bumps onto the bottom of the chip. The experiment used three solder bump sizes and three alignment methods. The response variable is alignment accuracy (in micrometers). The data are as follows:

package { import flash.display.*; import flash.events.MouseEvent; import flash.geom.Point; [SWF(backgroundColor="#000000")] public class ch36ex4 extends Sprite { protected var center:Point; protected var sourceBmp:BitmapData; protected var destBmp:BitmapData; protected var splitChannelsBitmap:Bitmap; public function ch36ex4() { //draw a white circle in the center center = new Point(stage.stageWidth/2, stage.stageHeight/2); var source:Shape = new Shape(); source.x = center.x; source.y = center.y; addChild(source); source.graphics.beginFill(0xffffff, 1); source.graphics.drawCircle(0, 0, 100); //capture a bitmap of the white circle in sourceBmp sourceBmp = new BitmapData(stage.stageWidth, stage.stageHeight, false, 0); destBmp = sourceBmp.clone(); sourceBmp.draw(stage); //create a holder for destBmp splitChannelsBitmap = new Bitmap(destBmp); addChild(splitChannelsBitmap); stage.addEventListener(MouseEvent.MOUSE_MOVE, onMouseMove); } protected function onMouseMove(event:MouseEvent):void { //hold mouse button to show source graphic splitChannelsBitmap.visible = !event.buttonDown; var dist:Number = Point.distance(new Point(stage.mouseX, stage.mouseY), center) / 2; //copy the white circle, offseting RGB channels based on mouse location destBmp.copyChannel(sourceBmp, sourceBmp.rect, new Point(0, -dist), BitmapDataChannel.RED, BitmapDataChannel.RED); destBmp.copyChannel(sourceBmp, sourceBmp.rect, new Point(-dist, dist), BitmapDataChannel.GREEN, BitmapDataChannel.GREEN); destBmp.copyChannel(sourceBmp, sourceBmp.rect, new Point(dist, dist), BitmapDataChannel.BLUE, BitmapDataChannel.BLUE); event.updateAfterEvent(); } } }

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Solder Bump Size (diameter in m) 75 130 260

You ll see that copyChannel() works much like copyPixels(). You also used the rect property of the BitmapData object to select the entire area of the bitmap for copying.

Alignment Method 1 4.60 4.53 2.33 2.44 4.95 4.55 2 1.55 1.45 1.72 1.76 2.73 2.60 3 1.05 1.00 0.82 0.95 2.36 2.46

Use the merge() method to blend data from two bitmaps. With this method, you can create a custom mix of the ARGB channels between the two images. I don t use this method often, but you can use it to quickly fade between two images. The method requires these parameters:

(a) Is there any indication that either solder bump size or alignment method affects the alignment accuracy Is there any evidence of interaction between these factors Use 0.05. (b) What recommendations would you make about this process (c) Analyze the residuals from this experiment. Comment on model adequacy. 14-45. An article in Solid State Technology (Vol. 29, 1984, pp. 281 284) describes the use of factorial experiments in photolithography, an important step in the process of manufacturing integrated circuits. The variables in this experiment (all at two levels) are prebake temperature (A), prebake time (B), and exposure energy (C), and the response variable is delta line width, the difference between the line on the mask and the printed line on the device. The data are as follows: (1) 2.30, a 9.87, b 18.20, ab 30.20, c 23.80, ac 4.30, bc 3.80, and abc 14.70. (a) Estimate the factor effects. (b) Use a normal probability plot of the effect estimates to identity factors that may be important. (c) What model would you recommend for predicting the delta line width response, based on the results of this experiment (d) Analyze the residuals from this experiment, and comment on model adequacy. 14-46. An article in the Journal of Coatings Technology (Vol. 60, 1988, pp. 27 32) describes a 24 factorial design used

sourceBitmapData The bitmap from which to copy a region. sourceRect The region of the source bitmap to copy, as a Rectangle. destPoint Where the copied pixels should appear in the destination bitmap, as a Point de ning the top-left corner. redMultiplier The weight the source image s red channel will be given, from

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