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The eld of statistical quality control can be broadly de ned as those statistical and engineering methods that are used in measuring, monitoring, controlling, and improving quality. Statistical quality control is a eld that dates back to the 1920s. Dr. Walter A. Shewhart of the Bell Telephone Laboratories was one of the early pioneers of the eld. In 1924 he wrote a memorandum showing a modern control chart, one of the basic tools of statistical process control. Harold F. Dodge and Harry G. Romig, two other Bell System employees, provided much of the leadership in the development of statistically based sampling and inspection methods. The work of these three men forms much of the basis of the modern eld of statistical quality control. World War II saw the widespread introduction of these methods to U.S. industry. Dr. W. Edwards Deming and Dr. Joseph M. Juran have been instrumental in spreading statistical quality-control methods since World War II. The Japanese have been particularly successful in deploying statistical quality-control methods and have used statistical methods to gain significant advantage over their competitors. In the 1970s American industry suffered extensively from Japanese (and other foreign) competition; that has led, in turn, to renewed interest in statistical quality-control methods in the United States. Much of this interest focuses on statistical process control and experimental design. Many U.S. companies have begun extensive programs to implement these methods in their manufacturing, engineering, and other business organizations.

package { import flash.display.*; import flash.events.Event; import flash.filters.DisplacementMapFilter; import flash.filters.DisplacementMapFilterMode; import flash.geom.*; import flash.net.URLRequest; [SWF(width="500",height="500",backgroundColor="#000000",frameRate="50")]

16-3

EXAMPLE 37-13

Sometimes we are interested in counting the number of ordered sequences for objects that are not all different. The following result is a useful, general calculation.

The number of permutations of n n1 n2 p nr objects of which n1 are of one type, n2 are of a second type, p , and nr are of an rth type is n! n1! n2! n3! p nr! (S2-3)

(continued)

EXAMPLE S2-3

to walk the reader through the complete process of translating a highlevel functional description of application functionality into deployable code for each node of a target network using the ATaG programming model and application development environment,

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public class ch37ex13 extends Sprite { protected const FLAG_WIDTH:Number = 315, FLAG_HEIGHT:Number = 170; protected const WIND_SPEED:Number = -15; protected const DISPLACEMENT:Number = 20; protected const OCTAVES:int = 3; protected const SHIFT_COLORS:ColorTransform = new ColorTransform(2, 2, 2, 1, -128, -128, -128, 0); protected var flag:DisplayObject; protected var fadeOutWave:Shape; protected var map:BitmapData; protected var offsets:Array; protected var perlinSeed:Number; protected var displacementFilter:DisplacementMapFilter; public function ch37ex13() { var l:Loader = new Loader(); l.load(new URLRequest("http://actionscriptbible.com/files/flag.swf")); l.contentLoaderInfo.addEventListener(Event.COMPLETE, onLoadComplete); } protected function onLoadComplete(event:Event):void { flag = LoaderInfo(event.target).content; flag.width = FLAG_WIDTH; flag.height = FLAG_HEIGHT; flag.x = 20; map = new BitmapData(FLAG_WIDTH, FLAG_HEIGHT, false, 0x808080); displacementFilter = new DisplacementMapFilter(map, new Point(), BitmapDataChannel.RED, BitmapDataChannel.RED, DISPLACEMENT*0.7, DISPLACEMENT, DisplacementMapFilterMode.COLOR); addChild(flag); flag.filters = [displacementFilter]; perlinSeed = int(Math.random() * int.MAX_VALUE); offsets = new Array(); for (var i:int = 0; i < OCTAVES; i++) offsets[i] = new Point(); fadeOutWave = new Shape(); var m:Matrix = new Matrix(); m.createGradientBox(FLAG_WIDTH/2, FLAG_HEIGHT); fadeOutWave.graphics.beginGradientFill(GradientType.LINEAR, [0x808080, 0x808080], [1, 0], [0, 255], m); fadeOutWave.graphics.drawRect(0, 0, FLAG_WIDTH/2, FLAG_HEIGHT); fadeOutWave.graphics.endFill(); var shadeBitmap:Bitmap = new Bitmap(map); shadeBitmap.height = FLAG_HEIGHT + DISPLACEMENT*2; shadeBitmap.width = FLAG_WIDTH + DISPLACEMENT; shadeBitmap.y = -DISPLACEMENT; addChild(shadeBitmap);

Consider a machining operation in which a piece of sheet metal needs two identical diameter holes drilled and two identical size notches cut. We denote a drilling operation as d and a notching operation as n. In determining a schedule for a machine shop, we might be interested in the number of different possible sequences of the four operations. The number of possible sequences for two drilling operations and two notching operations is 4! 2! 2! 6

shadeBitmap.blendMode = BlendMode.OVERLAY; shadeBitmap.alpha = 0.4; this.x = 50; this.y = 50; addEventListener(Event.ENTER_FRAME, onEnterFrame); } protected function onEnterFrame(event:Event):void { for (var i:int = 0; i < OCTAVES; i++) { offsets[i].x += Math.pow((1+i), 0.2) * WIND_SPEED; } map.perlinNoise(map.width, map.height * 6, OCTAVES, perlinSeed, false, true, 0, true, offsets); map.colorTransform(map.rect, SHIFT_COLORS); map.draw(fadeOutWave); displacementFilter.mapBitmap = map; flag.filters = [displacementFilter]; } } }

EXAMPLE S2-4 A part is labeled by printing with four thick lines, three medium lines, and two thin lines. If each ordering of the nine lines represents a different label, how many different labels can be generated by using this scheme From Equation S2-3, the number of possible part labels is 9! 4! 3! 2! 2520

Combinations Another counting problem of interest is the number of subsets of r elements that can be selected from a set of n elements. Here, order is not important. Every subset of r elements can be indicated by listing the elements in the set and marking each element with a * if it is to be included in the subset. Therefore, each permutation of r * s and n r blanks indicate a different subset and the number of these are obtained from Equation S2-3. For example, if the set is S = {a, b, c, d} the subset {a, c} can be indicated as a b c d * *

By using Perlin noise as a displacement map, you can simulate vertical and horizontal waves in the fabric of the ag. The displacement map pulls double duty to shade the ag for added realism. Another visual tweak blends the displacement toward a no-offset displacement as you approach the left side of the ag, which would be presumably tethered and less reactive to wind shear. Note the color transform applied to the bitmap. This shifts the ranges of the colors generated by the Perlin noise generator so that they are centered on 128.

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