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(a) Suppose that the process standard deviation is 8 and that the target value of concentration for this process is 100 Design a CUSUM scheme for the process Does the process appear to be in control at the target (b) How many batches would you expect to be produced with off-target concentration before it would be detected by the CUSUM control chart if the concentration shifted to 104 Use Table 16-9 16-41 Consider a standardized CUSUM with H 5 and K 1 2 Samples are taken every two hours from the process The target value for the process is 0 50 and 2 Use Table 16-9.

Animating using a Timer object gives you some distinct bene ts. When you are using a Timer object, you can set the frequency at which new frames are drawn completely independently of the published frame rate of the SWF. You can employ this to change the frame rate of programmed animations without interfering with timeline animations created by the Flash authoring tool or running two animations at different frame rates. For example, you can animate the main characters of a game at 30 fps but save some CPU time by animating the background at 15 fps. It s possible for events from a Timer object to re more frequently than the published frame rate of a movie, and you can ensure that the results of these events are made visible by calling

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(a) If the sample size is n 1, how many samples would be required to detect a shift in the process mean to 51 on average (b) If the sample size is increased to n 4, how does this affect the average run length to detect the shift to 51 that you determined in part (a) 16-42 A process has a target of 0 100 and a standard deviation of 4 Samples of size n 1 are taken every two hours Use Table 16-9 (a) Suppose the process mean shifts to 102 How many hours of production will occur before the process shift is detected by a standardized CUSUM with H 5 and K 1 2 (b) It is important to detect the shift de ned in part (a) more quickly A proposal is made to reduce the sampling frequency to 05 hour.

updateAfterEvent() on the event object. This can actually make Flash Player play faster than the published frame rate. However, updating more frequently than the frame rate without showing the results visually is a waste.

How will this affect the CUSUM control procedure How much more quickly will the shift be detected (c) Suppose that the 05 hour sampling interval in part (b) is adopted How often will false alarms occur with this new sampling interval How often did they occur with the old interval of two hours (d) A proposal is made to increase the sample size to n 4 and retain the two-hour sampling interval How does this suggestion compare in terms of average detection time to the suggestion of decreasing the sampling interval to 05 hour.

Example 39-1 animates a DisplayObject moving the object to the right at whatever frame rate is assigned to the fps variable (here, it is 60), regardless of the published frame rate (set to 1 here).

16-11

EXAMPLE 39-1

While the control chart is a very powerful tool for investigating the causes of variation in a process, it is most effective when used with other SPC problem-solving tools. In this section we illustrate some of these tools, using the printed circuit board defect data in Example 16-4. Figure 16-17 shows a U chart for the number of defects in samples of ve printed circuit boards. The chart exhibits statistical control, but the number of defects must be reduced. The average number of defects per board is 8 5 1.6, and this level of defects would require extensive rework. The rst step in solving this problem is to construct a Pareto diagram of the individual defect types. The Pareto diagram, shown in Fig. 16-22, indicates that insuf cient solder and solder balls are the most frequently occurring defects, accounting for (109 160) 100 68% of the

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package { import flash.display.*; import flash.events.TimerEvent; import flash.utils.Timer; [SWF(frameRate="1")] public class ch39ex1 extends Sprite { protected var ball:DisplayObject; public function ch39ex1() { ball = new Ball(); ball.y = stage.stageHeight/2; addChild(ball); // fps = frames/second var fps:int = 60; // 1/fps = seconds/frame, 1/fps*1000 = milliseconds/frame var mspf:int = Math.round(1 / fps * 1000); var t:Timer = new Timer(mspf); t.addEventListener(TimerEvent.TIMER, onTimer); t.start(); } protected function onTimer(event:TimerEvent):void { ball.x += 0.5; event.updateAfterEvent(); } } } import flash.display.Shape; class Ball extends Shape { public function Ball(color:uint = 0xff0000, size:Number = 50) { graphics.beginFill(color); graphics.drawCircle(0, 0, size); } }

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