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If the process is in control, all the plotted points should have an essentially random pattern Methods designed to nd sequences or nonrandom patterns can be applied to control charts as an aid in detecting out-of-control conditions A particular nonrandom pattern usually appears on a control chart for a reason, and if that reason can be found and eliminated, process performance can be improved There is a close connection between control charts and hypothesis testing Essentially, the control chart is a test of the hypothesis that the process is in a state of statistical control A point plotting within the control limits is equivalent to failing to reject the hypothesis of statistical control, and a point plotting outside the control limits is equivalent to rejecting the hypothesis of statistical control..

kernel Mirror <...> { input image4 source; output pixel4 result;

We give a general model for a control chart. Let W be a sample statistic that measures some quality characteristic of interest, and suppose that the mean of W is W and the standard deviation of W is W.* Then the center line, the upper control limit, and the lower control limit become

to discuss in detail the code to be associated with each element of the program by the programmer and the code that is automaticallygenerated by the software synthesis tool, and

(16-1)

void evaluatePixel() { float2 location = outCoord(); location.xy = location.yx; result = sample(source, location); } }

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where k is the distance of the control limits from the center line, expressed in standard deviation units. A common choice is k 3. This general theory of control charts was rst proposed by Dr. Walter A. Shewhart, and control charts developed according to these principles are often called Shewhart control charts. The control chart is a device for describing exactly what is meant by statistical control; as such, it may be used in a variety of ways. In many applications, it is used for online process monitoring. That is, sample data are collected and used to construct the control chart, and if the sample values of x (say) fall within the control limits and do not exhibit any systematic pattern, we say the process is in control at the level indicated by the chart. Note that we may be interested here in determining both whether the past data came from a process that was in control and whether future samples from this process indicate statistical control. The most important use of a control chart is to improve the process. We have found that, generally 1. 2. Most processes do not operate in a state of statistical control. Consequently, the routine and attentive use of control charts will identify assignable causes. If these causes can be eliminated from the process, variability will be reduced and the process will be improved.

You can see that the input is an entire image, even though the output is a single pixel. Given an input image source, you nd out which pixel you re supposed to be drawing. Instead of a at color, you pick the color from another pixel in the source image, because you have access to the whole image. You nd the location of the output pixel with outCoord(), switch its y and x coordinates, and then look up the color at the new location. You could have just as easily picked the color 30 pixels to the right, or you could have divided the x coordinate by 2 to stretch out the image horizontally. Maybe you want to draw a circle. To do so, you should pick a color to draw the pixels that fall inside the circle, and another for pixels that fall outside the circle:

This process-improvement activity using the control chart is illustrated in Fig. 16-2. Notice that:

kernel Circle <...> { input image4 source; output pixel4 result; const float2 circleCenter = float2(50.0, 50.0); const float circleRadius = 50.0; void evaluatePixel() { float2 location = outCoord(); if (distance(location, circleCenter) < circleRadius) { result = pixel4(1.0, 1.0, 1.0, 1.0); } else { result = pixel4(0.0, 0.0, 0.0, 1.0); } } }

* Note that sigma refers to the standard deviation of the statistic plotted on the chart (i.e., deviation of the quality characteristic.

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