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is the average number of defects per unit. A U chart may be constructed for such data. If the number of defects in a unit is a Poisson random variable with parameter , the mean and variance of this distribution are both . Each point on the chart is U, the average number of defects per unit from a sample of n units. Therefore, the mean of U is and the variance of U is n. UCL LCL 3 3 Bn Bn

This section investigates two advanced applications of Pixel Bender: using kernels to crunch different kinds of data ef ciently, and asynchronously These goals are far from mutually exclusive As I ve said before, even if a Pixel Bender kernel runs on the CPU, it may utilize the CPU better than ActionScript 30 would If you design your programs to break out time-critical vector processing routines into Pixel Bender kernels, you can make better use of the CPU and squeeze out more performance, especially on multicore machines Whether or not a kernel runs faster than equivalent ActionScript, the kernel is able to run asynchronously to ActionScript code For huge data sets, simply freeing up AVM2 to handle the application s interface and input handling is enough of a bene t.

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Rather than hang while the data is processed, the kernel can execute in one or more threads, ring an event back to ActionScript when its results are ready In other words, you may not be able to move processing off the CPU, but you can move it off the main thread To take advantage of Pixel Bender for generalized data processing, though, your problem should be compatible with Pixel Bender s pipeline Rather than run your kernel on every pixel of an image, it runs your kernel on every sample of the data (Actually, the kernel still runs on an image you just craft this image to store your data) So the problem should be highly parallelizable The result for any sample of the data can t rely on the result for another sample.

If there are m preliminary samples, and the number of defects per unit in these samples are U1, U2, . . . , Um, the estimator of the average number of defects per unit is U 1 m m ia Ui 1 (16-26)

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The input has to be one or more sets of data, and the output of the kernel must be a set of data You must be able to represent the input and output data as sequences or arrays of 32-bit oating-point numbers Also, you can only use the math functions and data types that Pixel Bender provides, so save it for crunching numbers, vectors, and matrices..

These control limits are based on the normal approximation to the Poisson distribution. When is small, the normal approximation may not always be adequate. In such cases, we may use control limits obtained directly from a table of Poisson probabilities. If u is small, the lower control limit obtained from the normal approximation may be a negative number. If this should occur, it is customary to consider zero as the lower control limit. EXAMPLE 16-5 Printed circuit boards are assembled by a combination of manual assembly and automation. A ow solder machine is used to make the mechanical and electrical connections of the leaded components to the board. The boards are run through the ow solder process almost continuously, and every hour ve boards are selected and inspected for process-control purposes. The number of defects in each sample of ve boards is noted. Results for 20 samples are shown in Table 16-5. The center line for the U chart is 1 20 u 20 ia i 1 u Bn 32 20

You can use multiple inputs in a kernel, but all inputs must be image types. Recall that image types in Pixel Bender have between one and four channels, which are stored as 32-bit precision oating-point

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var haiku:String = "Oh ActionScript three/ you make coding delightful / I think you are neat."; var lineDelimiter:RegExp = /\s*\/\s*/; var lines:Array = haiku.split(lineDelimiter); for (var i:int = 0; i < lines.length; i++) { trace(i, lines[i]); } //0 Oh ActionScript three //1 you make coding delightful //2 I think you are neat.

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The rst and second delimiters in the example have different formats, but the regular expression catches them both. Additionally, by interpreting the whitespace (represented by \s, as you ll learn in the next section, Constructing Expressions ) as part of the delimiter, it is not included in the split-up substrings. As you can see, all three lines print out without extra whitespace in the beginning.

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