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and this result is nearly the same as from r. The S chart is shown in Fig. 16-9. Because the control limits for the X chart calculated from s are nearly the same as from r, the chart is not shown. Suppose that all of these assignable causes can be traced to a defective tool in the waxmolding area. We should discard these ve samples and recompute the limits for the X and R charts. These new revised limits are, for the X chart, UCL LCL and for the R chart, UCL LCL

We now discuss the approaches to writing ATaG macroprograms for the object detection and tracking functionality At the high level, the program should determine the presence of objects of interest in the sensor field at all times We simplify the use case by assuming that identity maintenance and tracking is not a concern in this example In other words, if one or more objects of interest are in the sensor field, the application should only generate periodic reports that indicate the presence and the approximate location of each object The program is not required to be intelligent enough to detect if an object at some location X' at time T' is the same object as was detected at location X at an earlier time T As mentioned briefly in Section 2.

For example:

33.21 33.21

36.10 30.33

const float circleRadius = 25.0; input image4 inputImage; output pixel4 returnPixel;

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12.115215.02 10215.02 0

A constant should need no explanation. Flash Player usually assigns the inputs and outputs of a kernel automatically. That s where parameters come in. Parameters make up the public interface to the kernel. They may be modi ed by ActionScript code while the kernel is running, and you can tweak them by hand to test your kernel if you re using the IDE. You could convert the constant values that de ne a circle in your Circle kernel from earlier into parameters:

Figure 16-9.

<languageVersion: 1.0;> kernel Circle <namespace: "as3b"; vendor: ""; version: 2;> { input image4 source; output pixel4 result; parameter float2 circleCenter < minValue: float2(0.0, 0.0); maxValue: float2(1000.0, 1000.0); description: "Center point of the circle"; >;

42 40 38 36 x 34 32 30 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Estimation of limits X Chart 16 14 12 10 r 8 6 4 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Estimation of limits R Chart Sample number CL = 5.0 = not used in computing control limits Revised UCL = 10.57 Sample number Revised UCL = 36.10 CL = 33.21 Revised LCL = 30.33 = not used in computing control limits

parameter float circleRadius < minValue: 1.0; maxValue: 500.0; defaultValue: 25.0; >; void evaluatePixel() { float2 location = outCoord(); if (distance(location, circleCenter) < circleRadius) { result = sample(source, location); } else { result = pixel4(0.0, 0.0, 0.0, 0.0); } } }

The revised control charts are shown in Fig. 16-10. Notice that we have treated the rst 20 preliminary samples as estimation data with which to establish control limits. These limits can now be used to judge the statistical control of future production. As each new sample becomes available, the values of x and r should be computed and plotted on the control charts. It may be desirable to revise the limits periodically, even if the process remains stable. The limits should always be revised when process improvements are made. Computer Construction of X and R Control Charts Many computer programs construct X and R control charts. Figures 16-8 and 16-10 show charts similar to those produced by Minitab for the vane-opening data. This program will allow the user to select any multiple of sigma as the width of the control limits and use the Western Electric rules to detect out-of-control points. The program will also prepare a summary report as in Table 16-2 and exclude subgroups from the calculation of the control limits.

Table 16-2 Summary Report from Minitab for the Vane-Opening Data Test Results for Xbar Chart TEST 1. One point more than 3.00 sigmas from center line. Test Failed at points: 6 8 11 19 Test Results for R Chart TEST 1. One point more than 3.00 sigmas from center line. Test Failed at points: 9

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