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14-15. Consider the experiment in Exercise 14-14. Determine an appropriate model and plot the residuals against the levels of factors A, B, C, and D. Also construct a normal probability plot of the residuals. Comment on these plots. 14-16. The data shown here represent a single replicate of a 25 design that is used in an experiment to study the compressive strength of concrete. The factors are mix (A), time (B), laboratory (C), temperature (D), and drying time (E). 112 a b ab c ac bc abc d ad bd abd cd acd bcd abcd 700 900 3400 5500 600 1000 3000 5300 1000 1100 3000 6100 800 1100 3300 6000 e ae be abe ce ace bce abce de ade bde abde cde acde bcde abcde 800 1200 3500 6200 600 1200 3006 5500 1900 1500 4000 6500 1500 2000 3400 6800

One part of Example 35-16 that bugs me is that you have to pass the two Vectors in an anonymous Object to get them out of the function. That s not very object oriented! You should be able to encapsulate all knowledge about a path into one path object. Enter GraphicsPath. On one level, GraphicsPath is just a wrapper class for a path de ned as you have seen before, with the properties commands, data, and winding de ning the properties drawPath() expects. You can set these properties or assign some or all of them at construct time:

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14-18. An experiment described by M. G. Natrella in the National Bureau of Standards Handbook of Experimental Statistics (No. 91, 1963) involves ame testing fabrics after applying re-retardant treatments. The four factors considered are type of fabric (A), type of re-retardant treatment (B), laundering condition (C the low level is no laundering, the high level is after one laundering), and method of conducting the ame test (D). All factors are run at two levels, and the response variable is the inches of fabric burned on a standard size test sample. The data are: 112 a b ab c ac bc abc 42 31 45 29 39 28 46 32 d ad bd abd cd acd bcd abcd 40 30 50 25 40 25 50 23

(a) Estimate the factor effects. (b) Which effects appear important Use a normal probability plot. (c) If it is desirable to maximize the strength, in which direction would you adjust the process variables (d) Analyze the residuals from this experiment. 14-17. An article in the IEEE Transactions on Semiconductor Manufacturing (Vol. 5, no. 3, 1992, pp. 214 222) describes an experiment to investigate the surface charge on a silicon wafer. The factors thought to in uence induced surface charge are cleaning method (spin rinse dry or SRD and spin dry or SD) and the position on the wafer where the charge was measured. The surface charge ( 1011 q/cm3) response data are as shown. Test Position L R SD Cleaning Method SRD 1.66 1.90 1.92 4.21 1.35 2.08 1.84 1.84 1.62 7.58 2.20 5.36

var p1:GraphicsPath = new GraphicsPath(); p1.commands = commandsVector; p1.data = coordinatesVector; var p2:GraphicsPath = new GraphicsPath(commandsVector, coordinatesVector);

(a) Estimate the effects and prepare a normal plot of the effects. (b) Construct an analysis of variance table based on the model tentatively identi ed in part (a). (c) Construct a normal probability plot of the residuals and comment on the results. 14-19. An experiment was run in a semiconductor fabrication plant in an effort to increase yield. Five factors, each at two levels, were studied. The factors (and levels) were A aperture setting (small, large), B exposure time (20% below nominal, 20% above nominal), C development time (30 and 45 seconds), D mask dimension (small, large), and E etch time (14.5 and 15.5 minutes). The following unreplicated 25 design was run: 112 a b ab c ac bc abc d ad bd abd cd acd bcd abcd 7 9 34 55 16 20 40 60 8 10 32 50 18 21 44 61 e ae be abe ce ace bce abce de ade bde abde cde acde bcde abcde 8 12 35 52 15 22 45 65 6 10 30 53 15 20 41 63

On another level, GraphicsPath provides an easier way to construct the data that makes up a path. It contains methods to push each kind of path command onto the Vectors: moveTo(), lineTo(), curveTo(), and the wide methods wideLineTo() and wideMoveTo(). You call these just like you would call the corresponding methods on a Graphics object, but remember that they re used to modify the path stored in the GraphicsPath, not the canvas on-screen. Because these methods write to the vectors internally, you don t have to worry about modifying them manually. An error in writing to these vectors that puts the two out of sync by adding the wrong number of numbers to the coordinates vector, for instance ruins the rest of the path. Using the convenience functions prevents this.

(a) Estimate the factor effects. (b) Which factors appear important Use 0.05. (c) Analyze the residuals from this experiment.

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