# A critical dimension | Mathematics homework help

Consider the situation described in Exercise 6.70. A critical dimension (measured in mm) is of interest to the process engineer. Suppose that five fixed positions are used on each wafer (position 1 is the center) and that two consecutive wafers are selected from each batch. The data that result from several batches are shown in Table 6E.32.

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(a) What can you say about overall process capability?

(b) Can you construct control charts that allow within wafer variability to be evaluated?

(c) What control charts would you establish to evaluate variability between wafers? Set up these charts and use them to draw conclusions about the process.

(d) What control charts would you use to evaluate lotto- lot variability? Set up these charts and use them to draw conclusions about lot-to-lot variability.

 TABLE 6 E .32 Data for Exercise 6.71 Position Position Lot Wafer Lot Wafer Number Number 1 2 3 4 5 Number Number 1 2 3 4 5 1 1 2.15 2.13 2.08 2.12 2.10 11 1 2.15 2.13 2.14 2.09 2.08 2 2.13 2.10 2.04 2.08 2.05 2 2.11 2.13 2.10 2.14 2.10 2 1 2.02 2.01 2.06 2.05 2.08 12 1 2.03 2.06 2.05 2.01 2.00 2 2.03 2.09 2.07 2.06 2.04 2 2.04 2.08 2.03 2.10 2.07 3 1 2.13 2.12 2.10 2.11 2.08 13 1 2.05 2.03 2.05 2.09 2.08 2 2.03 2.08 2.03 2.09 2.07 2 2.08 2.01 2.03 2.04 2.10 4 1 2.04 2.01 2.10 2.11 2.09 14 1 2.08 2.04 2.05 2.01 2.08 2 2.07 2.14 2.12 2.08 2.09 2 2.09 2.11 2.06 2.04 2.05 5 1 2.16 2.17 2.13 2.18 2.10 15 1 2.14 2.13 2.10 2.10 2.08 2 2.17 2.13 2.10 2.09 2.13 2 2.13 2.10 2.09 2.13 2.15 6 1 2.04 2.06 1.97 2.10 2.08 16 1 2.06 2.08 2.05 2.03 2.09 2 2.03 2.10 2.05 2.07 2.04 2 2.03 2.01 1.99 2.06 2.05 7 1 2.04 2.02 2.01 2.00 2.05 17 1 2.05 2.03 2.08 2.01 2.04 2 2.06 2.04 2.03 2.08 2.10 2 2.06 2.05 2.03 2.05 2.00 8 1 2.13 2.10 2.10 2.15 2.13 18 1 2.03 2.08 2.04 2.00 2.03 2 2.10 2.09 2.13 2.14 2.11 2 2.04 2.03 2.05 2.01 2.04 9 1 1.95 2.03 2.08 2.07 2.08 19 1 2.16 2.13 2.10 2.13 2.12 2 2.01 2.03 2.06 2.05 2.04 2 2.13 2.15 2.18 2.19 2.13 10 1 2.04 2.08 2.09 2.10 2.01 20 1 2.06 2.03 2.04 2.09 2.10 2 2.06 2.04 2.07 2.04 2.01 2 2.01 1.98 2.05 2.08 2.06

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