Question: Consider the situation described in Exercise 6.80. A critical dimension (measured in ïm) is of interest to the process engineer. Suppose that five fixed positions

Consider the situation described in Exercise 6.80. A critical dimension (measured in ïm) 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.34.

(a) What can you say about overall process capability?
(b) Can you construct control charts that allow within-wafer variability to be evaluated?
To evaluate within-wafer variability, construct an R chart for each sample of 5 wafer positions (two wafers per lot number), for a total of 40 subgroups.
(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 lot-to-lot variability? Set up these charts and use them to draw conclusions about lot-to-lot variability.

TABLE 6E.34 Data for Exercise 6.81 Position Position Lot Wafer Number Numb Lot Wafer 234 Nuber Number 3 4 5 2.15 213 2.08 2.12 2.101 2 2.13 210 2.04 2.08 2.05 1 2.15 2.13 2.14 209 2.08 2 2.11 213 2.10 214 2.10 2.03 2.06 2.05 2.0 2.00 2.01 2.08 2.03 210 2.07 2.05 2.03 2.05 2.09 2.08 2 2.08 2.0 203 204 2.10 2.08 2.04 2.05 2.01 2.08 2 2.09 .1 206 204 205 L 2.14 2.13 2.10 210 2.08 2 2.13 2.10 209 213 2.15 2.06 2.08 2.05 2.03 2.09 2203 199 206 2.05 2.05 2.03 2.08 2.01 2.04 2 2.06 105 203 205 2.00 2.03 2.08 2.04 2.00 2.03 2 2.04 2.03 2.05 2.01 2.04 2.16 2.13 2.10 2.13 2.12 2 2.13 2.15 2.18 219 2.13 2.06 2.03 2.04 2.09 2.10 2 2.01 8 2.05 208 2.06 2.02 201 2.06 2.05 2.08 2 2.03 209 2.07 2.06 2.04 12 2.13 212 2.10 2 2.08 2 2.03 208 203 2.09 2.07 1 2.04 201 2.10 2. 2.0914 2 207 214 212 208 209 1 2.16 217 2.13 2.18 2.10 5 2 217 213 2.10 209 213 2.04 206 1.97 2.10 2.08 16 2 2.03 210 2.05 2.07 2.04 1 2.04 202 2.01 2.00 2.05 2 2.06 204 2.03 2.08 2.10 1 2.13 210 2.10 2.15 2.13 2 2.10 209 2.13 2.14 2.11 1.95 203 2.08 2.07 2.08 2 2.01 203 2.06 2.05 2.04 13 6 17 18 19 10 2.04 208 2.09 2.10 2.01 2 2.06 204 2.07 2.04 2.01 20

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