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