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OTE/SPH
OTE/SPH
August 31, 2006
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JWBK119-06
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Nested Design 81
Batches Batch Batch Batch Batch
Units Unit Unit Unit

Reading
Reading
Readings
Reading Reading
Reading Reading
Figure 6.4 A typical nested design.

or batches, and there is no physical relationship among sample 1 from group 1 and
sample 1 from group 2. A typical nested design is shown in Figure 6.4.
Suppose, for example, that in the following, two oxide thickness readings from four
different wafers produced in 21 different lots are taken (Table 6.3). The average and
range (difference between maximum and minimum) for each lot are given in the last
two columns. Figure 6.5 gives a graphical representation of this example.

Table 6.3 Oxide thickness for wafers from different lots.
Wafer 1 Wafer 2 Wafer 3 Wafer 4
Lot 1 2 1 2 1 2 1 2 Average Range

1 946 940 966 964 977 946 943 929 951.4 48
2 961 956 977 953 963 977 956 940 960.4 37
3 915 920 948 942 905 887 906 914 917.1 61
4 968 984 970 945 989 962 969 971 969.8 44
5 950 950 962 980 960 954 945 946 955.9 35
6 984 981 967 958 956 960 991 999 974.5 43
7 993 1026 984 959 1034 998 969 992 994.4 75
8 922 935 935 981 927 920 932 939 936.4 61
9 962 968 948 948 933 953 933 921 945.8 47
10 955 945 984 972 946 952 986 984 965.5 41
11 965 957 983 985 982 967 949 933 965.1 52
12 948 928 963 988 943 940 985 986 960.1 60
13 980 970 956 969 1009 1025 970 995 984.3 69
14 964 955 985 988 964 983 963 958 970.0 33
15 950 957 938 925 956 947 934 942 943.6 32
16 952 947 963 978 971 972 975 984 967.8 37
17 949 946 984 993 967 948 1006 1007 975.0 61
18 939 954 933 935 922 921 947 950 937.6 33
19 1010 992 987 987 972 1012 966 963 986.1 49
20 969 1009 958 955 977 979 952 958 969.6 57
21 995 983 999 1002 998 1016 980 975 993.5 41
Mean 963.0 48.4