Example 23. Model with Crossed and Nested Effects: Sconduct Data

In a semiconductor plant, an engineer is investigating the effect of several modes of a process condition (ET) on resistance in computer chips. 12 silicon wafers (WAFER) were drawn from a lot, and three wafers were randomly assigned to each of 4 modes of ET. Resistance (RESIST) in the chips was measured in 4 positions (POS) on each wafer, post processing. The data is shown below.

Source: Littell, R.C., Freund, R.J. and Spector, P.C. (1991). SAS System for Linear Models. SAS Institute Inc.

Table 23: Sconduct Data

OBS  RESIST   ET  WAFER   POS
  1    5.22    1      1     1
  2    5.61    1      1     2
  3    6.11    1      1     3
  4    6.33    1      1     4
  5    6.13    1      2     1
  6    6.14    1      2     2
  7    5.60    1      2     3
  8    5.91    1      2     4
  9    5.49    1      3     1
 10    4.60    1      3     2
 11    4.95    1      3     3
 12    5.42    1      3     4
 13    5.78    2      1     1
 14    6.52    2      1     2
 15    5.90    2      1     3
 16    5.67    2      1     4
 17    5.77    2      2     1
 18    6.23    2      2     2
 19    5.57    2      2     3
 20    5.96    2      2     4
 21    6.43    2      3     1
 22    5.81    2      3     2
 23    5.83    2      3     3
 24    6.12    2      3     4
 25    5.66    3      1     1
 26    6.25    3      1     2
 27    5.46    3      1     3
 28    5.08    3      1     4
 29    6.53    3      2     1
 30    6.50    3      2     2
 31    6.23    3      2     3
 32    6.84    3      2     4
 33    6.22    3      3     1
 34    6.29    3      3     2
 35    5.63    3      3     3
 36    6.36    3      3     4
 37    6.75    4      1     1
 38    6.97    4      1     2
 39    6.02    4      1     3
 40    6.88    4      1     4
 41    6.22    4      2     1
 42    6.54    4      2     2
 43    6.12    4      2     3
 44    6.61    4      2     4
 45    6.05    4      3     1
 46    6.15    4      3     2
 47    5.55    4      3     3
 48    6.13    4      3     4

Questions:

1. Discuss a suitable model to study the effect of the various factors on resistance.

Keywords: Crossed effects, nested effects