3. Production Process Characterization
3.5. Case Studies
3.5.1. Furnace Case Study

## Analysis of Variance

Analysis of Variance The next step is to confirm our interpretation of the plots in the previous section by running a nested analysis of variance.

 Source Degrees of Freedom Sum of Squares Mean Square Error F Ratio Prob > F Run 20 61,442.29 3,072.11 5.37404 0.0000001 Furnace Location [Run] 63 36,014.5 571.659 4.72864 3.85e-11 Within 84 10,155 120.893 Total 167 107,611.8 644.382

Components of Variance From the above analysis of variance table, we can compute the components of variance. Recall that for this data set we have 2 wafers measured at 4 furnace locations for 21 runs. This leads to the following set of equations.
3072.11 = (4*2)*Var(Run) + 2*Var(Furnace Location) + Var(Within)
571.659 = 2*Var(Furnace Location) + Var(Within)
120.893 = Var(Within)
Solving these equations yields the following components of variance.

Components of Variance
Component Variance Component Percent of Total Sqrt(Variance Component)
Run 312.55694 47.44 17.679
Furnace Location[Run] 225.38294 34.21 15.013
Within 120.89286 18.35 10.995