BCS interaction

The economics of the situation are desirable for factors B and C - lighter pressure would produce less wear on the machine and maintenance costs would be less the lighter weight packaging material would presumably cost less. However, an analysis of the main effects of B and C is insufficient in this example the interaction effects must also be examined. The three-factor interaction ABC is small. The AB and AC interactions are small. But the BC interaction is very large, larger than the largest main effect. 

Using the BH algorithm to estimate the effects, we note that column AB has the same signs as column C, column AC has those of column B, column BC those of column A and column ABC those of I. Hence the linear combination of observations in column A, 1a, can be used to estimate not only the main effect of A but also the BC interaction (1a = A + BC 1 a = A — BC if we select C = —AB as generator). Two (or more) effects that share this type of relationship are termed aliases". As a consequence, aliasing" is a direct result of fractional replication. In many practical situations, it will be possible to select a fraction of the experiments so that the main effect and the low-order interactions that are of interest become aliased (confounded) only with high-order interactions, which are probably negligible. 

We note that the atom-diatom dispersion coefficients are usually expressed in the center-of-mass coordinate system by an expansion in terms of Legendre polynomials Pn(cos0). For example, for the A---(BC) interaction, one gets... 

Although, in principle, four probabilities could be specified in (9), the circumstances under which (8a, 8b) = (0, 1) and (1,0) can be distinguished are uncommon. In some applications, n, 7r0, tt, n2 may vary for, say, effects associated with A and with B. To keep notation simple, this straightforward generalization is not discussed further. Probabilities for the AC and BC interactions being active are defined in a similar way. 

AB + C reaction and the shape of the product angular distribution is to assume the final momentum of the C product Pc as the result of two contributions the first one is the momentum that C would have if no momentum were transferred from the A BC interaction. In this case, by the conservation of linear momentum, one would write... 

---