Preliminary examples

(a) An industrial experiment is to be planned to investigate the effects of varying seven factors in a chemical process. It is decided to use two levels of each factor, and there is sufficient material and time to make observations on 64 treatment combinations. How should the 64 treatment combinations to be included in the experiment be chosen?

(b) An experiment on competition between grass and legume species is to be planned to investigate the effects and pairwise interactions of eight factors. The eight factors are:

1. (1) two different cutting regimes,

2. (2) two different grass species,

3. (3) two different legume species,

4. (4) two levels of phosphate,

5. (5) two levels of potassium,

6. (6) two levels of nitrogen,

7. (7) root competition between grass and legume allowed or restricted,

8. (8) shoot competition between grass and legume allowed or restricted.

The total number of experimental units that can be managed is 48. How should the 48 combinations be chosen?

(c) An experiment on making hot cross buns is to be planned to investigate the effects, both main effects and two-factor interactions, of six factors. The factors to be varied are: (i) three different forms of flour (F), (ii) three different temperatures for baking (T), (iii) three levels for the amount and pattern of dried fruit in the mixture (D) and (iv) two levels of each of three additives related to improving storage performance (A, B and C).