Question

1. Using the “Rule of Thumb” guideline flow chart, what would be the best choice for a 2-Level, 2-Factor Design?
   1. Taguchi L18 Design
   2. Box-Behnkin Design
   3. Screening Design
   4. Full Factorial Design
2. A 2-level design is said to be orthogonal if:
3. It is balanced vertically
4. The dot product of all column pairs is zero
5. Both a and b
6. none of the above

Answer 1

2nd question:

, A  designed experiment is orthogonal if the effects of any factor balance out (sum to zero) across the effects of the other factors. Orthogonality guarantees that the effect of one factor or interaction can be estimated separately from the effect of any other factor or interaction in the model.

An orthogonal matrix, that is to say that it is vertically and horizontally balanced.

Mathematically, vertical balancing occurs if the sum of each column is zero

So option both a and b are correct

1st Question:

Screening designs are mainly  of resolution III.

The reason is that resolution III designs permit one to explore the effects of many factors with an efficient number of runs. Sometimes designs of resolution IV are also used for screening designs. In these designs, main effects are confounded with, at worst, three-factor interactions.

The Box-Behnken design that requires only three levels to run an experiment. It is a special 3-level design because it does not contain any points at the vertices of the experiment region.

And also we use 3 factor in Full Factorial Design .

Taguchi designs can have factors with several levels, although two and three level designs are the most common. The L18 design is perhaps the most popular.

So best choice for a 2-level, 2-factor design is Tanguchi L18 Design.