By changing one factor after another, we carry out a Design Of Experiments. This traditional approach that we all know does not meet the specificity we are looking for in modeling.
Introduction
In the traditional method of experimentation, only one factor is varied at a time (OFAT: One factor at a time). For example, the different levels 1 and 2 of factor A are compared while all other factors remain fixed. It is the historical experimentation approach that is still very often used.
Effective in determining whether a factor influences a response, however, it is ineffective in quantifying and modeling a cause-and-effect relationship.
Why is this approach bad?
It is precisely because we vary one factor after another that this approach is not viable. By following this process, it is not possible to determine whether factor a in relation to factor B influences the response.
In other words, with such an approach, we are unable to say whether there is any interaction between the factors.
Nor is it possible to guarantee the reproducibility of the result in the real conditions, where the other factors can be altered. With such a process, the phenomena of ” noise” are not taken into account.
Construction of the test matrix and effects
The test and effects matrix is simple to build. We define a reference situation, for example-1, and then to each experiment, we vary a factor that have both levels. The number of experiments is equal to the number of factor plus 1.
For example for 7 factors, this gives us the following table:
Test number |
Factor 1 |
Factor 2 |
Factor 3 |
Factor 4 |
Factor 5 |
Factor 6 |
Factor 7 |
Answer |
1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
Y1 |
2 |
+1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
Y2 |
3 |
+1 |
+1 |
-1 |
-1 |
-1 |
-1 |
-1 |
Y3 |
4 |
+1 |
+1 |
+1 |
-1 |
-1 |
-1 |
-1 |
Y4 |
5 |
+1 |
+1 |
+1 |
+1 |
-1 |
-1 |
-1 |
Y5 |
6 |
+1 |
+1 |
+1 |
+1 |
+1 |
-1 |
-1 |
Y6 |
7 |
+1 |
+1 |
+1 |
+1 |
+1 |
+1 |
-1 |
Y7 |
8 |
+1 |
+1 |
+1 |
+1 |
+1 |
+1 |
+1 |
Y8 |
The conclusions of a traditional approach
We understand, with such a plan, it will be easy to determine if a factor has influence. For example, if Y1 = Y2 in the previous table, then it will be concluded that factor 1 has no influence on the response and can be removed from the model.
On the other hand, the effects can be calculated according to the following model:
- A_{1} = Y2-Y1
- A_{2} = Y3-Y1
- …
This will undoubtedly give us an ” order of Idea ” on the prediction model, but by not taking into account the phenomena of noise or the interactions, we will not be able to rely on the results. It is not recommended to use these results to establish a prediction model.
How to integrate a qualitative variable
This type of plan is used to identify the cause of a problem in the event that we suspect that only one parameter can be the source.
It is very effective to help select the factors to use during the study.
Source
S. Karam (2004) – Application of the methodology of experience plans and data analysis to the optimization of deposit processes
W. Tinsson (2010) – Plans of experiments: construction and statistical analysis