Six notions gouvernent tout le menu. Sans elles, les écrans et les plans d’expériences se lisent mal.
1. Facteur, niveau, essai
A factor (labeled X) is a variable that you control: a temperature, a pressure, a machine, or a supplier. Its levels are the values we will set it to: two levels (min/max), three (min/middle/max), or more. A essay is a line on the plan: a combination of levels to be achieved.
The table of factors, on the left side of each page, is the source of truth: you enter one factor per line, along with its levels. The number of factors and their levels determine which designs are suggested; they are not entered anywhere else.
2. Interaction
There are interaction between two factors when the effect of one depends on the level of the other: the hardener improves cold strength but reduces it at high temperatures. An interaction cannot be inferred from any factor-by-factor study; this is precisely what the design of experiments provides.
⚠️ Every interaction you want to estimate uses one degree of freedom, as an additional factor. That’s why declaring interactions causes the small tables to disappear from the list: there’s no longer room for them.
3. Alias et résolution
A fractional table only covers a portion of the possible combinations. The trade-off: some effects become aliases, that is, when combined, their columns are identical, and nothing in the data will indicate which of the two caused the observed discrepancy.
Visit resolution summarizes the seriousness of these misunderstandings:
| Resolution | What Is Being Confused | Reading |
| III | Major effects with interactions | Screening only. An effect may be a disguised interaction. |
| IV | Interactions among them; specific main effects | A good compromise: the results are reliable. |
| V and up | Almost nothing | Comfortable modeling. |
| Complete factorial | Nothing | All combinations have been completed. |
💡 The alias table, at the bottom of the Taguchi pages, lists—column by column—the factors and their interactions. This is the document you should read before to begin the trials: he states in advance what the plan will not be able to resolve.
4. Orthogonalité et corrélation
Two columns in the table are orthogonal when their correlation is zero: their effects are estimated independently. This is the design objective for all the plans in the menu, and what is verified by the correlation matrix Available on multiple pages. Outside the diagonal, we want white.
5. Points centraux et réplication
A key point is a midpoint test of all factors. It is not used to estimate an effect, but rather for two other purposes: to measure the repeatability of the process, and detect a curvature, if the observed value deviates from the average of the extremes, the response is not linear.
Reply One approach doubles the number of trials and removes aliases. This is the simplest—and most expensive—solution.
6. Degrés de liberté
The number of degrees of freedom (ddl) is the number of coefficients to be estimated: the constant, the main effects, the declared interactions, and the quadratic terms. A design requires at least as many trials as there are ddl, plus one additional trial per ddl, if residual variance is also to be estimated.
⚠️ This is a hard constraint of the design of experiments, and it is non-negotiable: requesting a rich model with a tight trial budget is impossible—not just imprecise. The menu pages use this constraint to hide tables that are too small, rather than letting you build an unusable design.