The 2 levels Taguchi plan

The reasoning behind the construction of this plan is the following:

  1. Define the factors and the levels
  2. Build the design of experiment
  3. Input the test results
  4. Analyze the plan
  5. Optimize the different responses to the plan if required

This window contains four buttons:
Delete line: Eliminate a factor
New: Re-initialize the sheet
Write a plan: Write a plan builds inside the spreadsheet in order to enter the results of the tests
Duplicate: Allows you to move from one table to its duplicate (example L8 to L16) by saving the tests that have already been carried out but improving the resolution.

Define the factors and the levels

The definition of the factors consists of defining for all factors :

Plan d'expérience 4

  • a long name;
  • a short name (3 characters) the system automatically uses A, B, C… But we recommend you create meaningful short names (example Time => tim);
  • the levels studied; Ellistat automatically determines whether it is a qualitative or quantitative factor

Constructing the design of experiment

Ellistat has an exclusive design of experiment creation engine.  It can find the plan with the best strategie possible taking into account the structure of data interactions.  The tables programmed in Ellistat are tables L4, L8, L12, L16, L20 and L32.
From the moment the plan creation engine is launched Ellistat will post the tables that can be used according to the number of factors studied on the bottom of the page.

The columns that have been check marked are those that you should use to gain maximum resolution and therefore a higher quality plan.

The resolution is provided in the second column. In the example above you have a choice between 4 tables:
• The L8 table with a resolution of III (high risk). In this case you can use any column.
• The L12 table with a resolution of III/IV (the clearing plan). In this case you can use any column.
• The L16 table with a resolution of V (low risk). The factors will be in columns 1,2,4,8,15
• The L20 table with a resolution of III/IV (clearing plan). In this case you can use any column.

You can create your own plans or let Ellistat choose the plan with the best resolution. In this case Ellistat applies the construction rules for 2 level plans (Learn more).

Choosing columns for interactions

When using tables allowing for an interaction study (Table 4, 8, 16, 32), Ellistat allows you to select the non-null supposed interactions.

Plan d'expérience 5

If desired, you can choose to prioritize a column for certain factors.

Click in the interaction table to select the interaction that you would like to save.  An “I” will appear.  Click once again on the interaction to eliminate a selection. If the column with the selected interaction is already reserved for a factor or another interaction then an alert message will appear.

The “Alias table”, in addition to providing selected factors and interactions, also provides the second degree reactions and their corresponding columns. The risks taken by carrying out the selected plans can therefore be easily visualized.

With a design of experiment we are always looking for the best resolution possible, i.e. the least amount of aliases possible. You can refer to specialized documentation for optimum column choice.

Choosing columns for factors

In example one we want powers to be in the first column because it is the most difficult to modify (the machine menu is not ergonomic) and because column 1 changes levels only one time.

We also want the second factor to be in column 3 as it is difficult to change.

Plan d'expérience 11

In this case we set the number of the Taguchi column as indicated above.  Ellistat finds (if possible) a solution under the imposed constraints.

In the example above, the plan found by Ellistat respects all the imposed constraints. This is exclusively possible with Ellistat which allows you to easily find any plan without being an expert in design of experiment.

You can also create your own plan by choosing the assignment factors for the tables and columns.

For each factor, you define the column in which you wish to assign the factor.  A summary of the contents of each column is posted in the “Alias table” frame.

Calculating the necessary table

Depending on the number of factors studied and the structure of the interactions, Ellistat calculates the most appropriate table satisfying two of the construction criteria for experimental plans: the number of degrees of freedom and the orthogonality of the plan, while still preserving a plan resolution of IV.

You can force the use of a desired table :

Plan d'expérience 6

Reminder:
No interaction: multiple of 4
Joint interactions: Multiple of 8
Disjoint Interactions: Multiple of 16
Disjoint Triangles: Multiple of 32

For two level plans the number of degrees of freedom is equal to the number of factors + the number of interactions + 1.

These rules are necessary but not sufficient. In certain configurations the existence of a L16 table is predicted but is not possible.  By using the automatic research function in this case, Ellistat will automatically use the L32 plan.

Studying quadratic factors

If the linearity hypothesis is not followed for certain factors, i.e. the evolution of there result is not linear when the factor varies from level 1 to level 2, Ellistat suggests that you increase the experimental plan in order to study the quadratic effects.

Effet quadratique

In order to study a factor with a non-linear effect it is necessary to add a central level to model the non-linear effect. To do this click on “Quadratic effect” and add the factors that you believe do not have a linear effect.

Plan d'expérience 8

Ellistat will then suggest an optimized plan to study these factors and their effects.

Writting the plan

Une fois le plan construit, cliquez sur le bouton “Ecrire le plan”, les essais relatifs au plan d’expérience défini seront inscrits dans le tableur, il vous suffira dès lors de réaliser les essais avant de pouvoir les analyser.

Plan d'expérience 10