Taguchi's experimental design is a statistical method used to improve the quality of products and manufacturing processes. Developed by Dr Genichi Taguchi, this design aims to identify the most influential factors on the variation of a product or process while minimising the number of experiments required.

This method organises experiments systematically and efficiently, enabling the effects of several variables to be analysed simultaneously. The main objective is to make the product or process robust against external and internal variations, thus ensuring stable, high-quality performance.

## Building an experimental plan

## Defining factors and levels

Defining the factors involves choosing the factors to be studied. To choose the right factors, we recommend that you first understand the process or product concerned, and then carry out the following steps:

- Organise brainstorming sessions with a multidisciplinary team to generate an exhaustive list of potential factors.
- Assess the importance of each factor in terms of its potential impact on the final result. Prioritise the factors that are likely to have a significant effect.
- Select the relevant factors for the experimental design based on the importance of the factor, your ability to control it and the ease of measuring it reliably.

For each factor identified, the levels studied must then be defined. It is important to choose relevant levels:

**Beach width**Select levels that cover a sufficiently wide range to detect the effects of factors, but without going to unrealistic extremes that could be unnecessary or dangerous.**Practical**To ensure that the levels chosen are achievable in a real production context.

## Choice of table

Once the factors have been identified, you need to create the experimental design. To do this, we recommend that you use Ellistat has an exclusive experiment design engine. It is capable of finding a design with the best possible strategy given a given structuring of interactions. The tables programmed in Ellistat are L4, L8, L12, L16, L20 and L32.

Here are the elements to bear in mind when creating your experience plan:

## Notion of interaction

*Example:*

Y=\alpha_0+\alpha_1*A+\alpha_2*B+\alpha_3*A*B

_{3}corresponds to the A*B interaction

## Notion of alias

A | B | Y |
---|---|---|

1 | 1 | 5 |

1 | 1 | 5 |

2 | 2 | 10 |

2 | 2 | 10 |

Factors A and B vary at the same time, so it is not possible to differentiate factor A from factor B, or to say which of the two causes the Y to vary from 5 to 10 when it goes from 1 to 2. We will say that these two factors are aliases.

- Factor a is aliased with interaction b*c
- The b factor is aliased with the a*c interaction
- Factor c is aliased with the a*b interaction

*c or the sum of the two. We will therefore assume that the interaction b*c is zero, but this remains to be verified experimentally.

## Solving an experimental design

The resolution of a design of experiment corresponds to the alias level of this design.

## Resolution III

## Resolution IV

- No factor is aliased with an interaction (order II)
- At least one interaction (order II) is aliased with another interaction (order II)

*Example:*

*b and c*d are aliased, so the plan is resolution IV.

## Resolution V

- No factor is aliased with an interaction (order II)
- No interaction (order II) is aliased with another interaction (order II) This type of design limits the number of trials compared with the complete design.