# Taguchi designs

## What is a Taguchi design (also called an orthogonal array)?

A Taguchi design is a designed experiment that lets you choose a product or process that functions more consistently in the operating environment. Taguchi designs recognize that not all factors that cause variability can be controlled. These uncontrollable factors are called noise factors. Taguchi designs try to identify controllable factors (control factors) that minimize the effect of the noise factors. During experimentation, you manipulate noise factors to force variability to occur and then determine optimal control factor settings that make the process or product robust, or resistant to variation from the noise factors. A process designed with this goal will produce more consistent output. A product designed with this goal will deliver more consistent performance regardless of the environment in which it is used.

A well-known example of Taguchi designs is from the Ina Tile Company of Japan in the 1950s. The company was manufacturing too many tiles outside specified dimensions. A quality team discovered that the temperature in the kiln used to bake the tiles varied, causing nonuniform tile dimension. They could not eliminate the temperature variation because building a new kiln was too costly. Thus, temperature was a noise factor. Using Taguchi designed experiments, the team found that by increasing the clay's lime content, a control factor, the tiles became more resistant, or robust, to the temperature variation in the kiln, letting them manufacture more uniform tiles.

Taguchi designs use orthogonal arrays, which estimate the effects of factors on the response mean and variation. An orthogonal array means the design is balanced so that factor levels are weighted equally. Because of this, each factor can be assessed independently of all the other factors, so the effect of one factor does not affect the estimation of a different factor. This can reduce the time and cost associated with the experiment when fractionated designs are used.

Orthogonal array designs concentrate primarily on main effects. Some of the arrays offered in Minitab's catalog let a few selected interactions to be studied.

You can also add a signal factor to the Taguchi design in order to create a dynamic response experiment. A dynamic response experiment is used to improve the functional relationship between a signal and an output response.

### Output tables for a Taguchi design

Minitab calculates response tables, linear model results, and generates main effects and interaction plots for:
• signal-to-noise ratios (S/N ratios, which provide a measure of robustness) vs. the control factors
• means (static design) or slopes (Taguchi dynamic design) vs. the control factors
• standard deviations vs. the control factors
• natural log of the standard deviations vs. the control factors

Use the results and plots to determine what factors and interactions are important and assess how they affect responses. To get a complete understanding of factor effects, you should usually assess signal-to-noise ratios, means (static design), slopes (Taguchi dynamic design), and standard deviations. Ensure that you choose a signal-to-noise ratio that is appropriate for the type of data you have and your goal for optimizing the response.

###### Note

If you suspect curvature in your model, select a design - such as 3-level designs - that lets you detect curvature in the response surface.

## A comparison of Taguchi static designs and Taguchi dynamic designs

Minitab provides two types of Taguchi designs that let you choose a product or process that functions more consistently in the operating environment. Both designs try to identify control factors that minimize the effect of the noise factors on the product or service.

Static response
In a static response design, the quality characteristic of interest has a fixed level.
Dynamic response

In a dynamic response design, the quality characteristic operates along a range of values and the goal is to improve the relationship between a signal factor and an output response.

For example, the amount of deceleration is a measure of brake performance. The signal factor is the degree of depression on the brake pedal. As the driver pushes down on the brake pedal, deceleration increases. The degree of pedal depression has a significant effect on deceleration. Because no optimal setting for pedal depression exists, it is not logical to test it as a control factor. Instead, engineers want to design a brake system that produces the most efficient and least variable amount of deceleration through the range of brake pedal depression.

## Example of a Taguchi design

The following table displays the L8 (27) Taguchi design (orthogonal array). L8 means 8 runs. 27 means 7 factors with 2 levels each. If the full factorial design were used, it would have 27 = 128 runs. The L8 (27) array requires only 8 runs - a fraction of the full factorial design. This array is orthogonal; factor levels are weighted equally across the entire design. The table columns represent the control factors, the table rows represent the runs (combination of factor levels), and each table cell represents the factor level for that run.

## How does Minitab choose the default Taguchi design?

For 2-level designs based on L8 (3 or 4 factors), L16 (3-8 factors), and L32 (3-16 factors) arrays, Minitab will choose a full factorial design if possible. If a full factorial design is not possible, then Minitab will choose a Resolution IV design.

For all other designs, the default designs in Minitab are based on the catalog of designs by Taguchi and Konishi.

Minitab takes a straightforward approach in determining the default columns that are used in any of the various orthogonal designs. Say you are creating a Taguchi design with k factors. Minitab takes the first k of columns of the orthogonal array.

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