# Design of Experiments - DoE

Design of Experiments, or DoE, is a systematic approach to planning, conducting, and analyzing experiments.

The goal of Design of Experiments is to explore how various input variables, called factors, affect an output variable, known as the response. In more complex systems, there may also be multiple responses to analyze.

Depending on the field of study, the system being investigated could be a process, a machine, or a product. But it can also be a human being, for example, when studying the effects of medication.

Each factor has multiple levels. For example, the factor 'lubrication' might have levels such as oil and grease, while the factor 'temperature' could have levels like low, medium, and high.

### Factors

These are the input variables or parameters that are changed or manipulated in the experiment. Each factor can have different levels, which represent the different values it can take.

**Examples:** temperature, pressure, material type, machine speed.

### Levels

These are the specific values that a factor can take in an experiment.

**Examples:** For the factor "temperature," the levels could be 100°C, 150°C, and
200°C.

### Response (or Output)

This is the measured outcome or result that changes in response to the factors being manipulated.

**Examples:** yield, strength, time to failure, customer satisfaction.

## When is a DoE used?

There are two primary applications of Design of Experiments (DOE): the first is to identify the key influencing factors, determining which factors have a significant impact on the outcome. The second is to optimize the input variables, aiming to either minimize or maximize the response, depending on the desired result.

Different experimental designs are selected based on the objective: screening designs are used to identify significant factors, while optimization designs are employed to determine the optimal input variables.

### Screening Designs

Screening Designs are used early in an experiment to identify the most important factors from a larger set of potential variables. These designs, such as Fractional Factorial Designs or Plackett-Burman Designs, focus on determining which factors have a significant effect on the response, often with a reduced number of runs.

### Optimization Designs

Optimization Designs, on the other hand, are used after the important factors have been identified. These designs are used to refine and optimize the levels of the significant factors to achieve an ideal response. Common examples include: full factorial designs, central composite designs (CCD), and Box-Behnken designs (BBD).

## The DoE Process

Of course, both steps can be carried out sequentially. Let's take a look at the process of a DoE project: planning, screening, optimization, and verification.

The first step, planning, involves three key tasks:

- 1) Gaining a clear understanding of the problem or system.
- 2) Identifying one or more responses.
- 3) Determining the factors that could significantly influence the response.

Identifying potential factors that influence the response can be quite complex and time-consuming. For this, an Ishikawa diagram can be created by the team.

#### Screening Design

The second step is Screening. If there are many factors that could have an influence (typically more than 4-6 factors), screening experiments should be conducted to reduce the number of factors.

Why is this important? The number of factors to be studied has a major impact on the number of experiments required.

In a full factorial design, the number of experiments is determined by n = 2 raised to the power of k, where n is the number of experiments, and k is the number of factors. Here's a small overview: if we have three factors, at least 8 experiments are required; for 7 factors, at least 128 experiments are needed, and for 10 factors, at least 1024 experiments are required.

Note that this table applies to a design where each factor has only two levels; otherwise, more experiments will be needed.

Depending on how complex each experiment is, it may be worthwhile to choose screening designs when there are 4 or more factors. Screening designs include fractional factorial designs and the Plackett-Burman design.

#### Optimization Designs

Once significant factors have been identified using screening experiments, and the number of factors has hopefully been reduced, further experiments can be conducted.

The obtained data can then be used to create a regression model, which helps determine the input variables that optimize the response.

#### Verification

After optimization, the final step is verification. Here, it is tested once again whether the calculated optimal input variables actually have the desired effect on the response!

### Detailed Steps in Conducting DOE

**Problem Definition:** Clearly define the objective of the experiment. Identify
the response variable and the factors that may affect it.

**Select Factors, Levels, and Ranges:** Determine the factors that will be studied
and the specific levels at which each factor will be set. Consider practical
constraints and prior knowledge.

**Choose an Experimental Design:** Select an appropriate design based on the number
of factors, the complexity of the interactions, and resource availability (time,
cost).

**Conduct the Experiment:** Perform the experiment according to the design. It is
essential to randomize the order of the experimental runs to avoid systematic errors.

**Collect Data:** Gather data on the response variable for each experimental run.

**Analyze the Data:** Use statistical methods such as analysis of variance (ANOVA),
regression, or specialized DOE software to analyze the results. The goal is to
understand the effects of factors and their interactions on the response.

**Draw Conclusions and Make Decisions:** Based on the analysis, draw conclusions
about which factors are significant, how they interact, and how the process or product
can be optimized.

**Validate the Results:** Confirm the findings by conducting additional experiments
or applying the findings to real-world situations. Validation ensures that the
conclusions are generalizable.

## Examples of Experimental Designs

There are various experimental designs, and here are some of the most common ones, which can easily be calculated using the DoE software DATAtab.

**Full Factorial Designs:** These
designs test all possible combinations of the factors and provide detailed information
about main effects and interactions.

**Fractional Factorial Designs:**
These designs use only a fraction of the possible combinations to increase efficiency
while still obtaining essential information.

**Plackett-Burman Designs:** A screening design that aims to quickly identify which
factors have the greatest effect.

**Response Surface Designs:** These include, for example, Central Composite Designs
(CCD), which are used to find optimal settings, especially in cases where there are
nonlinear relationships between factors and the response.

## Key Aspects of Experimental Design

**Efficiency:** DoE helps gather as much information as possible with a minimal
number of experiments. This is especially important when experiments are expensive or
time-consuming. Instead of testing all possible combinations of factors (as in full
factorial designs), statistical methods can significantly reduce the number of
experiments without losing essential information.

**Factor Effects and Interactions:** In an experiment, multiple factors often
influence the result simultaneously. Experimental design allows for the analysis of
isolated effects of these factors and their interactions. Interactions occur when the
simultaneous change of several factors has a greater effect on the outcome than the sum
of their individual effects.

## Creating a DoE with DATAtab

Of course you can create a test plan with DATAtab. To do this, simply click here: Create DoE online.

You can choose from a variety of designs and then specify the number of factors. The experimental plan created is then displayed.

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