definition of design of experiments

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Design of experiments

What is design of experiments.

Design of experiments (DOE) is a systematic, efficient method that enables scientists and engineers to study the relationship between multiple input variables (aka factors) and key output variables (aka responses). It is a structured approach for collecting data and making discoveries.

When to use DOE?

• To determine whether a factor, or a collection of factors, has an effect on the response.
• To determine whether factors interact in their effect on the response.
• To model the behavior of the response as a function of the factors.
• To optimize the response.

Ronald Fisher first introduced four enduring principles of DOE in 1926: the factorial principle, randomization, replication and blocking. Generating and analyzing these designs relied primarily on hand calculation in the past; until recently practitioners started using computer-generated designs for a more effective and efficient DOE.

Why use DOE?

DOE is useful:

• In driving knowledge of cause and effect between factors.
• To experiment with all factors at the same time.
• To run trials that span the potential experimental region for our factors.
• In enabling us to understand the combined effect of the factors.

To illustrate the importance of DOE, let’s look at what will happen if DOE does NOT exist.

Experiments are likely to be carried out via trial and error or one-factor-at-a-time (OFAT) method.

Trial-and-error method

Test different settings of two factors and see what the resulting yield is.

Say we want to determine the optimal temperature and time settings that will maximize yield through experiments.

How the experiment looks like using trial-and-error method:

1. Conduct a trial at starting values for the two variables and record the yield:

2. Adjust one or both values based on our results:

3. Repeat Step 2 until we think we've found the best set of values:

As you can tell, the  cons of trial-and-error  are:

• Inefficient, unstructured and ad hoc (worst if carried out without subject matter knowledge).
• Unlikely to find the optimum set of conditions across two or more factors.

One factor at a time (OFAT) method

Change the value of the one factor, then measure the response, repeat the process with another factor.

In the same experiment of searching optimal temperature and time to maximize yield, this is how the experiment looks using an OFAT method:

1. Start with temperature: Find the temperature resulting in the highest yield, between 50 and 120 degrees.

    1a. Run a total of eight trials. Each trial increases temperature by 10 degrees (i.e., 50, 60, 70 ... all the way to 120 degrees).

    1b. With time fixed at 20 hours as a controlled variable.

    1c. Measure yield for each batch.

2. Run the second experiment by varying time, to find the optimal value of time (between 4 and 24 hours).

    2a. Run a total of six trials. Each trial increases temperature by 4 hours (i.e., 4, 8, 12… up to 24 hours).

    2b. With temperature fixed at 90 degrees as a controlled variable.

    2c. Measure yield for each batch.

3. After a total of 14 trials, we’ve identified the max yield (86.7%) happens when:

• Temperature is at 90 degrees; Time is at 12 hours.

As you can already tell, OFAT is a more structured approach compared to trial and error.

But there’s one major problem with OFAT : What if the optimal temperature and time settings look more like this?

We would have missed out acquiring the optimal temperature and time settings based on our previous OFAT experiments.

Therefore,  OFAT’s con  is:

• We’re unlikely to find the optimum set of conditions across two or more factors.

How our trial and error and OFAT experiments look:

Notice that none of them has trials conducted at a low temperature and time AND near optimum conditions.

What went wrong in the experiments?

• We didn't simultaneously change the settings of both factors.
• We didn't conduct trials throughout the potential experimental region.

The result was a lack of understanding on the combined effect of the two variables on the response. The two factors did interact in their effect on the response!

A more effective and efficient approach to experimentation is to use statistically designed experiments (DOE).

Apply Full Factorial DOE on the same example

1. Experiment with two factors, each factor with two values. 

These four trials form the corners of the design space:

2. Run all possible combinations of factor levels, in random order to average out effects of lurking variables .

3. (Optional) Replicate entire design by running each treatment twice to find out experimental error :

4. Analyzing the results enable us to build a statistical model that estimates the individual effects (Temperature & Time), and also their interaction.

It enables us to visualize and explore the interaction between the factors. An illustration of what their interaction looks like at temperature = 120; time = 4:

You can visualize, explore your model and find the most desirable settings for your factors using the JMP Prediction Profiler .

Summary: DOE vs. OFAT/Trial-and-Error

• DOE requires fewer trials.
• DOE is more effective in finding the best settings to maximize yield.
• DOE enables us to derive a statistical model to predict results as a function of the two factors and their combined effect.

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Experimental Design: Definition and Types

By Jim Frost 3 Comments

What is Experimental Design?

An experimental design is a detailed plan for collecting and using data to identify causal relationships. Through careful planning, the design of experiments allows your data collection efforts to have a reasonable chance of detecting effects and testing hypotheses that answer your research questions.

An experiment is a data collection procedure that occurs in controlled conditions to identify and understand causal relationships between variables. Researchers can use many potential designs. The ultimate choice depends on their research question, resources, goals, and constraints. In some fields of study, researchers refer to experimental design as the design of experiments (DOE). Both terms are synonymous.

Ultimately, the design of experiments helps ensure that your procedures and data will evaluate your research question effectively. Without an experimental design, you might waste your efforts in a process that, for many potential reasons, can’t answer your research question. In short, it helps you trust your results.

Learn more about Independent and Dependent Variables .

Design of Experiments: Goals & Settings

Experiments occur in many settings, ranging from psychology, social sciences, medicine, physics, engineering, and industrial and service sectors. Typically, experimental goals are to discover a previously unknown effect , confirm a known effect, or test a hypothesis.

Effects represent causal relationships between variables. For example, in a medical experiment, does the new medicine cause an improvement in health outcomes? If so, the medicine has a causal effect on the outcome.

An experimental design’s focus depends on the subject area and can include the following goals:

• Understanding the relationships between variables.
• Identifying the variables that have the largest impact on the outcomes.
• Finding the input variable settings that produce an optimal result.

For example, psychologists have conducted experiments to understand how conformity affects decision-making. Sociologists have performed experiments to determine whether ethnicity affects the public reaction to staged bike thefts. These experiments map out the causal relationships between variables, and their primary goal is to understand the role of various factors.

Conversely, in a manufacturing environment, the researchers might use an experimental design to find the factors that most effectively improve their product’s strength, identify the optimal manufacturing settings, and do all that while accounting for various constraints. In short, a manufacturer’s goal is often to use experiments to improve their products cost-effectively.

In a medical experiment, the goal might be to quantify the medicine’s effect and find the optimum dosage.

Developing an Experimental Design

Developing an experimental design involves planning that maximizes the potential to collect data that is both trustworthy and able to detect causal relationships. Specifically, these studies aim to see effects when they exist in the population the researchers are studying, preferentially favor causal effects, isolate each factor’s true effect from potential confounders, and produce conclusions that you can generalize to the real world.

To accomplish these goals, experimental designs carefully manage data validity and reliability , and internal and external experimental validity. When your experiment is valid and reliable, you can expect your procedures and data to produce trustworthy results.

An excellent experimental design involves the following:

• Lots of preplanning.
• Developing experimental treatments.
• Determining how to assign subjects to treatment groups.

The remainder of this article focuses on how experimental designs incorporate these essential items to accomplish their research goals.

Learn more about Data Reliability vs. Validity and Internal and External Experimental Validity .

Preplanning, Defining, and Operationalizing for Design of Experiments

This phase of the design of experiments helps you identify critical variables, know how to measure them while ensuring reliability and validity, and understand the relationships between them. The review can also help you find ways to reduce sources of variability, which increases your ability to detect treatment effects. Notably, the literature review allows you to learn how similar studies designed their experiments and the challenges they faced.

Operationalizing a study involves taking your research question, using the background information you gathered, and formulating an actionable plan.

This process should produce a specific and testable hypothesis using data that you can reasonably collect given the resources available to the experiment.

• Null hypothesis : The jumping exercise intervention does not affect bone density.
• Alternative hypothesis : The jumping exercise intervention affects bone density.

To learn more about this early phase, read Five Steps for Conducting Scientific Studies with Statistical Analyses .

Formulating Treatments in Experimental Designs

In an experimental design, treatments are variables that the researchers control. They are the primary independent variables of interest. Researchers administer the treatment to the subjects or items in the experiment and want to know whether it causes changes in the outcome.

As the name implies, a treatment can be medical in nature, such as a new medicine or vaccine. But it’s a general term that applies to other things such as training programs, manufacturing settings, teaching methods, and types of fertilizers. I helped run an experiment where the treatment was a jumping exercise intervention that we hoped would increase bone density. All these treatment examples are things that potentially influence a measurable outcome.

Even when you know your treatment generally, you must carefully consider the amount. How large of a dose? If you’re comparing three different temperatures in a manufacturing process, how far apart are they? For my bone mineral density study, we had to determine how frequently the exercise sessions would occur and how long each lasted.

How you define the treatments in the design of experiments can affect your findings and the generalizability of your results.

Assigning Subjects to Experimental Groups

A crucial decision for all experimental designs is determining how researchers assign subjects to the experimental conditions—the treatment and control groups. The control group is often, but not always, the lack of a treatment. It serves as a basis for comparison by showing outcomes for subjects who don’t receive a treatment. Learn more about Control Groups .

How your experimental design assigns subjects to the groups affects how confident you can be that the findings represent true causal effects rather than mere correlation caused by confounders. Indeed, the assignment method influences how you control for confounding variables. This is the difference between correlation and causation .

Imagine a study finds that vitamin consumption correlates with better health outcomes. As a researcher, you want to be able to say that vitamin consumption causes the improvements. However, with the wrong experimental design, you might only be able to say there is an association. A confounder, and not the vitamins, might actually cause the health benefits.

Let’s explore some of the ways to assign subjects in design of experiments.

Completely Randomized Designs

A completely randomized experimental design randomly assigns all subjects to the treatment and control groups. You simply take each participant and use a random process to determine their group assignment. You can flip coins, roll a die, or use a computer. Randomized experiments must be prospective studies because they need to be able to control group assignment.

Random assignment in the design of experiments helps ensure that the groups are roughly equivalent at the beginning of the study. This equivalence at the start increases your confidence that any differences you see at the end were caused by the treatments. The randomization tends to equalize confounders between the experimental groups and, thereby, cancels out their effects, leaving only the treatment effects.

For example, in a vitamin study, the researchers can randomly assign participants to either the control or vitamin group. Because the groups are approximately equal when the experiment starts, if the health outcomes are different at the end of the study, the researchers can be confident that the vitamins caused those improvements.

Statisticians consider randomized experimental designs to be the best for identifying causal relationships.

If you can’t randomly assign subjects but want to draw causal conclusions about an intervention, consider using a quasi-experimental design .

Learn more about Randomized Controlled Trials and Random Assignment in Experiments .

Randomized Block Designs

Nuisance factors are variables that can affect the outcome, but they are not the researcher’s primary interest. Unfortunately, they can hide or distort the treatment results. When experimenters know about specific nuisance factors, they can use a randomized block design to minimize their impact.

This experimental design takes subjects with a shared “nuisance” characteristic and groups them into blocks. The participants in each block are then randomly assigned to the experimental groups. This process allows the experiment to control for known nuisance factors.

Blocking in the design of experiments reduces the impact of nuisance factors on experimental error. The analysis assesses the effects of the treatment within each block, which removes the variability between blocks. The result is that blocked experimental designs can reduce the impact of nuisance variables, increasing the ability to detect treatment effects accurately.

Suppose you’re testing various teaching methods. Because grade level likely affects educational outcomes, you might use grade level as a blocking factor. To use a randomized block design for this scenario, divide the participants by grade level and then randomly assign the members of each grade level to the experimental groups.

A standard guideline for an experimental design is to “Block what you can, randomize what you cannot.” Use blocking for a few primary nuisance factors. Then use random assignment to distribute the unblocked nuisance factors equally between the experimental conditions.

You can also use covariates to control nuisance factors. Learn about Covariates: Definition and Uses .

Observational Studies

In some experimental designs, randomly assigning subjects to the experimental conditions is impossible or unethical. The researchers simply can’t assign participants to the experimental groups. However, they can observe them in their natural groupings, measure the essential variables, and look for correlations. These observational studies are also known as quasi-experimental designs. Retrospective studies must be observational in nature because they look back at past events.

Imagine you’re studying the effects of depression on an activity. Clearly, you can’t randomly assign participants to the depression and control groups. But you can observe participants with and without depression and see how their task performance differs.

Observational studies let you perform research when you can’t control the treatment. However, quasi-experimental designs increase the problem of confounding variables. For this design of experiments, correlation does not necessarily imply causation. While special procedures can help control confounders in an observational study, you’re ultimately less confident that the results represent causal findings.

Learn more about Observational Studies .

For a good comparison, learn about the differences and tradeoffs between Observational Studies and Randomized Experiments .

Between-Subjects vs. Within-Subjects Experimental Designs

When you think of the design of experiments, you probably picture a treatment and control group. Researchers assign participants to only one of these groups, so each group contains entirely different subjects than the other groups. Analysts compare the groups at the end of the experiment. Statisticians refer to this method as a between-subjects, or independent measures, experimental design.

In a between-subjects design , you can have more than one treatment group, but each subject is exposed to only one condition, the control group or one of the treatment groups.

A potential downside to this approach is that differences between groups at the beginning can affect the results at the end. As you’ve read earlier, random assignment can reduce those differences, but it is imperfect. There will always be some variability between the groups.

In a  within-subjects experimental design , also known as repeated measures, subjects experience all treatment conditions and are measured for each. Each subject acts as their own control, which reduces variability and increases the statistical power to detect effects.

In this experimental design, you minimize pre-existing differences between the experimental conditions because they all contain the same subjects. However, the order of treatments can affect the results. Beware of practice and fatigue effects. Learn more about Repeated Measures Designs .

Design of Experiments Examples

For example, a bone density study has three experimental groups—a control group, a stretching exercise group, and a jumping exercise group.

In a between-subjects experimental design, scientists randomly assign each participant to one of the three groups.

In a within-subjects design, all subjects experience the three conditions sequentially while the researchers measure bone density repeatedly. The procedure can switch the order of treatments for the participants to help reduce order effects.

Matched Pairs Experimental Design

A matched pairs experimental design is a between-subjects study that uses pairs of similar subjects. Researchers use this approach to reduce pre-existing differences between experimental groups. It’s yet another design of experiments method for reducing sources of variability.

Researchers identify variables likely to affect the outcome, such as demographics. When they pick a subject with a set of characteristics, they try to locate another participant with similar attributes to create a matched pair. Scientists randomly assign one member of a pair to the treatment group and the other to the control group.

On the plus side, this process creates two similar groups, and it doesn’t create treatment order effects. While matched pairs do not produce the perfectly matched groups of a within-subjects design (which uses the same subjects in all conditions), it aims to reduce variability between groups relative to a between-subjects study.

On the downside, finding matched pairs is very time-consuming. Additionally, if one member of a matched pair drops out, the other subject must leave the study too.

Learn more about Matched Pairs Design: Uses & Examples .

Another consideration is whether you’ll use a cross-sectional design (one point in time) or use a longitudinal study to track changes over time .

A case study is a research method that often serves as a precursor to a more rigorous experimental design by identifying research questions, variables, and hypotheses to test. Learn more about What is a Case Study? Definition & Examples .

In conclusion, the design of experiments is extremely sensitive to subject area concerns and the time and resources available to the researchers. Developing a suitable experimental design requires balancing a multitude of considerations. A successful design is necessary to obtain trustworthy answers to your research question and to have a reasonable chance of detecting treatment effects when they exist.

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Methodology

• Guide to Experimental Design | Overview, Steps, & Examples

Guide to Experimental Design | Overview, 5 steps & Examples

Published on December 3, 2019 by Rebecca Bevans . Revised on June 21, 2023.

Experiments are used to study causal relationships . You manipulate one or more independent variables and measure their effect on one or more dependent variables.

Experimental design create a set of procedures to systematically test a hypothesis . A good experimental design requires a strong understanding of the system you are studying.

There are five key steps in designing an experiment:

• Consider your variables and how they are related
• Write a specific, testable hypothesis
• Design experimental treatments to manipulate your independent variable
• Assign subjects to groups, either between-subjects or within-subjects
• Plan how you will measure your dependent variable

For valid conclusions, you also need to select a representative sample and control any  extraneous variables that might influence your results. If random assignment of participants to control and treatment groups is impossible, unethical, or highly difficult, consider an observational study instead. This minimizes several types of research bias, particularly sampling bias , survivorship bias , and attrition bias as time passes.

Table of contents

Step 1: define your variables, step 2: write your hypothesis, step 3: design your experimental treatments, step 4: assign your subjects to treatment groups, step 5: measure your dependent variable, other interesting articles, frequently asked questions about experiments.

You should begin with a specific research question . We will work with two research question examples, one from health sciences and one from ecology:

To translate your research question into an experimental hypothesis, you need to define the main variables and make predictions about how they are related.

Start by simply listing the independent and dependent variables .

Then you need to think about possible extraneous and confounding variables and consider how you might control  them in your experiment.

Finally, you can put these variables together into a diagram. Use arrows to show the possible relationships between variables and include signs to show the expected direction of the relationships.

Here we predict that increasing temperature will increase soil respiration and decrease soil moisture, while decreasing soil moisture will lead to decreased soil respiration.

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Now that you have a strong conceptual understanding of the system you are studying, you should be able to write a specific, testable hypothesis that addresses your research question.

The next steps will describe how to design a controlled experiment . In a controlled experiment, you must be able to:

• Systematically and precisely manipulate the independent variable(s).
• Precisely measure the dependent variable(s).
• Control any potential confounding variables.

If your study system doesn’t match these criteria, there are other types of research you can use to answer your research question.

How you manipulate the independent variable can affect the experiment’s external validity – that is, the extent to which the results can be generalized and applied to the broader world.

First, you may need to decide how widely to vary your independent variable.

• just slightly above the natural range for your study region.
• over a wider range of temperatures to mimic future warming.
• over an extreme range that is beyond any possible natural variation.

Second, you may need to choose how finely to vary your independent variable. Sometimes this choice is made for you by your experimental system, but often you will need to decide, and this will affect how much you can infer from your results.

• a categorical variable : either as binary (yes/no) or as levels of a factor (no phone use, low phone use, high phone use).
• a continuous variable (minutes of phone use measured every night).

How you apply your experimental treatments to your test subjects is crucial for obtaining valid and reliable results.

First, you need to consider the study size : how many individuals will be included in the experiment? In general, the more subjects you include, the greater your experiment’s statistical power , which determines how much confidence you can have in your results.

Then you need to randomly assign your subjects to treatment groups . Each group receives a different level of the treatment (e.g. no phone use, low phone use, high phone use).

You should also include a control group , which receives no treatment. The control group tells us what would have happened to your test subjects without any experimental intervention.

When assigning your subjects to groups, there are two main choices you need to make:

• A completely randomized design vs a randomized block design .
• A between-subjects design vs a within-subjects design .

Randomization

An experiment can be completely randomized or randomized within blocks (aka strata):

• In a completely randomized design , every subject is assigned to a treatment group at random.
• In a randomized block design (aka stratified random design), subjects are first grouped according to a characteristic they share, and then randomly assigned to treatments within those groups.

Sometimes randomization isn’t practical or ethical , so researchers create partially-random or even non-random designs. An experimental design where treatments aren’t randomly assigned is called a quasi-experimental design .

Between-subjects vs. within-subjects

In a between-subjects design (also known as an independent measures design or classic ANOVA design), individuals receive only one of the possible levels of an experimental treatment.

In medical or social research, you might also use matched pairs within your between-subjects design to make sure that each treatment group contains the same variety of test subjects in the same proportions.

In a within-subjects design (also known as a repeated measures design), every individual receives each of the experimental treatments consecutively, and their responses to each treatment are measured.

Within-subjects or repeated measures can also refer to an experimental design where an effect emerges over time, and individual responses are measured over time in order to measure this effect as it emerges.

Counterbalancing (randomizing or reversing the order of treatments among subjects) is often used in within-subjects designs to ensure that the order of treatment application doesn’t influence the results of the experiment.

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Finally, you need to decide how you’ll collect data on your dependent variable outcomes. You should aim for reliable and valid measurements that minimize research bias or error.

Some variables, like temperature, can be objectively measured with scientific instruments. Others may need to be operationalized to turn them into measurable observations.

• Ask participants to record what time they go to sleep and get up each day.
• Ask participants to wear a sleep tracker.

How precisely you measure your dependent variable also affects the kinds of statistical analysis you can use on your data.

Experiments are always context-dependent, and a good experimental design will take into account all of the unique considerations of your study system to produce information that is both valid and relevant to your research question.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Student’s  t -distribution
• Normal distribution
• Null and Alternative Hypotheses
• Chi square tests
• Confidence interval
• Cluster sampling
• Stratified sampling
• Data cleansing
• Reproducibility vs Replicability
• Peer review
• Likert scale

Research bias

• Implicit bias
• Framing effect
• Cognitive bias
• Placebo effect
• Hawthorne effect
• Hindsight bias
• Affect heuristic

Experimental design means planning a set of procedures to investigate a relationship between variables . To design a controlled experiment, you need:

• A testable hypothesis
• At least one independent variable that can be precisely manipulated
• At least one dependent variable that can be precisely measured

When designing the experiment, you decide:

• How you will manipulate the variable(s)
• How you will control for any potential confounding variables
• How many subjects or samples will be included in the study
• How subjects will be assigned to treatment levels

Experimental design is essential to the internal and external validity of your experiment.

The key difference between observational studies and experimental designs is that a well-done observational study does not influence the responses of participants, while experiments do have some sort of treatment condition applied to at least some participants by random assignment .

A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.

In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.

In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.

The word “between” means that you’re comparing different conditions between groups, while the word “within” means you’re comparing different conditions within the same group.

An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not. They should be identical in all other ways.

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Statistical Design of Experiments (DoE)

• First Online: 17 April 2021

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In a cause–effect relationship, the design of experiments (DoE) is a means and method of determining the interrelationship in the required accuracy and scope with the lowest possible expenditure in terms of time, material, and other resources. In experiments, the question concerning which type and level of effect the influencing variables have on the result (target variable) is answered. Basic concepts for the design of experiments are introduced, and basic principles such as repeating experiments, randomization, blocking (block formation), and symmetrical structure are described. In this chapter, the general procedure for conducting experiments is discussed, and the various experiment designs are ultimately presented: full factorial experiment designs, Latin squares, fractional factorial experiment designs, factorial experiment designs with a center point, and central composite experiment designs and their properties.

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Box, G.E., Hunter, J.S.: Ann. Math. Stat. 28 (3), 195–241 (1957)

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Schiefer, H.: Spritzgießen von keramischen Massen mit der Gas-Innendruck-Technik. Lecture: IHK Pforzheim, 11/24/1998 (1998)

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Noack, C.: Leistungsmessungen eines elektrohydraulischen Antriebes in zwei Anwendungsfällen. Thesis: FH Furtwangen, 22 June 2004

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Schiefer, H., Schiefer, F. (2021). Statistical Design of Experiments (DoE). In: Statistics for Engineers. Springer, Wiesbaden. https://doi.org/10.1007/978-3-658-32397-4_1

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Design of Experiments: Definition, How It Works, & Examples

In the world of research, development, and innovation, making informed decisions based on reliable data is crucial. This is where the Design of Experiments (DoE) methodology steps in. DoE provides a structured framework for designing experiments that efficiently identify the factors influencing a process, product, or system.

DoE provides a strong tool to help you accomplish your objectives, whether you work in software development, manufacturing, pharmaceuticals, or any other industry that needs optimization.

This article by SkillTrans will analyze for you a better understanding of DoE through many different contents, including:

What is Design Of Experiments

Design Of Experiments Examples

Design Of Experiments Software

What Is Doe In Problem Solving

And What Is Doe In Testing

First of all, let's learn the definition of DoE.

What is Design of Experiments?

According to Wikipedia , DoE is defined as follows: 

“The design of experiments (DOE or DOX), also known as experiment design or experimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation.”

To put it more simply, Design of Experiments (DoE) is a powerful statistical methodology that revolutionizes the way we conduct experiments and gain insights. At its core, DoE is a systematic and efficient approach to experimentation, allowing researchers, engineers, and scientists to study the relationship between multiple input variables (factors) and key output variables (responses).

Why DoE is Superior to Traditional Testing

Traditional testing methods often rely on a "one-factor-at-a-time" (OFAT) approach, where only one factor is changed while holding others constant. 

This method has several limitations:

Time-Consuming: Testing each factor individually can be incredibly slow, especially when dealing with numerous variables.

Misses Interactions: OFAT fails to capture how factors might interact with each other, leading to incomplete or even misleading results.

Inefficient: It often requires a large number of experiments to gain a comprehensive understanding of a system.

How DoE Works

DoE takes a different approach by carefully planning experiments where multiple factors are varied simultaneously according to a predetermined design. This allows for the investigation of both the individual effects of each factor (main effects) and the combined effects of multiple factors (interaction effects) . 

By doing so, DoE provides a more holistic and accurate picture of the system being studied.

Statistical Power of DoE

DoE uses statistical analysis to interpret experiment outcomes. DoE can quantify the impact of the major factors influencing the response, identify the best settings or conditions, and identify the components that influence the response by using a variety of statistical models.

Benefits of DoE

Reduced Costs: DoE often requires fewer experimental runs than OFAT, saving time and resources.

Improved Understanding: DoE provides a deeper understanding of complex systems by uncovering interactions between factors.

Robust Solutions: DoE helps identify solutions that are more robust to variations in factors, leading to greater reliability.

Faster Optimization: By simultaneously exploring a wider range of conditions, DoE can accelerate the optimization process.

Applications for DoE can be found in many different areas, such as software development, marketing, manufacturing, medicines, and agriculture. It is a priceless tool for innovation and advancement in a variety of sectors due to its capacity to quickly and effectively address complicated difficulties.

We will learn more about the areas where DoE is commonly used in the next section.

Design of Experiments Examples

DoE has a proven track record of solving complex problems and driving innovation across a wide range of sectors. Here are some examples:

Design of Experiments Examples in Manufacturing

DoE is used to optimize manufacturing processes like casting, molding, machining, and assembly . It helps identify optimal settings for temperature, pressure, cycle time, and other variables, leading to improved quality, reduced scrap, and lower costs.

Design of Experiments Examples in Pharmaceuticals

DoE plays a crucial role in drug development, helping to determine optimal dosages, identify the most effective combinations of ingredients, and optimize manufacturing processes for quality and consistency.

Design of Experiments Examples in Agriculture

DoE is widely used in agriculture to optimize crop yields, improve soil fertility, and develop more sustainable farming practices. It helps researchers understand the complex interactions between environmental factors, plant genetics, and farming techniques.

Design of Experiments Examples in Software Development

DoE is applied in software testing to optimize test coverage, prioritize test cases, and identify software vulnerabilities. It also helps developers understand how different code changes impact performance and reliability.

Design of Experiments Examples in Marketing

DoE is utilized in marketing to optimize pricing strategies, advertising campaigns, and product launches. It helps marketers understand how different factors influence consumer behavior, allowing them to tailor their strategies for maximum impact.

These examples are just a glimpse into the vast potential of DoE. To better understand DoE's contribution to different fields, let's take a look at DoE in more detail.

Design of Experiments Software

While the principles of DoE are rooted in statistics and experimental design, the emergence of sophisticated software tools has democratized the methodology, making it accessible to a wider audience. These tools simplify the entire DoE workflow , from initial planning to final analysis, empowering users to design, execute, and interpret experiments with confidence.

Key Features and Benefits of DoE Software

Experiment design.

DoE software helps users choose the best experimental design depending on their objectives, considerations, and available resources. It facilitates the creation of effective experimental plans, randomization of runs, and design matrices.

Statistical Modeling

The statistical models that explain the connection between variables and responses are automatically created by the software. Response surface models, analysis of variance ( ANOVA ), and linear regression are among the models it can fit.

Data Analysis

DoE software offers strong analytical capabilities for data analysis , such as effect estimation, model diagnostics, and hypothesis testing. It assists users in locating important variables, estimating their influence, and choosing the best configurations.

Optimization

Optimization algorithms are a common feature of DoE software packages, which assist users in determining the combination of factor values that maximizes or minimizes a desired result.

Visualization

To assist users in efficiently interpreting and communicating their findings, DoE software provides a variety of visualization tools, including Pareto charts , interaction plots, and response surface plots.

Popular DoE Software Options

Here are a few well-known DoE software you might want to look into:

JMP is a feature-rich statistical software package with strong DoE capabilities that was developed by SAS. It provides a large selection of designs, sophisticated statistical modeling capabilities, and an intuitive user interface.

A well-liked statistics program with plenty of DoE tools and an intuitive user interface is Minitab . It provides a wide range of designs, simple analysis tools, and lucid visualizations.

Design-Expert

Specialized DoE software called Design-Expert concentrates on response surface methodology (RSM). It offers an easy-to-use interface for creating, evaluating, and refining complicated interaction experiments.

Stat-Ease 360

Stat-Ease 360 , a more comprehensive version of Design-Expert, interfaces with Python to enable custom scripting and sophisticated analysis.

Other Options

There are numerous other DoE software options available, each with its own strengths and target audience. Some examples include Cornerstone, MODDE, and Unscrambler .

The intricacy of the trials, financial limitations, features that are wanted, and the user's degree of statistical competence all influence the choice of DoE software. In order to provide consumers the opportunity to test out the features and functioning before deciding to buy, many software companies offer free trials.

DoE in Problem Solving

Identifying effective solutions and determining the underlying causes of complex problems can be challenging due to the presence of various interacting components. Design of Experiments (DoE) provides a methodical, data-driven approach to resolving these issues and making wise choices. 

Here's a closer look at the DoE problem-solving process :

Define the Problem with Metrics

The first step in using metrics and Design of Experiments to effectively address a problem is to precisely define the pertinent, quantifiable problem. For example, state the challenge as "reduce defect rate by 20% within six months" rather than aiming for something as abstract as "improve product quality." 

For the purpose of problem-solving, clearly define your aims and objectives and what you want to accomplish through experimenting. 

Furthermore, ascertain which important parties will be impacted by the issue and its resolution, and make sure that their requirements and viewpoints are taken into account at every stage of the process.

Identify Factors with Potential Impact

Start by thinking and making a list of every potential input variable that can have an impact on the result or response variable in order to uncover elements that could have an impact. These variables may include uncontrollable ones like raw material variability or ambient circumstances, as well as controllable ones like temperature, pressure, or ingredient proportions. 

After you have a complete list, rank the elements according to how they might affect the answer. You can determine the relative relevance of each item by utilizing previous information, professional judgment, or preliminary evidence. 

Furthermore, take into account how different elements interact with one another, as some may have an effect that is different from each of them alone.

Design the Experiment with Statistical Rigor

The first step in creating an experiment with statistical rigor is choosing an acceptable experimental design that takes into account the number of variables, the desired level of detail, and the resources that are available. Response surface designs, factorial designs, and fractional factorial designs are examples of common designs. 

Subsequently, ascertain the necessary number of experimental runs to attain statistically significant outcomes, taking into account variables like the intended confidence level, response variability, and the target effect size. 

In order to reduce the influence of uncontrollable circumstances and maximize the reliability and objectivity of the results, finally arrange the experimental runs in a random sequence.

Analyze the Results with Statistical Tools

In order to use statistical tools to analyze the outcomes, first gather data from the experiments and analyze it with applicable procedures like regression analysis, analysis of variance (ANOVA), or other pertinent statistical approaches. 

Determine which statistically significant variables actually affect the response. Calculate the ideal settings for each significant element by quantifying its effect size. 

To ensure a thorough grasp of how various variables affect the result, evaluate the interactions between components and ascertain their impact on the response.

Implement Solutions with Data-Driven Confidence

Start by creating workable solutions based on the findings of your study in order to execute solutions with confidence that is informed by evidence. These fixes could include updating designs, introducing new tactics, altering formulas, and adjusting process settings. 

To make sure the solutions are effective, validate them with more trials or pilot studies. After the solutions are put into place, keep an eye on them and evaluate their effects over time. Use the information gathered to make any necessary additional improvements or modifications.

DoE in Testing

The field of testing has seen a revolution in the evaluation and optimization of products and processes thanks to the Design of Experiments (DoE) approach. It offers a methodical and effective way to look into the various ways that variable inputs affect a system's quality, dependability, and performance across a broad spectrum of circumstances.

Why DoE is Essential for Testing

Traditional testing methods often involve changing one factor at a time, which can be time-consuming and may miss critical interactions between factors. DoE, on the other hand, allows testers to simultaneously manipulate multiple factors according to a carefully designed plan. 

This enables them to:

Identify Optimal Settings

DoE helps determine the combination of factor settings that yield the best possible results, whether it's maximizing a desired output (e.g., yield, efficiency) or minimizing an undesirable one (e.g., defects, variability).

Reduce Variability

DoE can assist in identifying methods to lessen or regulate system performance variability by understanding the various elements that contribute to this variability and how to achieve more consistent and predictable results.

Enhance Robustness

DoE can identify solutions that are robust to variations in factors, ensuring that the product or process performs well even under different operating conditions or with varying inputs.

Accelerate Testing

DoE can save time and money by strategically choosing experimental runs and evaluating the collected data, which can lower the number of experiments needed to produce trustworthy results.

Gain Deeper Insights

DoE provides a deeper knowledge of the behavior of the system by revealing intricate interconnections between components, going beyond just identifying key ones.

Examples of DoE in Testing

Here are a few examples of DoE in testing that you might find useful:

Software Testing

DoE is used to optimize software performance , identify bugs and vulnerabilities, and ensure compatibility across different platforms and configurations. For example, a software company might use DoE to test the impact of different hardware configurations, network conditions, and user behaviors on the performance of their application.

Product Testing

DoE is employed to evaluate the performance and reliability of products under various conditions, such as temperature, humidity, vibration, and stress. This helps manufacturers identify design weaknesses, improve product robustness, and ensure compliance with quality standards. For instance, an electronics company might use DoE to test the durability of their smartphones under extreme temperatures and humidity levels.

Process Testing

DoE is applied to optimize manufacturing processes, improve yield, reduce defects, and enhance overall efficiency. For example, a chemical company might use DoE to optimize the reaction conditions for a chemical synthesis process, such as temperature, pressure, and reactant concentrations.

Medical Device Testing

DoE is used to assess the effectiveness and safety of medical devices across a variety of patient groups, usage scenarios, and environmental settings. This ensures that medical gadgets function consistently well in real-world circumstances and satisfy regulatory standards.

A flexible approach, Design of Experiments enables organizations to solve complicated challenges, obtain deeper insights, and make data-driven decisions. You can reach a new level of productivity and creativity in your industry by adopting DoE and making use of the appropriate software solutions.

In search of DoE Courses? From introductory to advanced courses in Design of Experiments , SkillTrans has a lot to offer. Look through our collection to select the ideal training to advance your knowledge!

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• Science Snippets Blog

What is DOE? Design of Experiments Basics for Beginners

[This blog was a favorite last year, so we thought you'd like to see it again. Send us your comments!]. Whether you work in engineering, R&D, or a science lab, understanding the basics of experimental design can help you achieve more statistically optimal results from your experiments or improve your output quality.

This article is posted on our Science Snippets Blog .

Using  Design of Experiments (DOE)  techniques, you can determine the individual and interactive effects of various factors that can influence the output results of your measurements. You can also use DOE to gain knowledge and estimate the best operating conditions of a system, process or product.

DOE applies to many different investigation objectives, but can be especially important early on in a screening investigation to help you determine what the most important factors are. Then, it may help you optimize and better understand how the most important factors that you can regulate influence the responses or critical quality attributes.

Another important application area for DOE is in making production more effective by identifying factors that can reduce material and energy consumption or minimize costs and waiting time. It is also valuable for robustness testing to ensure quality before releasing a product or system to the market.

What’s the Alternative?

In order to understand why Design of Experiments is so valuable, it may be helpful to take a look at what DOE helps you achieve. A good way to illustrate this is by looking at an alternative approach, one that we call the  “COST”  approach. The COST ( C hange  O ne  S eparate factor at a  T ime) approach might be considered an intuitive or even logical way to approach your experimentation options (until, that is, you have been exposed to the ideas and thinking of DOE).

Let’s consider the example of a small chemical reaction where the goal is to find optimal conditions for yield. In this example, we can vary only two elements, or factors:

• the volume of the reaction container (between 500 and 700 ml), and
• the pH of the solution (between 2.5 and 5).

We change the experimental factors and measure the response outcome, which in this case, is the yield of the desired product. Using the COST approach, we can vary just one of the factors at time to see what affect it has on the yield.

So, for example, first we might fix the pH at 3, and change the volume of the reaction container from a low setting of 500ml to a high of 700ml. From that we can measure the yield.

Below is an example of a table that shows the yield that was obtained when changing the volume from 500 to 700 ml. In the scatterplot on the right, we have plotted the measured yield against the change in reaction volume, and it doesn’t take long to see that the best volume is located at 550 ml.

Next, we evaluate what will happen when we fix the volume at 550 ml (the optimal level) and start to change the second factor. In this second experimental series, the pH is changed from 2.5 to 5.0 and you can see the measured yields. These are listed in the table and plotted below. From this we can see that the optimal pH is around 4.5.

The optimal combination for the best yield would be a volume of 550 ml and pH 4.5. Sounds good right? But, let’s consider this a bit more.

Gaining a Better Perspective With DOE

What happens when we take more of a bird’s eye perspective, and look at the overall experimental map by number and order of experiments?

For example, in the first experimental series (indicated on the horizontal axis below), we moved the experimental settings from left to right, and we found out that 550 was the optimal volume.

Then in the second experimental series, we moved from bottom to top (as shown in the scatterplot below) and after a while we found out that the best yield was at experiment number 10 (4.5 pH).

The problem here is that we are not really certain whether the experimental point number 10 is truly the best one. The risk is that we have perceived that as being the optimum without it really being the case. Another thing we may question is the number of experiments we used. Have we used the optimal number of runs for experiments?

Zooming out and picturing what we have done on a map, we can see that we have only been exploiting a very small part of the entire experimental space. The true relationship between pH and volume is represented by the Contour Plot pictured below. We can see that the optimal value would be somewhere at the top in the larger red area.

So the problem with the COST approach is that we can get very different implications if we choose other starting points. We perceive that the optimum was found, but the other— and perhaps more problematic thing—is that we didn’t realize that continuing to do additional experiments would produce even higher yields.

How to Design Better Experiments

Instead, using the DOE approach, we can build a map in a much better way. First, consider the use of just two factors, which would mean that we have a limited range of experiments.  As the contour plot below shows, we would have at least four experiments (defining the corners of a rectangle.)

These four points can be optimally supplemented by a couple of points representing the variation in the interior part of the experimental design.

The important thing here is that when we start to evaluate the result, we will obtain very valuable information about the direction in which to move for improving the result. We will understand that we should reposition the experimental plan according to the dashed arrow.

However, DOE is NOT limited to looking at just two factors. It can be applied to three, four or many more factors.

If we take the approach of using three factors, the experimental protocol will start to define a cube rather than a rectangle. So the factorial points will be the corners of the cube.

In this way, DOE allows you to construct a carefully prepared set of representative experiments, in which all relevant factors are varied simultaneously.

DOE is about creating an entity of experiments that work together to map an interesting experimental region. So with DOE we can prepare a set of experiments that are optimally placed to bring back as much information as possible about how the factors are influencing the responses.

Plus, we will we have support for different types of regression models. For example, we can estimate what we call a linear model, or an interaction model, or a quadratic model. So the selected experimental plan will support a specific type of model.

Why Is DOE a Better Approach?

We can see three main reasons that DOE Is a better approach to experiment design than the COST approach.

DOE suggests the correct number of runs needed (often fewer than used by the COST approach)

DOE provides a model for the direction to follow

Many factors can be used (not just two)

In summary, the benefits of DOE are:

• An organized approach that connects experiments in a rational manner
• The influence of and interactions between all factors can be estimated
• More precise information is acquired in fewer experiments
• Results are evaluated in the light of variability
• Support for decision-marketing: map of the system (response contour plot)

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What is Design of Experiments (DOE)?

• Design of Experiments is a framework that allows us to investigate the impact of multiple different factors on an experimental process
• It identifies and explores the interactions between factors and allows researchers to optimize the performance and robustness of processes or assays
• The old conventional approach to scientific experimentation (one-factor-at-a-time, or “OFAT”) are limited in both the number of variables which you can investigate and, critically, preclude investigating how variables interact
• This blog introduces the principles of Design of Experiments, beginning with its origins
• If you’d like to keep learning about DOE after you're done with this article, make sure to  check out our other DOE blogs , download our  DOE for biologists ebook , or watch our  DOE Masterclass webinar series .

DOE Masterclass (Part 1)

What doe is and how it transforms your biological research.

A richer understanding of biological complexity .

What makes a good cup of tea?

A discussion about whether adding milk before or after the tea influences the taste may seem a long way from ensuring that Escherichia coli  expresses a particular plasmid, optimizing vaccine formulation and delivery, 1,2 or dissecting the intricacies of metabolomics. 3  

But it's closer than you think.

After all, scientific revolutions can arise from everyday observations: a falling apple inspired Isaac Newton to formulate gravitational theory.

Of all the places for a revolution to start, a tea party in 1920s Cambridge laid the foundations of a statistical technique called Design of Experiments (DOE), which allows researchers to investigate the impact of simultaneously changing multiple factors.

Design of Experiments (DOE): a surprising origin story .

One afternoon some dons, their wives, and guests were having afternoon tea. One lady said she could taste whether tea or milk was poured into the cup first. (Some people believe that hot tea scorches milk, for example.)

The statistician Ronald Fisher, who attended the tea party, devised an experiment to test her claim. The lady was randomly given four cups in which tea was poured before the milk and four where the milk was poured first.

To analyze the interactions between the factors (milk and tea), Ronald devised Fisher’s Exact Test. This determines if any association between the two categorical variables is statistically significant. 4  

As Figure 1 shows, even four cups of tea can give rise to numerous possible permutations. But this only scratches the surface of tea–making’s complexity.

A perfect cup of tea depends on multiple other factors, such as the blend, brewing time, and the addition of sugar. In other words, making a perfect cup of tea is complex and multidimensional. DOE allows researchers to investigate the effect of changing multiple factors simultaneously.

0= Incorrect; X=correct

Figure 1: Distribution factors assuming that the lady could not distinguish that milk was added before tea (null hypothesis)

In a series of blogs, we’re going to explore the basis of DOE, who should consider DOE, and some ways in which this methodology helps experimental biologists deal with life’s inherent complexity. We’ll begin, however, by going back to school.

School's out... and so is OFAT (one-factor-at-a-time) experimentation .

Our school teachers advocated a one-factor-at-a-time (OFAT) approach to scientific experimentation. So, pick a variable (factor) and vary the value (levels), while keeping everything else constant. 

That may be fine in the school lab. Unfortunately, biology doesn’t work that way .

Biological variation, for example, can mean results vary randomly around a set point even in a constant environment. Sample collection, transport, preservation, and measurement systems can introduce further sources of variation. 5  

DOE helps us understand emergent phenomena .

Biological phenomena, even life itself, are typically emergent . In other words, new patterns and structures appear through the interactions between autonomous elements. 6

Every living thing consists of numerous autonomous parts that interact dynamically and unpredictably as part of one or more systems. This means, for example, that you can’t predict cellular diversity by examining nucleotides’ chemical and physical properties.

You also can’t predict the products of cognition by analyzing neuroarchitecture. Emergence is one reason biologists often lack well-developed, robust theoretical frameworks to guide their experiments.

DOE is better for exploring biological complexity .

Most biological processes are complicated, complex, and multidimensional. 7 So, changing one factor probably changes something else .

For example, it isn't possible to fully understand the functional consequences of changing a protein's structure without understanding all the contexts in which it appears. Its interactions within biological networks are what really define its function, so even minor changes can produce a plethora of unpredictable down- and upstream effects.

DOE allows the explorations of complex, multidimensional experimental design spaces despite such methodological, biological, or chemical variations. 7  

OFAT ignores biology’s inherent complexity . It is limited in both the number of variables that you can investigate and, critically, it precludes any investigation of how variables interact.

It’s a bit like trying to analyze the perfect cup of tea by ignoring the temperature of the water, brew time, and blend, and instead just focusing on whether you add the milk first or second. 

Figure 2: OFAT may convince you you’ve found an optimum… but it may not be the real one.

Unsurprisingly, OFAT can often identify the wrong system state as the optimum .

Moreover, the lack of well-developed, robust theoretical frameworks can result in unconscious cognitive bias: it’s all too easy to develop OFAT experiments that confirm, rather than test, hypotheses. 7

DOE helps avoid unconscious cognitive bias and allows researchers to look behind the curtain of biological complexity to see what’s really going on.

What is Design of Experiments (DOE) ?

Design of Experiments is a framework that allows us to investigate the impact of multiple different factors—changed simultaneously—on an experimental process .

DOE also identifies and explores the interactions between those factors. This allows us to optimize the performance and robustness of our processes or assays.

Let’s apply DOE to another simple example: the strawberries you may have with the tea you’ve just added your milk to... 

DOE looks at different ranges within factors .

Numerous quantitative factors (e.g. hours of sunlight, grams of plant food, and liters of water) or qualitative factors (e.g. the cultivar) can influence the strawberry crop ( Figure 2 ).

You need to begin by setting a realistic range for each factor. So, testing 1kg of plant food could prove toxic and expensive. Strawberries also need plenty of water to ensure juiciness; applying 1ml of water would be difficult to accurately achieve and, possibly, trigger drought stress responses.

Figure 3: Design of Experiments (DOE) through the example of strawberries. How different factors and levels may impact the yield, weight, and taste of a crop of strawberries

DOE tests many factors at the same time .

The responses we are looking for in this experiment are the yield, the weight, and the taste of the strawberries. You may decide you want a high yield of the tastiest strawberries. 

Design of experiments allows you to test numerous factors to determine which make the largest contributions to yield and taste.

Based on this, you can fine-tune the experiment and use DOE to determine which combination of factors at specific levels gives the optimal balance of yield and taste.

You can also compare different levels for given factors, such as whether a cultivar from nursery A produces a higher yield, better taste, or both than a plant from nursery B.

DOE lets you investigate specific outcomes .

Design of Experiments also allows you to investigate specific outcomes (what combinations produce the best balance of yield and taste in a robust way) and reduce variability (define new conditions so the strawberry yield remains the same).

Cost may be another consideration. DOE lets you balance trade-offs , such as what conditions produce the most cost-effective way to achieve the highest yield of strawberries.

DOE Masterclass: Design of Experiments 101 for biologists .

DOE helps reduce the time, materials, and experiments needed to yield a given amount of information compared with OFAT.

As well as these savings, DOE achieves higher precision and reduced variability when estimating the effects of each factor or interaction than using OFAT. It also systematically estimates the interaction between factors, which is not possible with OFAT experiments.

This article offers only a very brief introduction to DOE.

Dive deeper into Design of Experiments:

• Why should I use Design of Experiments in Life Sciences

When and how to use Design of Experiments (DOE)

• DOE in the real world: when and how to use Design of Experiments
• Types of DOE design: a users' guide
• The DOE process: an overview
• Overcoming barriers to Design of Experiments (DOE)
• 3 reasons why DOE rollouts fail and what to do about it
• Four ways to cut R&D costs with DOE

Well, I’m off for a cup of tea.

Interested in learning more about DOE? Download our  DOE for biologists ebook , or watch our  DOE Masterclass webinar series . Catch the full series of recordings on our YouTube page .

• Ahl PL, Mensch C, Hu B et al. Accelerating vaccine formulation development using design of experiment stability studies. Journal of Pharmaceutical Sciences 2016;105:3046-3056
• Hashiba A, Toyooka M, Sato Y et al. The use of design of experiments with multiple responses to determine optimal formulations for in vivo hepatic mRNA delivery. Journal of Controlled Release 2020;327:467-476
• Surowiec I, Johansson E, Torell F et al. Multivariate strategy for the sample selection and integration of multi-batch data in metabolomics. Metabolomics 2017;13:114
• Bi J and Kuesten C. Revisiting Fisher’s ‘Lady Tasting Tea’ from a perspective of sensory discrimination testing. Food Quality and Preference 2015;43:47-52
• Badrick T. Biological variation: Understanding why it is so important? Practical Laboratory Medicine 2021;23:e00199
• Ikegami T, Mototake Y-i, Kobori S et al. Life as an emergent phenomenon: studies from a large-scale boid simulation and web data. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 2017;375:20160351
• Lendrem DW, Lendrem BC, Woods D et al. Lost in space: design of experiments and scientific exploration in a Hogarth Universe. Drug Discovery Today 2015;20:1365-1371

Michael "Sid" Sadowski, PhD

Michael Sadowski, aka Sid, is the Director of Scientific Software at Synthace, where he leads the company’s DOE product development. In his 10 years at the company he has consulted on dozens of DOE campaigns, many of which included aspects of QbD.

Other posts you might be interested in

Why Design of Experiments (DOE) is important for biologists

Why quality by design (qbd) is vital for pharmaceutical r&d.

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Maximizing Efficiency and Accuracy with Design of Experiments

Updated: April 21, 2024 by Ken Feldman

Design of experiments (DOE) can be defined as a set of statistical tools that deal with the planning, executing, analyzing, and interpretation of controlled tests to determine which factors will impact and drive the outcomes of your process. 

This article will explore two of the common approaches to DOE as well as the benefits of using DOE and offer some best practices for a successful experiment. 

Overview: What is DOE? 

Two of the most common approaches to DOE are a full factorial DOE and a fractional factorial DOE . Let’s start with a discussion of what a full factorial DOE is all about.

The purpose of the full factorial DOE is to determine at what settings of your process inputs will you optimize the values of your process outcomes. As an example, if your output is the fill level of a bottle of carbonated drink, and your primary process variables are machine speed, fill speed, and carbonation level, then what combination of those factors will give you the desired consistent fill level of the bottle?

With three variables, machine speed, fill speed, and carbonation level, how many different unique combinations would you have to test to explore all the possibilities? Which combination of machine speed, fill speed, and carbonation level will give you the most consistent fill? The experimentation using all possible factor combinations is called a full factorial design. These combinations are called Runs .  

We can calculate the total number of runs using the formula # Runs=2^k, where k is the number of variables and 2 is the number of levels, such as (High/Low) or (100 ml per minute/200 ml per minute). 

But, what if you aren’t able to run the entire set of combinations of a full factorial? What if you have monetary or time constraints, or too many variables? This is when you might choose to run a fractional factorial , also referred to as a screening DOE , which uses only a fraction of the total runs. That fraction can be one-half, one-quarter, one-eighth, and so forth depending on the number of factors or variables. 

While there is a formula to calculate the number of runs, suffice it to say you can just calculate your full factorial runs and divide by the fraction that you and your Black Belt or Master Black Belt determine is best for your experiment.

3 benefits of DOE 

Doing a designed experiment as opposed to using a trial-and-error approach has a number of benefits.  

1. Identify the main effects of your factors

A main effect is the impact of a specific variable on your output. In other words, how much does machine speed alone impact your output? Or fill speed?

2. Identifying interactions

Interactions occur if the impact of one factor on your response is dependent upon the setting of another factor. For example if you ran at a fill speed of 100 ml per minute, what machine speed should you run at to optimize your fill level? Likewise, what machine speed should you run at if your fill speed was 200 ml per minute? 

A full factorial design provides information about all the possible interactions. Fractional factorial designs will provide limited interaction information because you did not test all the possible combinations. 

3. You can determine optimal settings for your variables 

After analyzing all of your main effects and interactions, you will be able to determine what your settings should be for your factors or variables. 

Why is DOE important to understand? 

When discussing the proper settings for your process variables, people often rely on what they have always done, on what Old Joe taught them years ago, or even where they feel the best setting should be. DOE provides a more scientific approach. 

Distinguish between significant and insignificant factors

Your process variables have different impacts on your output. Some are statistically important, and some are just noise. You need to understand which is which.

The existence of interactions

Unfortunately, most process outcomes are a function of interactions rather than pure main effects. You will need to understand the implications of that when operating your processes. 

Statistical significance 

DOE statistical outputs will indicate whether your main effects and interactions are statistically significant or not. You will need to understand that so you focus on those variables that have real impact on your process.

An industry example of DOE 

A unique application of DOE in marketing is called conjoint analysis. A web-based company wanted to design its website to increase traffic and online sales. Doing a traditional DOE was not practical, so leadership decided to use conjoint analysis to help them design the optimal web page.

The marketing and IT team members identified the following variables that seemed to impact their users’ online experience: 

• loading speed of the site
• font of the text
• color scheme
• primary graphic motion
• primary graphic size 
• menu orientation

They enlisted the company’s Master Black Belt to help them do the experiment using a two-level approach.

In a conjoint analysis DOE, you would create mockups of the various combinations of variables. A sample of customers were selected and shown the different mockups. After viewing them, the customer then ranked the different mockups from most preferred to least preferred. The ranking provided the numerical value of that combination. To keep matters simple, they went with a quarter fraction design, or 16 different mockups. Otherwise, you’re asking customers to try and differentiate their preference and rank way too many options.

Once they gathered all the data and analyzed it, they concluded that menu orientation and loading speed were the most significant factors. This allowed them to do what they wanted with font, primary graphic, and color scheme since they were not significant.

3 best practices when thinking about DOE 

Experiments take planning and proper execution, otherwise the results may be meaningless. Here are a few hints for making sure you properly run your DOE. 

1. Carefully identify your variables

Use existing data and data analysis to try and identify the most logical factors for your experiment. Regression analysis is often a good source of selecting potentially significant factors. 

2. Prevent contamination of your experiment

During your experiment, you will have your experimental factors as well as other environmental factors around you that you aren’t interested in testing. You will need to control those to reduce the noise and contamination that might occur (which would reduce the value of your DOE).

3. Use screening experiments to reduce cost and time

Unless you’ve done some prior screening of your potential factors, you might want to start your DOE with a screening or fractional factorial design. This will provide information as to potentially significant factors without consuming your whole budget. Once you’ve identified the best potential factors, you can do a full factorial with the reduced number of factors.

Frequently Asked Questions (FAQ) about DOE

What does “main effects” refer to.

The main effects of a DOE are the individual factors that have a statistically significant effect on your output. In the common two-level DOE, an effect is measured by subtracting the response value for running at the high level from the response value for running at the low level. The difference is the effect of that factor.

How many runs do I need for a full factorial DOE?

The formula for calculating the number of runs of a full factorial DOE is # Runs=X^K where X is the number of levels or settings, and K is the number of variables for factors.

Are interactions in DOE important? 

Yes. Sometimes your DOE factors do not behave the same way when you look at them together as opposed to looking at the factor impact individually. In the world of pharmaceuticals, you hear a lot about drug interactions. You can safely take an antihistamine for your allergies. You can also safely take an antibiotic for your infection. But taking them both at the same time can cause an interaction effect that can be deadly.

In summary, DOE is the way to go

A design of experiments (DOE) is a set of statistical tools for planning, executing, analyzing, and interpreting experimental tests to determine the impact of your process factors on the outcomes of your process. 

The technique allows you to simultaneously control and manipulate multiple input factors to determine their effect on a desired output or response. By simultaneously testing multiple inputs, your DOE can identify significant interactions you might miss if you were only testing one factor at a time. 

You can either use full factorial designs with all possible factor combinations, or fractional factorial designs using smaller subsets of the combinations.

About the Author

Ken Feldman

Table of Contents

What is the design of experiments (doe), importance of doe in various fields, examples of design of experiments (doe), types of design of experiments, phases of design experiments, benefits of implementing doe, future trends and innovations in doe, design of experiments (doe): a guide to data-driven decisions.

When faced with a dilemma at work, it might be challenging to decide which course of action to take. Following your instincts may give you greater confidence in your decisions, but will they be the best ones for your team? When you use facts to inform your decisions , you can feel more at rest, knowing that they are supported by data and intended to maximize the impact on your organization. 

Gaining a basic understanding of experimental design can help you improve the quality of your output or get more statistically optimal findings from your products, regardless of whether you work in R&D, engineering, or production.

The Design of Experiment (DoE) approach is a useful tool for solving problems in general and for enhancing or streamlining production and product design procedures. It is an effective method for gathering and analyzing data that may be applied in various experimental scenarios.

DoE Design of Experiments is a revolutionary approach to transforming several work environments; it is more than just a methodology. It is used to methodically organize, carry out, evaluate, and interpret experiments to produce accurate and dependable results. It makes it possible for experts to quickly investigate and pinpoint the key elements affecting the effectiveness of a procedure or result. 

For designers to consistently improve their products and the user experience as a whole, experimentation in the design field helps supply knowledge for stronger decision-making . Investigators can quickly extract useful information with the help of DoE software, which helps them refine goods and procedures. Here are several reasons for its significance: 

• Understanding the cause-and-effect relationship between several elements is beneficial. It allows you to enter several manipulable factors to assess their reaction.
• It helps identify a significant reaction that is only visible when several factors are applied simultaneously, as you can look at the effects of each component separately and in combination.
• You can run experiments with or just some of the factors.
• Since DoE assists in identifying the important elements and quantities, you can conduct trials for the entire range of investigations by setting the best possible settings for each factor.
• DoE is a useful tool for determining the statistical significance of your responses and experiments.

A design of experiments example is found in interior design. When designing the interior of a new home, many variables come into play, including the color of the walls, the lighting, the flooring, where different objects are placed around the space, the sizes and forms of the objects, and much more. All these elements will affect how interior design turns out in the end. While variations in just one of these elements alone can have an impact, variations in multiple factors acting simultaneously can also impact the outcome. 

In Six Sigma 

Six Sigma approaches, which aim to achieve process excellence and lower variance, include DoE as a fundamental component. Organizations can improve overall quality by minimizing defects and variances, implementing strategies to achieve optimal levels, and identifying essential process parameters through DoE.  

In Manufacturing

DoE assists in discovering the underlying reasons for differences and flaws in a manufacturing process. Quality engineers can identify the causes of problems and create plans to lessen or eliminate them by conducting experiments and evaluating the outcomes. It can be used to minimize process variability, which is a quality measure, find the source of a quality issue, or optimize the manufacturing process of a part. 

In Food Industry

DOE is used in the food industry to enhance the flavor and texture of various food items. Businesses can create more consumer-pleasing items by understanding the various aspects that impact food's taste and texture. Sales may rise, and the brand's reputation may improve.

In Agriculture

DOE is employed in agriculture to increase crop yields and decrease the usage of fertilizers and pesticides. It can be used to optimize plant development conditions in controlled environments, find the optimal fertilizer and irrigation rate combination to maximize crop yields, and much more. 

In Marketing

DOE can test and optimize advertisement elements, including graphic design , headline, wording, and call-to-action. It can also compare various pricing methods and their effects on consumer behavior, buy intent, and profitability.

You can choose from some designs at any point throughout your DoE campaign based on your objectives, assumptions, run available numbers, and other factors.

However, nothing is worse than having too many options when you're new to DoE. The various types of DoE are: 

Response Surface Methodology (RSM) Designs

Response Surface Methodology (RSM) is used to investigate numerous components, although just two are often examined. Using a sequence of full factorial DoEs, RSM maps out the response and develops equations describing the factors' effects on the response. After an experiment like the Plackett-Burman has established a crucial main effect, processes are refined using RSM designs. The parameters of the factors can then be adjusted to produce the appropriate answer. 

Factorial Designs

In full factorials, you can examine every treatment combination related to the components and their levels. This examines all of the interactions between the major factors and their influence on the measured responses. If numerous components at various levels are examined, full factorial experiments can require numerous experimental runs. 

In order to use a fractional factorial, it is necessary to make the important assumption that higher-order interactions—those involving three or more factors—are not significant.

Full factorial matrices are the source of fractional factorial designs created by adding new factors and higher-order interactions. While fractional factorials do not exclude the major factor effects, they result in trade-offs when examining interaction effects.

Space Filling Designs

This method provides sequences that are reasonably uniformly distributed when terminated at any point, or it offers the most uniform filling of the design space for a specific number of samples. Space-filling DoE's uniformity in the design space is one of its key characteristics. 

If you want to look into your system in more detail, have little prior understanding, or want to find a place to start when it comes to pre-screening optimization , space-filling designs can be helpful. Space-filling designs look into various aspects without assuming anything about the sort of model or the structure of the space. It also suggests that certain statistical features of traditional DoE designs, including factorials, and some of their efficiency are lost. 

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The Design of Experiments (DoE) comprises five distinct phases: 

You can steer clear of any obstacles by paying close attention to detail and organizing your plans carefully. This involves setting the goal, picking the variables to be examined, and figuring out the parameters, or levels, for every variable. You also identify the reaction of interest at this stage. Your available resources would often restrict your ability to conduct experiments. The goal would be to do the fewest number of runs necessary to achieve the greatest outcomes. 

You also need to figure out how many repeat samples each experiment will need at this step. If there are a lot of factors to be studied, mostly more than five, the first step would be to run screening experiments to narrow the list. The number of runs is mostly dependent on the number of elements to be examined. Usually, the screening process involves the following designs: Fractional Factorial Design, The Plackett-Burman Model and Definitive Screening Designs. 

In order to achieve the desired result, you would optimize the process conditions after determining the important elements and modeling the relationship between factors and response. This stage involves figuring out the ideal ratio of variables and intensities to yield the best results. In addition to the statistical data produced by the program utilized for the experiment, you can make use of the graphs and charts. 

Verification is carried out following the achievement of the optimal condition. It involves carrying out a follow-up experiment in the anticipated ideal circumstances to validate the optimization outcomes. With the aid of verification, you can verify whether the optimized condition was truly optimal. If not, you would adjust the experimental design appropriately. You can also verify the outcomes by estimating which setting will work best for each aspect and then attempting this setting one or more times. 

DoE has been utilized in every industry during the past few years. The following are the benefits of design of experiments implementation: 

• Saves Time: By helping to concentrate on the most important variables and the levels rather than relying solely on instinct or a hunch, DoE saves a substantial amount of time.  Organizations can speed up product development cycles and accelerate time to market by decreasing the duration of experimentation and process development.
• Effective Resource Deployment: By pinpointing the most important variables, DoE enables firms to deploy their resources most effectively. By concentrating on these elements, businesses can streamline their operations and attain notable enhancements in quality without needless spending. 
• Cost-Effective: DoE assists in the identification of cost-effective solutions by methodically investigating process variables and their interconnections. Rework, scrap, and material consumption costs can be reduced for companies through defect reduction, waste elimination, and process parameter optimization.
• Better decision-making: A focused approach, a systematic process, and thorough analysis facilitate effective and well-informed operational and financial decision-making. The organized approach to testing that DoE offers produces trustworthy and statistically valid data. This makes it possible to make well-informed decisions that are devoid of hunches or speculation and grounded in facts. 
• Improved understanding of complex frameworks: By methodically dividing up each important component, evaluating its reaction, merging several components, and evaluating the combined effect, DoE helps to dismantle any complicated system. This makes it easier to examine a complicated system's constituent parts clearly. 

DoE provides the modern solutions needed for today's concerns. These days, it's common practice to investigate several factors at once and how they interact, which enables producers to comprehend a system comprehensively. Numerous noteworthy trends define the use of AI in DoE. 

The Design of Experiments (DoE) method is undergoing a significant transformation as a result of the use of Artificial Intelligence (AI) in digital manufacturing. AI is also making predictive modeling in DoE easier. Manufacturers can now simulate experiments and forecast results before physically carrying them out, which saves time and money. 

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1. What are the prerequisites for conducting a successful DoE? 

Identifying the problem is the first step in creating a DOE. Engineers and experts in quality control choose the goal, be it enhancing a procedure or a product. They then choose the study's parameters and determine the kind and scope of data to be gathered. 

2. How can I choose the right experimental design for my study? 

Selecting a design that calls for a few fewer runs than the budget allows is a smart idea. The study topic, independent and dependent variables, sample size and selection, treatment and control groups, data collecting and analysis techniques, and practical and ethical considerations should all be taken into account. 

3. What role does statistical analysis play in DoE? 

The statistical analysis breathes life into a set of lifeless data by providing meaning to otherwise meaningless figures. They help in eliminating known sources of bias or systematic error, guarding against unknown sources of bias,ensuring that the experiment provides precise information about the responses of interest, and guaranteeing that excessive experimental resources are not needlessly wasted through the use of an uneconomical design.

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What is experimental design or DOE? What are the goals or uses of DOE? What are the steps in DOE?

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What is Design of Experiments (DOE)? Your Method to Optimize Results

Learn about Design of Experiments and how it can help you achieve optimal results from your experiments

What is Design of Experiments (DOE)?

Design of Experiments (DOE) is a systematic method used in applied statistics to evaluate the many possible alternatives in one or more design variables. It allows the manipulation of various input variables (factors) to determine what effect they could have in order to get the desired output (responses) or improve on the result.

In DoE, experiments are being used to find an unknown outcome or effect, to test a theory, or to demonstrate an already known effect. T hey are done by scientists and engineers, among others, in order to understand which inputs have a major impact on output and what input levels should be targeted to reach a desired outcome (output). Simply put, DoE is a way to collect information during the experiment and then determine what factors or which processes could lead to the desired result.

History of Design of Experiments

The term “Design of Experiments,” also known as experimental design, was coined by Ronald Fisher in the 1920s. He used it to describe a method of planning experiments to find the best combination of factors that affect the response or output. It is used to reduce design expenses because analysis of input parameters or factors gives way in identifying waste and which processes can be eliminated. It also helps remove complexities and streamlining the design process for cost management in the manufacturing process.

The key concept behind this methodology is that there is a relationship between the factors affecting the response. ISixSigma defined it as determining the “cause and effect relationships” of factors. Therefore, a complete experimental plan consists of the combination of factors used to evaluate their effects on the response.

Components of Experimental Design

MoreSteam gave a simple illustration to explain the components of the experiment—the three aspects that need to be analyzed in the design experiments—and understanding the meaning of each is crucial in defining DoE.

Cake-baking Process showing the Components of Experimental Design source: MoreSteam

• Controllable variables – pertains to factors that can be modified or changed in an experiment or a process. For example, in the cake-baking process, these factors may include what will be used in baking such as the oven, sugar, flour, and eggs.
• Uncontrollable variables – pertains to factors that cannot be changed. For example, in the cake baking process, this may be the room temperature in the kitchen. They must be recognized to understand how they may affect the response.
• Levels or settings of each factor – they pertain to the quantity or quality that will be used in the experiment. In the cake-baking process example, this includes the oven temperature setting and the quantity of sugar, flour, and eggs.
• Responses – pertains to the outcome of the process that gages the desired effect. In the cake-baking example, the taste, appearance, and consistency of the cake are the responses. They are influenced by the factors and their levels. This is the purpose of experimentation—analyzing each factor to determine which of them provides the best overall outcome or the same quality.

Purpose of Design of Experiments

Experimental design is not only conducted by scientists or engineers. It can be used by different industries who want to maximize the results they’re getting. DoE is conducted to:

Compare alternatives

Conducting experimental design allows you to look at different alternatives. It helps in making an informed decision on what to use or what to change. This methodology can also be used to discover the best combination of alternatives in the experiment.

Maximize process response

With DoE, the factors and their levels are checked and see which of them when used are giving the exact quality in the response.

Reduce variations

Excess variations in the process are the cause of added expense. It affects the cycle time that causes quality differences. With DoE, factors are identified, responses are interpreted, and waste is eliminated or changed.

Process Improvement

Performing a DOE can uncover significant issues that are typically missed when conducting an experiment. These areas will be corrected thus improving the process.

Evaluate the effect of change/s

With DoE, you can determine the effects of changes made with the factors and their levels that influences the response.

Quality Control

DOE can also help improve manufacturing efficiency by identifying factors that reduce material and energy use, costs, and waiting time. It is also used to test a product or system before releasing it to market.

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Examples and Applications of Experimental Design

Below are some practical applications or examples on where DoE is applied:

Pharmaceutical Industry

In the pharmaceutical industry, DOE is most typically used throughout the drug formulation and manufacturing phases. Qualitty is critical for drug products because health and safety of consumers are at risk when a product doesn’t meet the standards. DoE is used in drug testing, reducing impurities in the process of making drugs, before releasing it for consumer use.

DoE is used especially in drugs that are best delivered via a time-release schedule,. It means that it takes time to dissolve slowly in the body. Because one component of DoE is the settings of factors, performing an experimental runs are applicable here.

Fast-Moving Consumer Goods (FMCG) industry

FMCG industry is a part of consumer goods industry that includes all the products which are sold to the general public by any means such as retail stores, internet or by phone. These are mostly used by the consumers in their daily life and may include food, drinks, health and hygiene, cosmetics, household appliances, among others. DoE helps in comparing alternatives or options to get the response where price will be cheaper but does not compromise on quality.

Product Design

DoE is a useful tool for determining specific factors affecting defect levels in a product, which may be used to improve the design of the product.

6 Steps Design of Experiments

Standard DoE processes are often structured around seven or fewer steps. The steps in experimental design will take you through the process of determining what is the best response that you could use in your study, workplace, or procedures.

Steps of Design of Experiments (DOE). Source: JMP

• Describe – this is a critical part wherein you determine what is your goal or what do you want to achieve, which is followed by determining what is your desired response. The first step includes determining your goal, your desired response, and factors.
• Specify – this is the part where you need to specify what variables describe the physical situation, or the factors.
• Design – this is the part where you generate an experimental design model from which you will draw evaluations after run/s or trial/s.
• Collect– this is the part where you execute the design, collect information from the run/s and record the responses that you get.
• Fit – this is the part where you review the responses if it does fit in the generated experimental design model. In some cases, runs should be repeated in order to correct model ambiguity.
• Predict – the last step wherein you predict the results and determine which factor best optimizes the response.

SafetyCulture (formerly iAuditor) for Experimental Design

Why safetyculture.

Perform a DoE to optimize any procedure in your workplace and integrate your experimentation with SafetyCulture . A powerful tool used by multiple industries in performing a more convenient and efficient way to monitor, collect, record, inspect, and audit data.

With the support of SafetyCulture as a Design of Experiments software , engineers, scientists, manufacturers, and researchers, among others, can do the following during the experimental design:

• Monitor and identify if there are process drifts and changes in variables during the run with sensors and the monitoring feature.
• Record the responses that you generate through your experimental runs in a secured cloud and easily access it anywhere when needed through the app.
• Specify which factors have defects using Quality Control Check Sheet.
• Modify quality inspections templates tailored to your specifications to support your experimentation.
• Notify or alert your team about modifications on data collected real-time.

Browse checklists helpful to experimental design:

• DMAIC Template Checklist
• Manufacturing Quality Control Checklist
• Product Evaluation Template Checklist
• DMADV Template Checklist

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Keyboard Shortcuts

1.1 - a quick history of the design of experiments (doe).

The textbook we are using brings an engineering perspective to the design of experiments. We will bring in other contexts and examples from other fields of study including agriculture (where much of the early research was done) education and nutrition. Surprisingly the service industry has begun using design of experiments as well.

  All experiments are designed experiments, it is just that some are poorly designed and some are well-designed.  

Engineering Experiments Section  

If we had infinite time and resource budgets there probably wouldn't be a big fuss made over designing experiments. In production and quality control we want to control the error and learn as much as we can about the process or the underlying theory with the resources at hand. From an engineering perspective we're trying to use experimentation for the following purposes:

• reduce time to design/develop new products & processes
• improve performance of existing processes
• improve reliability and performance of products
• achieve product & process robustness
• perform evaluation of materials, design alternatives, setting component & system tolerances, etc.

We always want to fine-tune or improve the process. In today's global world this drive for competitiveness affects all of us both as consumers and producers.

Robustness is a concept that enters into statistics at several points. At the analysis, stage robustness refers to a technique that isn't overly influenced by bad data. Even if there is an outlier or bad data you still want to get the right answer. Regardless of who or what is involved in the process - it is still going to work. We will come back to this notion of robustness later in the course (Lesson 12).

Every experiment design has inputs. Back to the cake baking example: we have our ingredients such as flour, sugar, milk, eggs, etc. Regardless of the quality of these ingredients we still want our cake to come out successfully. In every experiment there are inputs and in addition, there are factors (such as time of baking, temperature, geometry of the cake pan, etc.), some of which you can control and others that you can't control. The experimenter must think about factors that affect the outcome. We also talk about the output and the yield or the response to your experiment. For the cake, the output might be measured as texture, flavor, height, size, or flavor.

Four Eras in the History of DOE Section  

Here's a quick timeline:

• R. A. Fisher & his co-workers
• Profound impact on agricultural science
• Factorial designs, ANOVA
• Box & Wilson, response surfaces
• Applications in the chemical & process industries
• Quality improvement initiatives in many companies
• CQI and TQM were important ideas and became management goals
• Taguchi and robust parameter design, process robustness
• The modern era, beginning circa 1990, when economic competitiveness and globalization are driving all sectors of the economy to be more competitive.

Immediately following World War II the first industrial era marked another resurgence in the use of DOE. It was at this time that Box and Wilson (1951) wrote the key paper in response surface designs thinking of the output as a response function and trying to find the optimum conditions for this function. George Box died early in 2013. And, an interesting fact here - he married Fisher's daughter! He worked in the chemical industry in England in his early career and then came to America and worked at the University of Wisconsin for most of his career.

The Second Industrial Era - or the Quality Revolution

W. Edwards Deming

The importance of statistical quality control was taken to Japan in the 1950s by W Edward Deming. This started what Montgomery calls a second Industrial Era, and sometimes the quality revolution. After the second world war, Japanese products were of terrible quality. They were cheaply made and not very good. In the 1960s their quality started improving. The Japanese car industry adopted statistical quality control procedures and conducted experiments which started this new era. Total Quality Management (TQM), Continuous Quality Improvement (CQI) are management techniques that have come out of this statistical quality revolution - statistical quality control and design of experiments.

Taguchi, a Japanese engineer, discovered and published a lot of the techniques that were later brought to the West, using an independent development of what he referred to as orthogonal arrays. In the West, these were referred to as fractional factorial designs. These are both very similar and we will discuss both of these in this course. He came up with the concept of robust parameter design and process robustness.

The Modern Era

Around 1990 Six Sigma, a new way of representing CQI, became popular. Now it is a company and they employ a technique which has been adopted by many of the large manufacturing companies. This is a technique that uses statistics to make decisions based on quality and feedback loops. It incorporates a lot of previous statistical and management techniques.

Clinical Trials

Montgomery omits in this brief history a major part of design of experimentation that evolved - clinical trials. This evolved in the 1960s when medical advances were previously based on anecdotal data; a doctor would examine six patients and from this wrote a paper and published it. The incredible biases resulting from these kinds of anecdotal studies became known. The outcome was a move toward making the randomized double-blind clinical trial the gold standard for approval of any new product, medical device, or procedure. The scientific application of the statistical procedures became very important.

What is a designed experiment?

A designed experiment is a series of runs, or tests, in which you purposefully make changes to input variables at the same time and observe the responses. In industry, designed experiments can be used to systematically investigate the process or product variables that affect product quality. After you identify the process conditions and product components that affect product quality, you can direct improvement efforts to enhance a product's manufacturability, reliability, quality, and field performance.

For example, you work at an offset printing company where some customers have complained of pages coming unattached from their books' bindings. You suspect several factors: glue temperature, paper type, and cooling time. You want to determine which factors, or combinations of factors, significantly affect the effectiveness of your company's binding technique. When you create a designed experiment, Minitab automatically randomizes the run order of the design and displays the design in your worksheet. The run order is the ordered sequence of factor combinations. You can use the worksheet to record your responses when you do your experiment.

• Screening designs
• Factorial designs
• Response surface designs
• Mixture designs
• Taguchi designs

Designed experiments are often done in four phases: planning, screening (also called process characterization), optimization, and verification.

Our intent is to provide only a brief introduction to the design of experiments. There are many resources that provide a thorough treatment of these methods.

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Response surface design models to predict the strength of iron tailings stabilized with an alkali-activated cement.

1. Introduction

2. materials and methods, 2.1. materials, 2.2. description of the statistical model, 2.3. specimen preparation and testing procedure, 3. results and discussion, 3.1. evaluation of specimen preparation procedure, 3.2. unconfined compressive strength, 3.3. statistical modeling, 3.3.1. fitted models.

• The actual concentration ( c A ) of the mixture is highly dependent on the variable t L (r = 0.841, p < 0.1%); therefore, its inclusion as an input parameter to the statistical model together with t L is not possible;
• There is no significant correlation between q u values and the mass variation (Δ m ) during curing. The p -value associated with the hypothesis of no correlation between these parameters is equal to 22.1%; therefore, there is no evidence of correlation between q u and Δ m ;
• The factor that most contributes to the maximum peak strength response is t FA , followed at some distance by the c SH and the t L . The t L is the least important factor of the three in explaining the response, although it is still significant ( p -value = 4.9%).

3.3.2. Performance Measures

3.3.3. validation of the fitted models.

• For both models, all experimental q u values fall inside the 95% predicted intervals, showing a good agreement with the fitted models;
• The error between the experimental and the predicted q u values is not large;
• Apparently, both models overestimate the q u value in the right upper region shown in Figure 14 and Figure 15 . This region was not contemplated in a preliminary phase of the designed plan.

3.4. Definition of a Mixture Index

• Models 3 to 5 provide similar coefficients of determination, all of the three slightly higher than those of the previous models (Models 1 and 2);
• Even in an experimental plan where all the mixtures have approximately the same porosity (see Figure 11 ), the porosity/cement ratio (Model 4) seems to perform slightly better than C iv (Model 3);
• Model 5 has slightly higher values of R 2 and R 2 adj , and the estimates of the constants in the model are not very large values, as is the case on the other models (e.g., 10 13.795 in Model 4), which is in favor of Model 5 for practical use.

4. Conclusions

• The most influencing factor on the unconfined compression strength was the fly ash content, although the sodium hydroxide concentration and the mixture liquid content were also significant;
• Two statistical models were initially proposed based on those three factors. Although they provide a similar performance, the second model provides a slightly better fit, having the additional advantage of requiring just two variables;
• Higher strengths were obtained when the input variables were on the upper values of their range, but when tests were performed outside this range, the strength decreased, suggesting a nonlinear relation outside the initial interval;
• Towards the definition of a mixture index that could represent the mixture components, other statistical models depending on different indexes were proposed. The best-performing model was based on the porosity/cement ratio proposed by [ 34 ], even when the mixture’s liquid content varies.

Supplementary Materials

Author contributions, institutional review board statement, informed consent statement, data availability statement, conflicts of interest.

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Caetano, I.; Rios, S.; Milheiro-Oliveira, P. Response Surface Design Models to Predict the Strength of Iron Tailings Stabilized with an Alkali-Activated Cement. Appl. Sci. 2024 , 14 , 8116. https://doi.org/10.3390/app14188116

Caetano I, Rios S, Milheiro-Oliveira P. Response Surface Design Models to Predict the Strength of Iron Tailings Stabilized with an Alkali-Activated Cement. Applied Sciences . 2024; 14(18):8116. https://doi.org/10.3390/app14188116

Caetano, Isabela, Sara Rios, and Paula Milheiro-Oliveira. 2024. "Response Surface Design Models to Predict the Strength of Iron Tailings Stabilized with an Alkali-Activated Cement" Applied Sciences 14, no. 18: 8116. https://doi.org/10.3390/app14188116

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