# What is Design of Experiment in Statistics? Complete guide

Do you want to ensure that your products and services constantly meet customer expectations? Then you need a breakthrough improvement tool called Design of Experiment (DOE) in statistics.

Design of Experiment (DOE) is a breakthrough tool that helps businesses identify and optimize critical factors in their processes, leading to improved efficiency, reduced costs, and increased customer satisfaction.

In this article, we will delve into the world of Design of Experiment (DOE) in statistics in detail, exploring what it is, the basic terminologies of DOE, and different types of DOE, and lastly, we will also discuss one practical example of how to perform DOE step by step.

So buckle up and get ready to take your business to the next level with the power of DOE. Let’s get started…

## What is the Design of an experiment in statistics?

The design of an experiment in statistics is a powerful statistical tool used in Lean Six Sigma methodology to identify and optimize the key factors that influence a process or system.

It helps you identify the cause-and-effect relationship between input variables (known as factors) and output variables (known as responses) of any process or system.

The basic objective of the Design of an experiment in statistics is to improve the quality, efficiency, and overall performance of a process by controlling the input variables that affect the output.

With the help of DOE, you actually identify which factors (input variables) that have a significant impact on the output variable, so that you can optimize the process and improve its performance.  You can adjust those factors in order to achieve better results.

Let’s see some practical examples where DOE is used:

• Example-1: A manufacturing company wants to improve the quality of its products. They use DOE to determine the optimal combination of factors that impacts the quality of the product.
• By manipulating input variables such as temp, pressure, and speed, they can determine the best combination of factors that can produce the highest quality output.
• Example-2: A hospital wants to reduce the time it takes to discharge patients. They use DOE to identify the factors that impact patient discharge time, such as the time it takes to complete paperwork,
• The time it takes to receive test results, and the availability of staff. By manipulating these input variables, they can identify the most efficient process for discharging patients.
• Example-3: A software development company wants to improve the performance of its application. They use DOE to determine the optimal combination of factors that impacts the performance of the application.
• Such as memory usage, processor speed, and network bandwidth. By manipulating these input variables, they can identify the most efficient way to optimize the performance of the application.

I hope with this example you got how and where you can use DOE. See, the process of conducting Design of an experiment in statistics is very simple. First, you need to define the problem and the goals of the experiment.

Next, you need to identify the factors that may affect the process output and determine the range of values to be tested (set range for each factor or input variable).

Then you need to design the experiment by selecting the appropriate experimental design (there are 3 major types of experimental design we will discuss later) and determining the number of trials or runs required.

Once the experiment is designed and conducted, you need to analyze the data and identify the key factors that have the most significant impact on the output. Finally, you can use that information to optimize the process and achieve the desired results.

Don’t worry if you can’t understand the process of Design of an experiment, we will discuss this process with the help of one example later in this article. Before that let’s see some of the important terminologies used in DOE.

### Terminologies of DOE

There are some important terminologies used in the Design of an experiment in statistics (DOE) that you need to know while performing DOE at your workplace. Let’s see the basic meaning of these terminologies one by one.

Factors:

Factors are the input variables (X) or process parameters that are intentionally changed during an experiment to understand their impact on the output response.

Factors can be continuous variables like temperature, and pressure or discrete ones like machine settings, and material type in nature.

Levels:

Levels are the specific values or settings chosen for each factor during an experiment. For example, if you were testing the effect of temperature on a chemical reaction, the levels might be 25, 30, 35 degrees Celsius, and so on.

Response:

Responses are the output variables (Y) or process performance measures that are measured or observed during an experiment.

Responses can be quantitative like length, weight, and speed, or qualitative like pass/fail, good/bad in nature.

Treatment:

This is a combination of specific factor levels that you use in your experiment. For eg, if you were testing the effect of temp and pressure on a chemical reaction, a treatment might be 30 degrees and 10 psi, and another treatment could be 45 degrees and 15 psi.

Experimental design:

This is the overall plan or strategy that you use to conduct your experiment. There are different types of experimental designs, including half/full factorial designs, response surface designs, and mixture designs.

Replication:

Replication is the process of repeating the same experiment with the same factor settings multiple times to assess the experimental error and variability in the results. Replication helps to improve the reliability and robustness of the experiment conclusions.

Randomization:

Randomization is the process of randomly assigning experimental runs to different factor combinations in order to minimize the impact of confounding variables and bias.

Randomization helps ensure that the experiment results are statistically valid and can be generalized to the larger population.

Blocking:

Blocking is a technique used to account for known sources of variability in an experiment by grouping experimental runs into homogeneous sets or blocks based on a blocking factor (eg, time, location, batch).

Blocking helps to reduce the impact of nuisance variables and improve the precision of the estimated effects.

Main effects:

Main effects are the changes in the response due to changes in the levels of individual factors while holding all other factors constant. Main effects provide information about the independent contribution of each factor to the variation in the response.

Interactions:

Interactions are the combined effects of two or more factors that are not additive, meaning that the effect of one factor depends on the level of another factor. Interaction effects are important to understand, as they can significantly impact the process performance.

### Types of DOE

There are two main types of DOE and these two types are further categorized into 6 more types. Let’s first understand two main types.

Screening Experiment:

These experiments are used to identify the most important factors that significantly impact the output response. In the screening experiment, we vary the values of different factors over a certain range, while keeping other factors constant.

By analyzing the results, we can identify the factors that have the most significant impact on the output response and focus our efforts on further studying those factors in more detail.

Optimization Experiment:

Once we have identified the most significant factors through screening experiments, we can conduct optimization experiments to determine the optimal settings of those factors that lead to the best output response.

In the optimization experiment, we vary the values of the significant factors within their optimal ranges to find the combination of settings that results in the best outcome.

Both screening and optimization experiments can further be categorized into some more types of Design of an experiment in statistics. Let’s see them –

One factor at a time (OFAT):

OFAT involves changing one factor at a time while keeping other factors constant and observing the effect on process performance.

While OFAT is simple and easy to implement, it may not be efficient in identifying the interactions between the factors and may result in poor solutions.

Full factorial design:

In a full factorial design, we vary all factors at all possible levels. This allows us to study the main effects (influence of each factor on its own) as well as the interaction effect (combined effect of multiple factors) between the factors.

However, full factorial designs can become impractical if the number of factors and levels is large, as the number of experiments required increases exponentially. For example, let’s say you are optimizing the baking time and temperature for a cake recipe.

You could conduct a full factorial DOE by testing all possible combinations of different baking times (eg- 10min, 15min, and 20min) and temperatures (eg- 150°C, 175°C, and 200°C ) to determine the optimal settings for achieving the desired cake quality.

Fractional factorial design:

This type of Design of an experiment in statistics is a more efficient version of full factorial designs, where only a fraction of all possible combinations of input variables and their levels are tested.

Fractional factorial designs are useful when there are many input variables and testing all possible combinations is not feasible due to resource limitations.

These designs are carefully selected to provide information on the most important input variables interactions while reducing the number of experiments required.

For example, if you have 6 factors with 2 levels each, a full factorial design would require 2^6 = 64 experiments. However, a fractional factorial design such as a 1/2 or 1/4 design would only require 32 or 16 experiments. This can save time & resources by providing valuable insights.

Response Surface design:

RSM is used to model the relationship between input factors and the response or output variables of interest. This type of design involves testing a set of experiments with varying levels of input factors, typically at intermediate levels.

Typically at intermediate levels, to create a mathematical model that can be used to optimize the response. RSM is commonly used when the relationship between input factors and the response is complex or non-linear.

For example, in a chemical process, you could use RSM to model the relationship between factors such as reactant concentration. temp, reaction time, and yield of the product to identify the optimal factor settings for maximizing the product yield.

Plackett Burman design:

The Plackett Burman design is a type of screening design that is used to identify the most important factors affecting a process or product while minimizing the number of experiments required.

This design allows for the testing of a large number of factors at two levels (low and high) in a relatively small number of experiments.

PMDs are commonly used when the focus is on identifying the key factors that have a significant impact on the process or product.

For example, in the pharmaceutical manufacturing process, you could use a PMD design to quickly screen a large number of factors such as raw material quality, process parameters, and equipment settings to identify the critical factors that significantly impact product quality.

Taguchi design:

Taguchi design also known as Robust design is a type of experimental design that aims to make a process or product less sensitive to variations in input factors also known as noise factors.

Taguchi designs typically involve testing a small number of experiments with a focus on identifying the optimal settings of the factors that are robust to variations in noise factors.

This type of design is often used when the goal is to improve the performance or quality of a process or product under real-world, noisy conditions.

For example, in a manufacturing process, you could use Taguchi design to optimize the performance of a product by varying factors such as material thickness, machine speed, and temperature, while also considering noise factors such as humidity and ambient temp that may affect the process.

These are some of the main types of Design of an experiment in statistics that are used in Lean Six Sigma. Each type of DOE has its own strengths and weaknesses.

The choice of these designs depends on the specific goals, resources, and characteristics of the process or product being studied.

In the upcoming articles, we will discuss these types one by one with some practical examples. For now, just understand the fundamental concept of each type. Right!

## Steps to perform the design of an experiment in statistics?

You understood the terminologies as well as different types of Design of an experiment in statistics, right! Now let’s see the simple 7-step process you need to follow to perform DOE and get breakthrough results in the end.

Step: 1 – Define the problem and select factors:

The first step in conducting a DOE is to define the problem or process improvement objective. Clearly define what you want to achieve with the DOE, such as improving product quality, reducing defects, or increasing process efficiency.

Establish measurable goals and set targets for improvement. Then identify the factors that may affect the response variable. Factors are variables that you want to manipulate during the experiment.

They can be qualitative (eg- material type, operator) and quantitative (eg- temperature, time). Select the appropriate number of levels for each factor which could be two levels (eg- high (+) and low (-)).

Example – Let’s say you are conducting an experiment to optimize the baking time and temperature for a new cake recipe. Your objective is to create a tasty cake recipe.

The factors to be considered are baking time (2 levels: 10 min, 20 min) and baking temperature (2 levels: 150°C, 180 °C).

Step: 2 – Define the experimental design

Choose the type of experimental design that suits your objectives and factors. Common designs used in the design of an experiment in statistics include full factorial design, fractional factorial design, response surface designs, etc.

Example – In this example, we choose a full factorial design, to test all possible combinations of factor levels. The number of experimental runs required for a full factorial design is the product of the number of levels for each factor.

For the cake-baking experiment, use a simple formula to determine the number of experiments, Runs = X^n where X is the number of levels and n is the number of factors.

In this example, the factors are 2 and the levels are 2 hence runs = 2^2 = 4 experimental runs to test all possible combinations.

Step: 3 – Conduct the experiment.

Perform the experimental runs according to plan, carefully controlling all other variables that could affect the response variable, Record the observed response variable data for each run.

Example – Bake the cake according to planned combinations (4 runs) of two factors baking time and temperature and then measure the quality of the cakes (like taste, & texture) as the response variable for each run.

Step: 4 – Analyze the data

Analyze the collected data of the response variable for all experimental runs using a statistical technique to determine the effects of each factor on the response variable.

Common analysis methods include ANOVA, regression analysis, & graphical methods such as scatter plots & interaction plots.

Example – Use statistical software to analyze the collected data and identify the significant effects of baking time and temperature on the quality of the cakes. Determine the optimal levels of these factors that result in the best cake quality.

Step: 5 – Draw conclusions and make recommendations

Based on the result of the data analysis, draw conclusions about the effects of the factors on the response variable and make recommendations for optimizing the process, product, or system. Consider factors that have significant effects and potential interactions between factors.

Example – Based on the analysis, you may conclude that longer baking time and higher baking temperature results in better cake quality. You may recommend using a baking time of 20 min, and a temperature of 180°C for the optimal cake recipe.

Step: 6 – Verify and validate the results.

Perform additional experiments, if needed to verify and validate the optimal factor levels and recommendations. This helps to ensure the reliability and reproducibility of the results.

Example – Perform additional cake baking experiments using the recommended factors level to confirm that the optimal baking time and temperature indeed result in the desired cake quality.

Step: 7 – Document and communicate the results.

Document the results of DOE, including the experimental design, data analysis, and recommendations. Communicate the findings to relevant stakeholders, process owners, managers,s and team members.

Use the results to drive continuous improvement efforts and supports decision-making. This is the last step of the design of an experiment in statistics which is useful for building a problem-solving mindset and continuous improvement culture in the organizations.

Increased understanding of the process:

Design of an experiment in statistics (DOE) helps in identifying and quantifying the factors that have a significant impact on the process output or performance.

This increased understanding of the process enables process improvement teams to focus their efforts on the most critical process parameters that drive the process output.

Reduced experimentation time and cost:

DOE enables the design and execution of experiments in an efficient and effective manner. with DOE, process improvement teams can conduct experiments using fewer resources and in less time, thereby reducing experimentation costs.

Minimization of process variability:

DOE allows organizations to identify and control the factors that contribute to process variability, resulting in more consistent and predictable outcomes.

By optimizing process parameters through DOE, organizations can minimize the variability of their processes and reduce defects which can lead to improved product quality, and increased customer satisfaction.

Optimization of process parameters:

DOE can help in determining the optimal values for process parameters that lead to the desired process output. This optimization can lead to significant improvements in process performance such as reduced defects, increased throughput, and improved quality.

Improved decision-making:

DOE provides process improvement teams with valuable insights into the process and its parameters. These insights can help in making data-driven decisions about process changes, leading to more effective and efficient process improvement efforts.

Faster problem-solving:

Design of an experiment in statistics (DOE) can help organizations identify the root cause of process problems more quickly and accurately, allowing them to implement solutions more efficiently. This can help reduce downtime, improve throughput, and increase productivity.

Complexity:

Design of an experiment in statistics (DOE) can be quite complex and time-consuming to design and implement, especially for complex and big processes. This can lead to increased costs and delays in implementation.

Complexity of analysis:

Analyzing the data collected from DOE experiments can be complex, requiring specialized statistical software and expertise. This can be a challenge for organizations that lack the necessary resources and expertise.

Risk of incorrect conclusion:

If the design of the DOE experiment is flawed or if the data is not properly collected and analyzed, it can lead to incorrect conclusions and suboptimal solutions.

Limited scope:

DOE is most effective when used to analyze a limited number of variables, typically less than 10. When the number of variables increases, the complexity of the experimental design grows exponentially, making it difficult to draw meaningful conclusions from the data.

## Applications of Design of an Experiment in Statistics

DOE is used in many fields like manufacturing, service, healthcare, agriculture, marketing, and research analysis for breakthrough improvement and problem-solving. Let’s see some of the important applications of DOE –

Product development:

Design of an experiment in statistics can be used in product development to identify the factors that are most important for the performance of the product.

By testing the product under different conditions and analyzing the results, the design team can identify the key factors and optimize the product design for maximum performance.

Process optimization:

Design of an experiment in statistics can be used to optimize any process (manufacturing, service, healthcare) by identifying the optimal settings of the input variables that will produce the desired output.

For example, the manufacturing process may have several input variables such as temp, pressure, flow rate, etc. DOE can help determine the best combination of these variables to produce the desired quality of the product.

Quality control/improvement:

Design of an experiment in statistics can be used to determine the sources of variation in a process and to identify the factors that are causing defects or non-conformance.

By understanding the sources of variation and their effects, quality control teams can implement corrective actions to improve product quality & reduce defects/variability.

Root cause analysis:

Design of an experiment in statistics can be used as a tool for root cause analysis to identify the underlying causes of process failures or defects. (Check out – How to use Root cause analysis?)

By systematically testing the process under different conditions and analyzing the results, DOE can help identify the factors that are contributing to the problem and help develop solutions to address them.

Supplier evaluation:

Design of an experiment in statistics can be used to evaluate suppliers by testing the quality of their products under different conditions and determining which suppliers produce the most consistent and reliable products.

Agriculture:

In agriculture, Design of an experiment in statistics (DOE) can be used to optimize crop yield, reduce crop losses, and improve soil quality. For example, DOE can help identify the optimal combination of fertilizer, irrigation, and planting density to achieve the highest crop yield.

Healthcare:

In healthcare, DOE can be used to optimize medical treatments and improve patient outcomes. For example, DOE can help identify the optimal combination of treatment variables to achieve the best patient response.

Marketing:

In marketing, DOE can be used to test different promotional strategies and improve customer engagement. For example, DOE can help identify the most effective combination of marketing channels, messaging, and incentives to drive customer acquisition and retention.

## Conclusion

Design of an experiment in statistics is a powerful and systematic approach that allows the organization to optimize its processes, products, and services for improved performance and enhanced customer satisfaction.

By carefully planning, executing, and analyzing controlled experiments, organizations can uncover valuable insights, identify critical factors, and make data-driven decisions to achieve optimal results.

Design of an experiment in statistics empowers businesses to minimize waste, reduce variability, and optimize resources, ultimately leading to cost savings, increased efficiency, and enhanced competitiveness in today’s dynamic business environment.

Throughout this article, we discussed all the important concepts of DOE in detail with a practical example. If you found this article useful then please share it in your network and subscribe to get more such articles every week.

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