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Design of Experiments

Design of experiments (DOE) is a rigorous methodology that enables scientists and engineers to study the relationship between multiple input variables, or factors , on key output variables, or responses .

In this module, you will learn why designed experiments are better than trial and error and one-factor-at-a-time approaches to gain an understanding of cause and effect relationships and interactions between factors. You will be introduced to several types of designs such as factorial, response surface and custom designs. Finally, you will learn some DOE guidelines and best practices which will help you succeed with experimentation.

Estimated time to complete this module: 3 to 4 hours

Design of Experiments Overview (1:01)

Specific topics covered in this module include:

Introduction to doe.

• What is DOE?
• Conducting Ad Hoc and One-Factor-at-a-Time (OFAT) Experiments
• Why Use DOE?
• Terminology of DOE
• Types of Experimental Designs

Factorial Experiments

• Designing Factorial Experiments
• Analyzing a Replicated Full Factorial
• Analyzing an Unreplicated Full Factorial

Screening Experiments

• Screening for Important Effects
• A Look at Fractional Factorial Designs
• Custom Screening Designs

Response Surface Experiments

• Introduction to Response Surface Designs
• Analyzing Response Surface Experiments
• Creating Custom Response Surface Designs
• Sequential Experimentation

DOE Guidelines

• Introduction to DOE Guidelines
• Defining the Problem and the Objectives
• Identifying the Responses
• Identifying the Factors and Factor Levels
• Identifying Restrictions and Constraints
• Preparing to Conduct the Experiment

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Keyboard Shortcuts

Lesson 1: introduction to design of experiments, overview section  .

In this course we will pretty much cover the textbook - all of the concepts and designs included. I think we will have plenty of examples to look at and experience to draw from.

Please note: the main topics listed in the syllabus follow the chapters in the book.

A word of advice regarding the analyses. The prerequisite for this course is STAT 501 - Regression Methods and STAT 502 - Analysis of Variance . However, the focus of the course is on the design and not on the analysis. Thus, one can successfully complete this course without these prerequisites, with just STAT 500 - Applied Statistics for instance, but it will require much more work, and for the analysis less appreciation of the subtleties involved. You might say it is more conceptual than it is math oriented.

  Text Reference: Montgomery, D. C. (2019). Design and Analysis of Experiments , 10th Edition, John Wiley & Sons. ISBN 978-1-119-59340-9

What is the Scientific Method? Section  

Do you remember learning about this back in high school or junior high even? What were those steps again?

Decide what phenomenon you wish to investigate. Specify how you can manipulate the factor and hold all other conditions fixed, to insure that these extraneous conditions aren't influencing the response you plan to measure.

Then measure your chosen response variable at several (at least two) settings of the factor under study. If changing the factor causes the phenomenon to change, then you conclude that there is indeed a cause-and-effect relationship at work.

How many factors are involved when you do an experiment? Some say two - perhaps this is a comparative experiment? Perhaps there is a treatment group and a control group? If you have a treatment group and a control group then, in this case, you probably only have one factor with two levels.

How many of you have baked a cake? What are the factors involved to ensure a successful cake? Factors might include preheating the oven, baking time, ingredients, amount of moisture, baking temperature, etc.-- what else? You probably follow a recipe so there are many additional factors that control the ingredients - i.e., a mixture. In other words, someone did the experiment in advance! What parts of the recipe did they vary to make the recipe a success? Probably many factors, temperature and moisture, various ratios of ingredients, and presence or absence of many additives.  Now, should one keep all the factors involved in the experiment at a constant level and just vary one to see what would happen?  This is a strategy that works but is not very efficient.  This is one of the concepts that we will address in this course.

• understand the issues and principles of Design of Experiments (DOE),
• understand experimentation is a process,
• list the guidelines for designing experiments, and
• recognize the key historical figures in DOE.

Six Sigma Study Guide

Study notes and guides for Six Sigma certification tests

Design of Experiments Study Guide

Posted by Ted Hessing

Design of Experiments is a difficult topic for many Six Sigma certificate applicants to master. Not to worry, we’ve got you covered with a comprehensive study guide.

The objective of Design of Experiments (DOE) is to establish optimal process performance by finding the right settings for key process input variables. The DOE is a way to intelligently form frameworks to decide which course of action you might take. This is helpful when you are trying to sort out what factors impact a process.

Basic Flow for Design of Experiments

The overall process of a DOE is as follows:

• Define objective(s)
• Gather knowledge about the process
• Develop a list and select your variables
• Assign levels to variables
• Conduct experiments
• Data analysis and conclusions

Learning Design of Experiments

Factors in an experiment.

In most experiments, you’ll have several factors to deal with. These are elements that affect the outcomes of your experiment. They fall into a few basic categories:

• Experimental factors are those you can specify and set yourself. For example, the maximum temperature to which a solution is heated.
• Classification factors can’t be specified or set, but they can be recognized, and your samples selected accordingly. For example, a person’s age or gender.
• Treatment factors are those which are of interest to you in your experiment and that you’ll want to manipulate in order to test your hypothesis.
• Nuisance factors aren’t of interest to you for the experiment but might affect your results regardless.

There are two basic types of treatment factors that you’ll use:

• Quantitative factors can be set to any specific level required–for example, pH levels.
• Qualitative factors contain several categories–for example, different plant species or a person’s gender.

A popular example in explaining factors is the simple-sounding task of baking cookies. Most people would simply follow a recipe–or, let’s face it, buy the cookie dough pre-made and bake whatever we don’t eat raw. But how did the recipe come to be in the first place? Someone had to experiment with ingredients and a baking method to get just the right combination.

• Flour: The ratios of flour to liquid and flour to fat are crucial to the texture of a cookie. Too much flour and you end up with a dry, crumbly cookie. Too little, and you end up with an overly flat, crispy cookie.
• Sugar: The type of sugar used can change the way a cookie reacts to the baking process. Using granulated (white) sugar usually creates a crisper, flatter cookie. Using brown sugar creates a moister, chewier cookie.
• Fat: Rubbing the fat into the flour creates a softer cookie. Using butter creates a flatter cookie than using margarine.
• Eggs: Eggs create a less crumbly, chewier cookie.
• Baking powder: Using baking powder causes a cookie to rise or spread, creating a ‘cakey’ texture or a more crisp cookie.
• Temperature: Low-temperature baking gives a cookie more time to spread out while cooking, meaning it’s more likely to be flatter and crisper.

Think of each ingredient and the baking temperature as factors in an experiment. You can’t test each factor independently–you must have all ingredients to produce the cookies. But you can modify the amount, type of ingredient, and temperature at which they’re baked, to find the combination that yields your perfect cookie.

Other Terminology

Review the common terminology used in Design of Experiments Factorial Design.

Planning and Organizing Designed Experiments

Determine the factors.

Next, we must understand the factors that can affect an outcome to create the appropriate design to determine how to structure our experiment.

It’s also helpful to see an example of the kinds of Factors that are in an Experiment.  These are our variables for the possible and desired outcomes.

Determine the Appropriate Design for the Experiment (Full Factorial or Partial)

Here we want to define the interactions that will be in the experiment and understand how to analyze those interactions.

One Factor at a Time (OFAT)

The (OFAT) approach is to doggedly explore every single factor independently. This is a brute force technique that you can get by with when you have just a few variables or interactions. The downside is that with large variable (factor) sets, you will spend a lot of resources doing this. You may miss the complicated interactions other more sophisticated designed experiments will give you.

One Factor at a Time vs. Full Factorial.

Factorial Design

I’ve included a quick overview of different types of factorial design. For a full description, see this overview of Full Factorial Design and see an overview of Partial or Fractional Factorial Design here.

Full Factorial Design

Full Factorial Design is a thorough and exhaustive way of determining how each factor or combination of factors affects the outcome of an experiment—at least one trial for all possible combinations of factors and levels.

2^5-2 means that there are 5 factors at 2 levels and 2 generators. The generator determines what effects are confounded or combined with one another.

We would call this example a 1/L^g fractional factorial.

Thus, 2^5-2 is a 2 level, 5-factor, 1/4th fractional design.

Partial Factorial Design

Finally, there is a Partial (or Fractional) Factorial Design . Often doing a full factorial design analysis is impossible or impractical. Here’s how you can optimize your resources and still achieve a rigorously-supported decision.

Other Designed Experiment Types

You can find notes on other Design of Experiment types here.

Items to Avoid When Conducting a Designed Experiment:

• Unwarranted assumptions of the process.
• Undesirable combinations of the factors.
• Violation of known laws of physics.
• Too large or small design sizes.
• Inappropriate confounding .
• Imprecise measurement.
• Unacceptable prediction error (Type 1 & type 2 errors).
• Undesirable run order.

Introduction to Design of Experiments Video

Full Lecture here:

Six sigma black belt certification design of experiments questions:.

Question: In comparison to a full-factorial design of experiment (DOE) , a traditional, one-at-a-time approach will: (Taken from ASQ sample Black Belt exam .)

(A) Miss interactions (B) Gain efficiencies (C) Save time (D) Cost less

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Comments (6)

I don’t see DOE in IASSC BOK, Am i required as IASSC GB aspirant to study DOE ?

That’s a good question for the IASSC. I would assume not, but organizations have been known to put items not necessarily on their BOK on their exams.

10.15.2020 Very true… in my Green Belt IASSC exam, there were questions I know now were from the Black Belt level.

The wording of the test questions also is a bit challenging… or unclear …or confusing. Isn’t the test difficult enough already?

Dude… I’m hooked now that you applied Design of Experiment to creating a cookie recipe. As a cookie connoisseur myself, I can’t wait to apply DoE in the kitchen!

But really! DoE has been a hard topic for me to swallow until now.

I’m glad!

I do end up using many cooking analogies in my descriptions (Hypothesis Testing overview being another prime example).

While we’re all in different industries and will see different applications of the material, we all have to eat and many of us cook. It’s a helpful shared experience to draw from.

I want to know how much the design of experiments course and study guide cost? Are there any CE’s available and if so how many

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Understanding Design of Experiments (DoE) in the Pharmaceutical Industry

12/13 October 2021, Heidelberg, Germany

Course No. 18390

Dr. Raphael Bar

BR Consulting

This course will explain the basics of DoE with practicing with factorial and fractional DoE as well as DoE by RSM If you have no or little previous knowledge with DoE, you will learn how to set up an experimental design and how to explore the effect of factors that influence either a development/production process or an analytical procedure  while taking into account interactions between the factors.   To better understand and assimilate the DoE  principles, you will learn first to calculate the main effects and factors  interactions by simple manual calculations (with Excel). Then, you will learn how to use Minitab  software program to create a variety of DoE designs, analyze and interpret them. Multiple exercises and examples from pharmaceutical development and laboratory analysis such as robustness studies will be solved by the participants. The participants will learn how to interpret the output of a DoE programme.

With FDA´s Process Validation Guidance for Industry from 2011 and the Annex 15 Revision 2015 process validation has changed to a life cycle. And the life cycle starts with the development which delivers process knowledge and the critical process parameters. To get there the FDA mentions „Design of Experiments“ (DoE). Therefore, DoE is a tool for implementing the process validation life cycle.   Also, ICH Guidelines Q8 (Pharmaceutical Development) and ICH Q9 (Quality Risk Management) speak about DoE as a tool, also in relation to Quality by Design (QbD= approaches).   Meanwhile, DoE is also common practice in other pharmaceutical areas, i.e. in the analytical development or as a CAPA measure for process optimisation.

Target Group

The addressees of the event are employees from the development, quality control lab and  quality assurance departments who are using DoE or wanted to use DoE in the future. We address also GMP auditors and inspectors and validation personnel also involved in DoE.

Each participant should bring a laptop with Excel and a previously downloaded 30 day free-trial Minitab 19 program from http://www.minitab.com . This program should be downloaded on a laptop a few days before the beginning date of the course and verified that it works on the laptop.

Seminar Programme as PDF

• DoE and Quality by Design
• Regulations (EU and FDA)
• A factorial experiment
• DoE vs one-at-a-time experiment
• Where is DoE applied in development and validation of analytical methods
• Where is DoE applied in manufacturing process
• development and validation
• Factorial experiments (categorical and numeric factors)
• Two and three factorial designs
• Manual calculation of main effects
• Manual calculation of interactions
• What is an orthogonal DoE
• Exercises with Excel
• Basic structure of Minitab software
• Input of data
• Running a DoE
• Plotting output results
• Practicing with Minitab
• Diagnostics for goodness of fit to model
• Deviations from normality plot
• Making replicate experiments
• Adding experiments at centre points
• Using known variability
• Two factor full DoE experiments
• Interactions between two factors
• Plotting Main effects and Interactions
• Interpretation of DoE Minitab output
• Does the linear fit the model?
• Significance with p values
• General full factorial DoE
• Exercises in interpretation of Minitab outputs
• Two and three factor experiments with Minitab
• Aliasing in DoE experiments
• Resolution of  DoE experiments
• 4-7 fractional factorial DoE
• Blackett-Burmann designs
• Definitive screening design
• Robustness of HPLC method with fractional DoE
• Optimisation of a process with fractional DoE
• 22 factorial experiments with RSM
• Contour plot
• Surface plot
• Concept of Design Space
• Exercises: optimization of drug solubility with RSM design
• Effect of process parameters on dissolution assay and variability
• Why we use DoE in the pharmaceutical development?
• Example: DoE for formulation selection / optimization
• Example: DoE for manufacturing process optimization
• DoE vs “traditional” approach – when to use which?
• Screening experiments
• Fractional experiments
• Full factorial experiments
• Optimisation experiments: Surface Response Methodology
• Design Space versus Proven Operating Range (PAR)
• Normal Operating Range (NOR)
• Robustness of experiments of a process/method

This course is part of the GMP Certification Programme "ECA Certified Validation Manager" Learn more

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