## Design of Experiments for Optimisation

### What you’ll learn

– Basic concepts of regression models;

– Factorial designs with central points;

– Lack-of-fit test;

– Inaccurate levels in the design factors and missing observations

– Response surface methodology;

– Path of the steepest ascent;

– Central Composite Designs;

– Face-Centred Composite Designs;

– Box-Behnken Designs.

– Analysing several responses simultaneously.

### Requirements

The student must be familiar with the basic concepts of the design of experiments such as:

– Analysis of variance (ANOVA)

– Factorial Designs

Concepts as designs in blocks and fractional designs also help with the understanding.

### Description

Welcome to “Design of Experiments for Optimisation”!Experimentation plays an important role in science, technology, product design and formulation, commercialization, and process improvement. A well-designed experiment is essential once the results and conclusions that can be drawn from the experiment depend on the way the data is collected.This course will cover the basic concepts behind the Response Surface Methodology and Experimental Designs for maximising or minimising response variables.This is not a beginner course, so to get the most of it, you need to be familiar with some basic concepts underlying the design of experiments, such as analysis of variance and factorial designs.You can find it in my course “Design and Analysis of Experiments” or on several other courses and resources on the market.The course starts with a basic introduction to linear regression models and how to build regression models to fit experimental data and check the model adequacy. The next section covers experimental designs for linear models and the use of central points to check the model’s linearity (lack-of-fit). By the end of the section, we will be using linear models to fit experiments with inaccurate levels in the design factors and missing observations.By then, we will be ready for Response Surface Methodology. We will start with a factorial design to fit a linear model and find the path of the steepest ascent. And then, we are going to use a central composite design to fit a quadratic model and find the experimental conditions that maximise the response. Moreover, we will see how to analyse several responses simultaneously using two very illustrative and broad examples.Finally, we will see how to use three-level designs: Box-Behnken and face-centred composite designs.The whole learning process is illustrated with real examples from researchers in the industry and in the academy.The analysis of the data will be performed using R-Studio. Although this is not an R course, even students that are not familiar with R can enrol in it. The R codes and the data files used in the course can be downloaded, the functions will be briefly explained, and the codes can be easily adapted to analyse the student’s own data.However, if you are already familiar with using other DoE software, feel free to download the data and reproduce the analysis using the software of your choice. The results will be exactly the same.Any person who performs experiments can benefit from this course, mainly researchers from the academy and the industry, Master and PhD students and engineers.

### Overview

Section 1: Welcome and Get Prepared!

Lecture 1 Welcome!

Lecture 2 Installing R and R Studio

Section 2: Linear Regression Models

Lecture 3 Introduction to Linear Regression Models

Lecture 4 Fitting Linear Regression Models to Experimental Data

Lecture 5 Building Linear Models in R

Lecture 6 Analysis of Variance of the Regression Model

Lecture 7 Residuals Plots

Lecture 8 Visualisation and Interpretation of the Results

Lecture 9 Multiple Linear Regression Models

Lecture 10 Multiple Linear Regression Models for Designed Experiments

Section 3: Designs for Linear Models

Lecture 11 Designs for Linear Models – 2ˆk Design

Lecture 12 Adding Central Points to the 2ˆk Design

Lecture 13 Building a 2ˆ3 design with central points in R

Lecture 14 Analysing a 2ˆ3 design with central points in R

Lecture 15 Interpreting the results

Lecture 16 Designs with missing observations and inaccurate levels of design factors

Lecture 17 Solving a design with missing observations and inaccurate levels

Section 4: Response Surface Methodology

Lecture 18 Introduction to Response Surface Methodology

Lecture 19 The Starting Design

Lecture 20 Analysing the First Design

Lecture 21 The Method Steepest Ascent

Lecture 22 Interpreting Lousy Fitting

Lecture 23 The Central Composite Design

Lecture 24 Building a Central Composite Design in R

Lecture 25 Analysing a Central Composite Design in R

Lecture 26 Analysing Multiple Responses Simultaneously (1)

Lecture 27 Analysing Multiple Responses Simultaneously (2)

Lecture 28 Desirability Functions for Optimising Multiple Responses

Lecture 29 Desirability Functions – R tutorial

Section 5: Central Composite Design for 3 Factors

Lecture 30 Central Composite Design for 3 Factors

Lecture 31 Case Study: The Starbucks Coffee Bag – 1

Lecture 32 Case Study: The Starbucks Coffee Bag – 2

Lecture 33 Case Study: The Starbucks Coffee Bag – R tutorial – Adding the Coded Variables

Lecture 34 Case Study: The Starbucks Coffee Bag – Analysing the Tear Results

Lecture 35 Case Study: The Starbucks Coffee Bag – Analysing the Leakage Results

Lecture 36 Case Study: The Starbucks Coffee Bag – Final Interpretation of the Results

Lecture 37 6.H Applying Desirability functions to The Starbucks Coffee Bag Case Study

Section 6: Three-level Designs for Second-Order Models

Lecture 38 Face-Centred and Box-Behnken Designs

Lecture 39 Workflow for Response Surface Analysis

Lecture 40 Solving a Box-Behnken Design

Lecture 41 Building BBD and FCCD in R

Section 7: Final Considerations on Experimental Designs

Lecture 42 Desirable Features for Experimental Designs

Lecture 43 How Many Runs Does a Design Need?

Section 8: Closing

Lecture 44 Thank you!

Lecture 45 Bonus lecture!

Researchers;,Graduate students;,Engineers;,Anyone who performs and analyse experiments.

#### Course Information:

Udemy | English | 2h 58m | 1.51 GB

Created by: Rosane Rech

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