Summer School 2018

Optimal and Orthogonal Design of Experiments

The 2018 Summer School on Optimal and Orthogonal Design of Experiments will take place in Leuven from 18 till 22 June 2018. It will involve two courses:

June 18-20: Optimal Design of Experiments (by Peter Goos)

June 20-22: Orthogonal Design of Experiments (by Eric Schoen)

The Summer School will start with a thorough introduction of the theory of optimal experimental design, for models ranging from the simple linear regression model to multiple linear regression models and nonlinear regression models. Next, the focus will shift to orthogonal experimental designs which are especially useful for screening experiments. These are experiments involving many factors and relatively small numbers of observations.

The main differences between the Summer School and the Spring School are the following:

• The Summer School pays attention to theoretical results in the literature and involves more mathematics than the Spring School, which is based on case studies.
• The Summer School pays substantial attention to algorithms for constructing optimal experimental designs. The functioning of point-exchange and coordinate-exchange algorithms and enumeration algorithms for orthogonal designs is demonstrated in detail at the Summer School.
• While the Spring School is hands-on throughout and uses the user-friendly JMP software, the optimal design course of the Summer School involves only a few hands-on sessions and discusses several software packages. The orthogonal design course uses the programming-oriented Matlab software as well as dedicated enumeration software.
• The Spring School was designed with an applied audience in mind, while the Summer School was set up for researchers in design of experiments and statisticians lacking knowledge on experimental design.

University of Leuven - Kasteelpark Arenberg 30, 3001 Leuven-Heverlee (LAND.91.0030)

The lecture room is  about 2 km from the town center. There are frequent buses from the town center and the Leuven train station to the Heverlee campus. Probably, the best thing to do is to seek accommodation in the town center or near the train station, and take a bus to the lecture room. The youth hostel is within walking distance of the train station. Hotels near the train station are generally cheaper than those in the town center. Registrants can find information about places to stay on the website of the town of Leuven.

Travel information

Leuven is easy to reach by train from the Brussels train stations (roughly 20-30 minutes), from Liège (30 minutes) and from the Brussels national airport (15 minutes by train). Note that the Brussels South airport is further.


One Course

  • 200 € – PhD students
  • 250 € – other academics and attendees from non-profit organisations
  • 750 € – other
  • 10 € – invoice

Both Courses

  • 250 € –  PhD students
  • 325 € – other academics and attendees from non-profit organisations
  • 1000 € – other
  • 10 € – invoice


With invoice

Register now

Without invoice

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PART 1: Optimal design of experiments

June 18, 19 & 20, 2018

The target audience for the course is starting Ph.D. students and anyone else who would like a primer on optimal design of experiments. Prerequisites for the course are knowledge of basic statistics and regression analysis. Familiarity with classical design of experiments is not required. The course is not highly mathematical and therefore accessible to a broad audience.

The course will start with an intuitive introduction of the topic and gradually builds up to more complicated situations. Examples for the course will be taken from industry, marketing, chemistry, medicine, … to show the wide applicability of the optimal design techniques. The attention will not be restricted to optimal design for linear regression models, but Bayesian optimal design and minimax designs for nonlinear regression models will also be discussed. The strengths and weaknesses of optimal design will be illustrated, and some remedies to overcome some of the problems will be given. A unique feature of the course is that it discusses and illustrates the working of algorithms for constructing optimal experimental designs.

The course will take place in a computer class so that the course participants can work on a few algorithms and examples themselves. Various software packages are demonstrated as well.

In total, the course takes 2.5 days.

For further information, please contact Peter Goos. (


Introduction to design of experiments

Intuitive introduction to optimal design of experiments

Optimal design for linear regression models (first-order models, second-order models, constrained design regions, algorithms)

Optimal design for nonlinear regression models (local optimal design, Bayesian optimal design, minimax design, algorithms)

Extensions to non-standard design problems (blocked experiments, paired comparison and choice experiments, experiments with hard-to-change factors (split-plot experiments), model uncertainty)

The last half day is reserved for advanced topics like split-split-plot designs, strip-plot designs, and computationally efficient methods for Bayesian optimal design.


Peter Goos

A full professor at the Faculty of Bio-Science Engineering of the University of Leuven and at the Faculty of Applied Economics of the University of Antwerp, where he teaches various introductory and advanced courses on statistics and probability. His main research area is the statistical design and analysis of experiments.

PART 2: Orthogonal Design of Experiments

June 20, 21 & 22, 2018

The target audience for the course is starting PhD students who have taken introductory courses in linear regression, design of experiments and matrix algebra. The mathematical level is not very high, as the emphasis is on calculation and enumeration.

The course features the use of orthogonal arrays as statistical designs of experiments. Orthogonal arrays are rectangular arrangements of symbols, where the rows correspond to the different tests and the columns to different experimental factors. The symbols in each column are the settings of the corresponding factor. For a given run size, a given number of factors and a given number of factor settings, there can be many different arrays. Some are downright disastrous to use, while others can be very good.

The course has two main themes. First, different criteria are explained to quantify the usefulness of an orthogonal array as an experimental design. The second theme is the generation of all orthogonal arrays of a given set of parameters (run size, number of factors and number of factor settings) using a powerful algorithm.

There is a mix of lectures and computer exercises. The course will therefore take place in a computer class. The exercises involve Matlab as well as an easy-to-use program to generate all orthogonal arrays for a given set of parameters. There is no need to be a Matlab expert as many freshly written procedures will be made available to perform the calculations. However, it is convenient to have some experience using this package.

The “Orthogonal Design of Experiments” course will start on Wednesday (June 20) after lunch and finish on Friday (June 22) around 4 pm.

At the end of the course, the participants should be able to

  • Appreciate how data of experiments based on orthogonal arrays are analyzed.
  • Enumerate series of small orthogonal arrays.
  • Compare the potential of alternative orthogonal arrays with a given set of parameters as experimental designs.

For further information, please contact Eric Schoen at eric.schoen ( at )


  • Practical example of an orthogonal array
  • Orthogonality in orthogonal arrays
  • Analysis of data from orthogonal array-based designs
  • Orthogonal arrays with two levels
  • Multi-level arrays
  • Enumeration of orthogonal arrays

Eric Schoen

A guest professor at the Faculty of Bioscience Engineering of the KU Leuven and a senior statistical consultant at the contract research organization TNO in the Netherlands, he teaches the experimental design course for master students at Leuven. His main research area is the construction of orthogonal experimental designs.

Orthogonal Array