Summer School 2023

Optimal and Orthogonal Design of Experiments

The 2023 Summer School on Optimal and Orthogonal Design of Experiments will take place in Leuven from 18 till 22 September 2023. It will involve two courses:

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

September 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 2023 Summer School and some of the previous summer, winter and spring schools are the following:

• The Summer School pays attention to theoretical results in the literature and involves more mathematics than the previous schools, which were 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 will be demonstrated in detail at the Summer School.
• While other summer, winter or spring schools we organize were hands-on throughout and used the 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 Python software as well as dedicated enumeration software.
• While other summer, winter or spring schools were organized with an applied audience in mind, the 2023- Summer School is set up for researchers in design of experiments and statisticians lacking knowledge on experimental design.

University of Leuven

The lecture room is room VHI 01.22 in the building called Van Den Heuvelinstituut (Dekenstraat 2, KU Leuven), which is within walking distance of the train station. All hotels within the Leuven ring road and even the youth hostel are within walking distance of the venue for the Summer School. 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

Book: 65 €


Note that all participants will receive a certificate of payment and a certificate of participation at the 2023 Summer School, even when you do not require an invoice. So, do not ask an invoice simply because you want a certificate of payment!


With invoice

Register now

Without invoice (bank transfer, credit card or KU Leuven)

Register now

PART 1: Optimal design of experiments

September 18, 19 and 20, 2023

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 utilize a few software packages (SAS and JMP) and work on a few examples themselves. Various software packages other than SAS and JMP will be briefly discussed as well. Note that SAS and JMP will be available to all course participants as the course takes place in a PC lab.

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 dedicated to advanced topics locally, Bayesian and minimax design for generalized linear and nonlinear regression models.


Peter Goos

A full professor at the Faculty of Bio-Science Engineering of the University of Leuven and at the Faculty of Business and 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

September 20, 21 & 22, 2023

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. For these exercises, you need to bring your own laptop with Python. There is no need to be a Python expert but it is convenient to have at least some previous programming experience with this language. Note that Python is open source so that there are no extra costs involved.

The “Orthogonal Design of Experiments” course will start on Wednesday (September 20) after lunch and finish on Friday (September 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 with 30+ years of experience as senior statistical consultant at the contract research organization TNO in the Netherlands, he advises PhD students at KU Leuven. His main research area is the construction of orthogonal experimental designs.

Orthogonal Array