The PhD student will work in the context of the PrimaVera project (primavera-project.com), a national consortium involving several universities and industrial partners. This prestigious project is one of the 17 projects of the funded by the Dutch Academy of Sciences in the context of the national Dutch Science Agenda. Within PrimaVera, the PhD student will work on a subproject that pertains specifically to developing mathematical models for the accurate prediction of machine reliability, the remaining useful lifetime (RUL) and the failure rate. There are multiple challenges associated with this research direction due to among others scarcity of failures, dependencies between components and heterogeneous data with different time scales. Both frequentist and Bayesian approaches will be explored, building upon the available limited literature. Moreover, these models will serve as the basis for spare part and inventory management policies and preventive maintenance planning by integrating learning and decision making. A promising possible approach is to incorporate a Bayesian learning approach to the stochastic optimisation problem. However, the limitation of this approach is that it requires knowledge of the underlying stochastic model and it suffers from computational complexity issues outside of conjugate updating families. This could be overcome by considering a Bayesian optimisation algorithm for reinforcement learning. Effectively, the Bayesian optimisation framework for optimal decision making addresses the exploration-exploitation trade-off. The project aims to address such issues and is thus at the exciting interface of statistics and stochastic operations research.

The research is fundamental in nature, but it is inspired by real-life problems arising from practical situations. The PhD student will be employed by the Department of Mathematics and Computer Science of TU/e but work in close collaboration with ASML - the world-leading manufacturer of integrated-circuit lithography machines. There will be ample opportunities to implement and test novel methodologies in a cutting-edge industrial research environment. This PhD position offers a unique opportunity to work in the interface of academic and industrial research.

The Primavera project is supported by two groups in ASML, that are both part of the ASML Development and Engineering sector. The first group is the Robust Design group. This group is providing the methods, tools, and expertise in the areas of Reliability Engineering, FMEA (Failure Mode and Effect Analysis) and Six Sigma methodology. Important aspects of the Reliability Engineering work that link to the Primavera project include reliability risk assessment of new systems and modules, modelling and prediction of reliability of new systems and modules. The second group is the Spare Parts Quality group. This group provides analysis of reliability performance and problem-solving activities of products in the field and enables closing of the feedback loop for current and future products. The information covers topics like failure behaviour, failure modes, failure rates and useful life of individual parts and the reliability of the complex behaviour in ASML equipment. Reliability models like Crow-AMSAA and Weibull are used to determine failure behaviour and reliability growth and, amongst others, techniques as 5 times Why and 8-D.

At TU/e, both the Department of Mathematics and Computer Science and the Department of Industrial Engineering and Innovation Sciences are involved in the PrimaVera project. This PhD project will be executed within statistics and stochastic operations research groups of the Department of Mathematics and Computer Science.

The statistics group at TU/e focusses both on theoretical and applied research. The research areas cover a wide range of topics: hypothesis testing (equivalence, non-inferiority), statistical process monitoring, survival and reliability theory, causality, mixed and latent variable models, non-parametric statistics, high-dimensional statistics, and statistical learning theory.

The stochastic operations group at TU/e primarily focuses on disciplinary excellence and model-based analysis, but it also places an intensified effort in data-driven modelling and optimization approaches. Moreover, the hybrid data-driven and stochastic learning approaches with online learning and data-driven optimization lie at the heart of the stochastic operations group.

Both groups actively explore new research lines in Data Science and have strong ties with industrial partners in various business domains, particularly the high-tech industry in the Brainport region around Eindhoven.

The statistics and the stochastic operations groups are part of the SPOR (Statistics, Probability The-ory and Operations Research) cluster within the TU/e subdepartment Mathematics. The SPOR-cluster currently has 4 full professors, 6 part-time professors, 3 associate professors and 14 assis-tant professors. In addition, the cluster is strongly intertwined with EURANDOM, the European institute for research in Statistics, Probability and Stochastic Operations Research. EURANDOM is a workshop and visitor centre that exists since 1998.

The Department of Mathematics and Computer Science consists of three charters: Mathematics, Computer Science, and Data Science. Knowledge valorisation within the department takes place through the Project Development Office (PDO). The department actively participates in EAISI, the Eindhoven Artificial Intelligence Systems Institute, a research institute covering many facets of data science and artificial intelligence. In the education and research areas, the department works close-ly together with other universities and with companies. TU/e is located in Brainport, an interna-tionally renowned high-tech industrial area around Eindhoven with companies like Philips, ASML and NXP. Brainport also hosts the High Tech Campus, where 5000 industrial researchers from com-panies work together. This stimulating industrial environment enables TU/e to maintain close links with industry, healthcare and the building and logistics sectors.

Applicants are required to have an MSc degree in mathematics or statistics, with a strong back-ground in statistics (in particular estimation procedures, preferably both frequentist and Bayesian approaches), probability theory, stochastic processes, and stochastic optimization. In view of the close collaboration with industrial partners, applicants should have interest in both fundamental and applied research in an industrial context and have the proficiency necessary to implement and test novel computational methodologies in an industrial setting.

• A meaningful job in a dynamic and ambitious university with the possibility to present your work at international conferences.
• A full-time employment for four years, with an intermediate evaluation (go/no-go) after nine months.
• To support you during your PhD and to prepare you for the rest of your career, you will make a Training and Supervision plan and you will have free access to a personal development program for PhD students (PROOF program).
• A gross monthly salary and benefits (such as a pension scheme, pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labor Agreement for Dutch Universities.
• Additionally, an annual holiday allowance of 8% of the yearly salary, plus a year-end allowance of 8.3% of the annual salary.
• Should you come from abroad and comply with certain conditions, you can make use of the so-called '30% facility', which permits you not to pay tax on 30% of your salary.
• A broad package of fringe benefits, including an excellent technical infrastructure, moving expenses, and savings schemes.
• Family-friendly initiatives are in place, such as an international spouse program, and excellent on-campus children day care and sports facilities.