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Equipment degradation is a common phenomenon in engineering applications. Unexpected equipment failures can lead to process downtime and significant cost. Information regarding the health of equipment is often uncertain and based on limited, potentially noisy or corrupted data. Optimising the production and maintenance of technical processes often requires taking these challenging aspects into consideration. To this end, this thesis applies data-driven robust optimization to applications with degrading equipment and develops new methods and tools in the process. As a first step, we consider a variant of the state-task-network with uncertain equipment degradation. We use data-based stochastic process models common in condition-based maintenance to construct uncertainty sets. This allows us to incorporate information from the stochastic models into a process level mixed-integer optimization problem while retaining computational tractability. We apply this framework to several instances of the state-task-network and demonstrate that it can efficiently compromise between equipment availability and cost of maintenance. Next, we extend our approach to an industrial drill scheduling case study. The uncertain degradation in this problem is represented by black-box constraints. We model these uncertain functions using (warped) Gaussian processes, use the models to generate uncertainty sets, and develop new reformulations for the resulting robust optimization problems. Unlike most robust optimization problems, this approach considers uncertain functions, not uncertain parameters. We analyze convexity conditions and propose a custom global optimization strategy for non-convex cases. The approach effectively mitigates uncertainty in the learned degradation curves. Finally, we aim to make the methods developed and robust optimization as a whole more accessible to practitioners. To this end we introduce ROmodel, a Python package that extends the modeling capabilities of the popular modeling language Pyomo to robust optimization problems and automates the reformulation of robust optimization problems. ROmodel allows the definition of custom uncertainty sets using Pyomo constraints, but also contains a library containing commonly used uncertainty sets and our (warped) Gaussian process-based sets. ROmodel implements both robust reformulation and a cutting plane based solver. We demonstrate ROmodel's capabilities by applying it to a number of instances of several case studies.