Models are of great interest in many fields of engineering as they enable prediction of a systems behaviour, given an initial mode of the system. However, in the field of model-based diagnosis the models are used in a reverse manner, as they are combined with the observations of the systems behaviour in order to estimate the system mode. This thesis describes computation of diagnostic systems based on models implemented in Dymola. Dymola is a program that uses the language Modelica. The Dymola models are translated to Matlab, where an application called Fault Diagnosis Toolbox, FDT is applied. The FDT has functionality for pinpointing minimal overdetermined sets of equations, MSOs, which is developed further in this thesis. It is shown that the implemented algorithm has exponential time complexity with regards to what level the system is overdetermined,also known as the degree of redundancy. The MSOs are used to generate residuals, which are functions that are equal to zero given that the system is fault-free. Residual generation in Dymola is added to the original methods of the FDT andthe results of the Dymola methods are compared to the original FDT methods, when given identical data. Based on these tests it is concluded that adding the Dymola methods to the FDT results in higher accuracy, as well as a new way tocompute optimal observer gain. The FDT methods are applied to 2 models, one model is based on a system ofJAS 39 Gripen; SECS, which stands for Secondary Enviromental Control System. Also, applications are made on a simpler model; a Two Tank System. It is validated that the computational properties of the developed methods in Dymolaand Matlab differs and that it therefore exists benefits of adding the Dymola implementations to the current FDT methods. Furthermore, the investigation of the potential isolability based on the current setup of sensors in SECS shows that full isolability is achievable by adding 2 mass flow sensors, and that the isolability is not limited by causality constraints. One of the found MSOs is solvable in Dymola when given data from a fault-free simulation. However, if the simulation is not fault-free, the same MSO results in a singular equation system. By utilizing MSOs that had no reaction to any modelled faults, certain non-monitored faults is isolated from the monitored ones and therefore the risk of false alarms is reduced. Some residuals are generated as observers, and a new method for constructing observers is found during the thesis by using Lannerheds theorem in combination with Pontryagin’s Minimum Priniple. This method enables evaluation of observer based residuals in Dymola without any selection of a specific operating point, as well as evaluation of observers based on high-index Differential Algebraic Equations, DAEs. The method also results in completely different behaviourof the estimation error compared to the method that is already implemented inthe FDT. For example, one of the new observer-implementations achieves both an estimation error that converges faster towards zero when no faults are implementedin the monitored system, and a sharper reaction to implemented faults.