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E-health systems can be used to monitor people in real-time, offering a range of multimedia-based health services, at the same time reducing the cost since cheaper devices can be used to compose it. However, any downtime, mainly in the case of critical health services, can result in patient health problems and in the worst case, loss of life. In this paper, we use an interdisciplinary approach combining stochastic models with optimisation algorithms to analyse how failures impact e-health monitoring system availability. We propose surrogate models to estimate the availability of e-health monitoring systems that rely on edge, fog, and cloud infrastructures. Then, we apply a multi-objective optimisation algorithm, NSGA-II, to improve system availability considering component costs as constraint. Results suggest that replacing components with more reliable ones is more effective in improving the availability of an e …