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Model-based diagnosis concerns using a model of the structure and behaviour of a system or device in order to establish why the system or device is malfunctioning. Traditionally, little attention has been given to the problem of dealing with uncertainty in model-based diagnosis. Given the fact that determining a diagnosis for a problem almost always involves uncertainty, this situation is not entirely satisfactory. This paper builds upon and extends previous work in model-based diagnosis by supplementing the well-known model-based framework with mathematically sound ways for dealing with uncertainty. The resulting method integrates logical reasoning with probabilistic reasoning, and reasoning about the structure and behaviour of a system with reasoning by taking stochastic independence assumptions into account.