We propose a method of diagnosis that tackles multiple diagnoses of reliable devices with large numbers of components. We use prior component failure probability and compute posterior probabilities of diagnoses. Bayesian networks allow to take into account the structure of the device but also knowledge about good and bad working order of each individual components and their reliability. The general reliability of such systems means that no list of breakdown scenarios can be exploited to guide the diagnosis. We exploit a list of observed values that reveal a failure of the system in order to find the states of the system that best explain these observations. The large number of components and the possibility of multiple failures mean that lots of sets of failing components can explain the observations. In order to rank them, we propose an algorithm to compute the best diagnoses and an approximation of their posterior probabilities.