Computer-based advisory systems form with their users composite, human-machine systems. Redundancy and diversity between the human and the machine are often important for the dependability of such systems. We discuss the modelling approach we applied in a case study. The goal is to assess failure probabilities for the analysis of X-ray films for detecting cancer, performed by a person assisted by a computer-based tool. Differently from most approaches to human reliability assessment, we focus on the effects of failure diversity — or correlation — between humans and machines. We illustrate some of the modelling and prediction problems, especially those caused by the presence of the human component. We show two alternative models, with their pros and cons, and illustrate, via numerical examples and analytically, some interesting and non-intuitive answers to questions about reliability assessment and design choices for human-computer systems.