Complex diseases involve both a genetic component and a response to environmental factors or lifestyle changes. Recently, genome-wide association studies (GWAS) have succeeded in identifying hundreds of polymorphisms that are statistically associated with complex diseases. However, the association is usually weak and none of the associated allelic forms is either necessary or sufficient for the disease occurrence. We argue that this promotes a network view, centred on functional redundancy. We adapted reliability theory to the concerned sub-network, modelled as a parallel array of functional modules. In our model, as long as one module remains active, the function correlated with the respective disease is ensured and disease does not occur. Genetic factors reduce the initial number of available modules while environment, contingent surroundings, personal history, epigenetics, and some intrinsic stochasticity influence their persistence time. This model reproduces age-specific incidence curves and explains the influence of environmental changes. It offers a new paradigm, according to which disease occurs due to a lack of functional elements, depending on many idiosyncratic factors. Genetic risk assessed from GWAS is only a statistical notion with no direct interpretation at the individual level. However, genomic profiling could be useful at population level in devising models to guide decisions in health care policy.