The prediction of pipe failures in water distribution systems is an essential planning tool for water companies. Previous methods focus on the prediction of either future failure numbers or aspects of pipe condition. However, most of these only predict at the level of large pipe groups (of similar characteristics) and often cannot provide uncertainty bounds. Here, a new statistical method is developed to predict the probability of failure at the single pipe level. The method extends the Non-Homogeneous Poisson Process (NHPP) in two ways: firstly, it incorporates pipe-specific random effects to account for unmeasured information on the factors affecting the pipe failures. Secondly, the method explicitly accounts for zero inflation, that is the possibility that more zero failures occur than expected from a simple Poisson assumption. This zero-inflated NHPP (ZINHPP) model was applied to two real-life datasets, one from North America and one from New Zealand. The results clearly demonstrate improved prediction capability, especially in the New Zealand data, which contain a much larger percentage of pipes with zero failures.