Because pipeline systems represent more than 80% of the total asset value of water-distribution systems, their management is an important issue for water utilities. A pipeline deteriorates over time after installation and, along with the deterioration, pipe bursts can occur as various types, and the choice of a maintenance and repair strategy will depend on the burst types. It is therefore important to forecast the occurrence probability of each burst type. This paper addresses a competing deterioration-hazard model that allows modelling of deterioration by multiple types of failure and focuses on the bursts which occur in the pipe body or connection. The Weibull hazard model is used to address the lifetime of each pipeline, measured from when it was buried, and the model takes into account the competing nature of various types of failure by using a competing hazard model. The competing deterioration-hazard model allows us to determine the probability of deterioration in the pipe body and connection. The model is estimated by Bayesian inference using a Markov chain Monte Carlo method. The applicability of the method to data for an existing pipeline system is examined.