The Birnbaum-Saunders distribution is a useful model for describing fatigue and reliability data. This model allows us to relate the total time until the failure to some type of cumulative damage. The majority of the models based on the Birnbaum-Saunders distribution have assumed fixed-effects, and a few have been investigated for correlated data. In this work, we introduce Birnbaum-Saunders mixed models for censored data. Specifically, we estimate their parameters by means of the Gauss-Hermite quadrature approximation, carry out a residual analysis for these models, and conduct an application using real censored reliability data. This application illustrates the utility of a Birnbaum-Saunders random intercept model.