  Predicting the remaining useful life (RUL) of ball bearings plays an
important role in predictive maintenance. A common definition of the RUL is the
time until a bearing is no longer functional, which we denote as an event, and
many data-driven methods have been proposed to predict the RUL. However, few
studies have addressed the problem of censored data, where this event of
interest is not observed, and simply ignoring these observations can lead to an
overestimation of the failure risk. In this paper, we propose a probabilistic
estimation of RUL using survival analysis that supports censored data. First,
we analyze sensor readings from ball bearings in the frequency domain and
annotate when a bearing starts to deteriorate by calculating the
Kullback-Leibler (KL) divergence between the probability density function (PDF)
of the current process and a reference PDF. Second, we train several survival
models on the annotated bearing dataset, capable of predicting the RUL over a
finite time horizon using the survival function. This function is guaranteed to
be strictly monotonically decreasing and is an intuitive estimation of the
remaining lifetime. We demonstrate our approach in the XJTU-SY dataset using
cross-validation and find that Random Survival Forests consistently outperforms
both non-neural networks and neural networks in terms of the mean absolute
error (MAE). Our work encourages the inclusion of censored data in predictive
maintenance models and highlights the unique advantages that survival analysis
offers when it comes to probabilistic RUL estimation and early fault detection.
