Usage-Specific Survival Modeling Based on Operational Data and Neural
  Networks
Olov Holmer Mattias Krysander Erik Frisk
Accurate predictions of when a component will fail are crucial when planning
maintenance, and by modeling the distribution of these failure times, survival
models have shown to be particularly useful in this context. The presented
methodology is based on conventional neural network-based survival models that
are trained using data that is continuously gathered and stored at specific
times, called snapshots. An important property of this type of training data is
that it can contain more than one snapshot from a specific individual which
results in that standard maximum likelihood training can not be directly
applied since the data is not independent. However, the papers show that if the
data is in a specific format where all snapshot times are the same for all
individuals, called homogeneously sampled, maximum likelihood training can be
applied and produce desirable results. In many cases, the data is not
homogeneously sampled and in this case, it is proposed to resample the data to
make it homogeneously sampled. How densely the dataset is sampled turns out to
be an important parameter; it should be chosen large enough to produce good
results, but this also increases the size of the dataset which makes training
slow. To reduce the number of samples needed during training, the paper also
proposes a technique to, instead of resampling the dataset once before the
training starts, randomly resample the dataset at the start of each epoch
during the training. The proposed methodology is evaluated on both a simulated
dataset and an experimental dataset of starter battery failures. The results
show that if the data is homogeneously sampled the methodology works as
intended and produces accurate survival models. The results also show that
randomly resampling the dataset on each epoch is an effective way to reduce the
size of the training data.