  We show how Markov mixed membership models (MMMM) can be used to predict the
degradation of assets. We model the degradation path of individual assets, to
predict overall failure rates. Instead of a separate distribution for each
hidden state, we use hierarchical mixtures of distributions in the exponential
family. In our approach the observation distribution of the states is a finite
mixture distribution of a small set of (simpler) distributions shared across
all states. Using tied-mixture observation distributions offers several
advantages. The mixtures act as a regularization for typically very sparse
problems, and they reduce the computational effort for the learning algorithm
since there are fewer distributions to be found. Using shared mixtures enables
sharing of statistical strength between the Markov states and thus transfer
learning. We determine for individual assets the trade-off between the risk of
failure and extended operating hours by combining a MMMM with a partially
observable Markov decision process (POMDP) to dynamically optimize the policy
for when and how to maintain the asset.
