  [This paper was initially published in PHME conference in 2016, selected for
further publication in International Journal of Prognostics and Health
Management.]
  This paper describes an Autoregressive Partially-hidden Markov model (ARPHMM)
for fault detection and prognostics of equipments based on sensors' data. It is
a particular dynamic Bayesian network that allows to represent the dynamics of
a system by means of a Hidden Markov Model (HMM) and an autoregressive (AR)
process. The Markov chain assumes that the system is switching back and forth
between internal states while the AR process ensures a temporal coherence on
sensor measurements. A sound learning procedure of standard ARHMM based on
maximum likelihood allows to iteratively estimate all parameters
simultaneously. This paper suggests a modification of the learning procedure
considering that one may have prior knowledge about the structure which becomes
partially hidden. The integration of the prior is based on the Theory of
Weighted Distributions which is compatible with the Expectation-Maximization
algorithm in the sense that the convergence properties are still satisfied. We
show how to apply this model to estimate the remaining useful life based on
health indicators. The autoregressive parameters can indeed be used for
prediction while the latent structure can be used to get information about the
degradation level. The interest of the proposed method for prognostics and
health assessment is demonstrated on CMAPSS datasets.
