  This paper presents a new and flexible prognostics framework based on a
higher order hidden semi-Markov model (HOHSMM) for systems or components with
unobservable health states and complex transition dynamics. The HOHSMM extends
the basic hidden Markov model (HMM) by allowing the hidden state to depend on
its more distant history and assuming generally distributed state duration. An
effective Gibbs sampling algorithm is designed for statistical inference of an
HOHSMM. The performance of the proposed HOHSMM sampler is evaluated by
conducting a simulation experiment. We further design a decoding algorithm to
estimate the hidden health states using the learned model. Remaining useful
life (RUL) is predicted using a simulation approach given the decoded hidden
states. The practical utility of the proposed prognostics framework is
demonstrated by a case study on NASA turbofan engines. The results show that
the HOHSMM-based prognostics framework provides good hidden health state
assessment and RUL estimation for complex systems.

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