Reliability Analysis and Maintenance Optimization using Hidden Markov Models (HMM). The use of HMMs to model the state of a system which is not directly observable and instead certain indicators (signals) of the true situation are provided via a control system. A hidden model can provide key information about the system dependability, such as the reliability of the system and related measures. An estimation procedure is implemented based on the Baum-Welch algorithm. Classical structures such as K-out-of-N systems and Shock models are illustrated. Finally, the maintenance of the system is considered in the HMM context and two functions for new preventive maintenance strategies are considered. Maintenance efficiency is measured in terms of expected cost. Methods are described in Gamiz, Limnios, and Segovia-Garcia (2023) <doi:10.1016/j.ejor.2022.05.006>.

Solves Hidden Markov Models (HMMs) via matrix and tensor
    decomposition. Converts observation sequences to co-occurrence
    matrices/tensors and applies Symmetric Non-negative Matrix
    Factorization (symNMF), Singular Value Decomposition (SVD),
    CANDECOMP/PARAFAC (CP) decomposition, or Tensor-Train (TT)
    decomposition to recover HMM parameters.
    Also provides standard HMM algorithms (Forward, Backward, Viterbi,
    Baum-Welch) for comparison.
    The spectral learning approach for HMMs is based on
    Hsu, Kakade, and Zhang (2012) <doi:10.1016/j.jcss.2011.12.025>.
    The symNMF method is described in
    Kuang, Yun, and Park (2015) <doi:10.1007/s10898-014-0247-2>.
    The Tensor-Train decomposition is described in
    Oseledets (2011) <doi:10.1137/090752286>.

Fitting hidden Markov models using automatic differentiation 
  and Laplace approximation, allowing for fast inference and flexible covariate
  effects (including random effects and smoothing splines) on model parameters.
  The package is described by Michelot (2025) <doi:10.18637/jss.v114.i05>.

Statistical analysis of static chamber concentration data for trace gas flux estimation.