A Hidden Semi‐Markov Model with Duration‐Dependent State Transition Probabilities for Prognostics

Realistic prognostic tools are essential for effective condition‐based maintenance systems. In this paper, a Duration‐Dependent Hidden Semi‐Markov Model (DD‐HSMM) is proposed, which overcomes the shortcomings of traditional Hidden Markov Models (HMM), including the Hidden Semi‐Markov Model (HSMM): (1) it allows explicit modeling of state transition probabilities between the states; (2) it relaxes observations’ independence assumption by accommodating a connection between consecutive observations; and (3) it does not follow the unrealistic Markov chain’s memoryless assumption and therefore it provides a more powerful modeling and analysis capability for real world problems. To facilitate the computation of the proposed DD‐HSMM methodology, new forward‐backward algorithm is developed. The demonstration and evaluation of the proposed methodology is carried out through a case study. The experimental results show that the DD‐HSMM methodology is effective for equipment health monitoring and management.