Int J Performability Eng ›› 2015, Vol. 11 ›› Issue (3): 213-228.doi: 10.23940/ijpe.15.3.p213.mag

• Original articles • Previous Articles     Next Articles

A Comparison of Hidden Markov and Semi-Markov Modeling for a Deterioration System subject to Vibration Monitoring

Chen Lin and Viliam Makis   

  1. Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON M5S 3G8, CANADA


We compare a hidden Markov and Erlang semi-Markov modeling of a partially observable deteriorating system operating under a varying load and subject to multi-sensor vibration monitoring. The evolution of the unknown state process is described by a hidden, two state semi-Markov process with an Erlang sojourn time distribution in the healthy state. The unknown model parameters are estimated using the EM algorithm. We derive explicit formulae for the parameter re-estimation in the EM algorithm, which leads to a fast estimation procedure. An optimal Bayesian maintenance policy is developed minimizing the long run expected average cost per unit time and a formula for the mean residual time in the healthy state is derived as a function of the posterior probability statistic. The results show that a simple hidden Erlang model performs better than a hidden Markov model, which is encouraging for considering a more general hidden semi-Markov modeling in future research.

Received on August 29, 2014, revised on November 12, 2014 and February 06, 2015
References: 21