A Multi-state Markov Model to Infer the Latent Deterioration Process From the Maintenance Effect on Reliability Engineering of Ships

Maintenance optimization of naval ship equipment is crucial in terms of national defense. However, the mixed effect of the maintenance and the pure deterioration processes in the observed data hinders an exact comparison between candidate maintenance policies. That is, the observed data-annual failure counts of naval ships reflect counteracting actions between the maintenance and deterioration. The inference of the latent deteriorating process is needed in advance for choosing an optimal maintenance policy to be carried out. This study proposes a new framework for the separation of the true deterioration effect by predicting it from the current maintenance effect through the multi-state Markov model. Using an annual engine failure count of 99 ships in the Korean navy, we construct the framework consisting of imputation, transition matrix design, optimization, and validation. The hierarchical Gaussian process model is used for the imputation and the three-state Markov model is applied for the estimation of parameters in the deterioration and maintenance effect. To consider the natural (deterioration) and artificial (maintenance) effect respectively, the Bayesian HMM model with a categorical distribution is employed. Computational experiments under multiple settings showed the robustness of the estimated parameters, as well as an accurate recovery of the observed data, thereby confirming the credibility of our model. The framework could further be employed to establish a reliable maintenance system and to reduce an overall maintenance cost.