Predictive analytics using a nonhomogeneous semi-Markov model and inspection data

Predicting the remaining useful life plays an important role in minimizing the overall maintenance cost of mechanical systems. Although most conventional reliability models deal with binary systems to perform such predictions, in most practical cases, mechanical systems experience multiple levels of degradation states before failure. When the degradation level associated with such a multistate deteriorating process is monitored only at fixed inspection points, extracted monitoring data are interval-censored. Interval censoring can influence both the parameter estimation (model training) and the calculation of principal reliability measures. This article studies the problem of parameter estimation and the development of principal prognostic-based reliability measures, including reliability function and mean residual life, for a multistate device under limited inspection capacity. The correctness of the introduced models is demonstrated through simulation-based numerical experiments. Finally, an example of the wear process of the shell of a bearing is used to demonstrate the application of the proposed models.