Abstract
Multistate reliability has received significant attention over the past decades, particularly its application to mechanical devices that degrade over time. This degradation can be represented by a multistate continuous-time stochastic process. This article considers a device with discrete multistate degradation, which is monitored by a condition monitoring indicator through an observation process. A general stochastic process called the nonhomogeneous continuous-time hidden semi-Markov process is employed to model the degradation and observation processes associated with this type of device. Then, supervised parametric and nonparametric estimation methods are developed to estimate the maximum likelihood estimators of the main characteristics of the model. Finally, the correctness and empirical consistency of the estimators are evaluated using a simulation-based numerical experiment.
