A stochastic time scale based framework for system reliability under a Markovian dynamic environment

Most engineering systems operate under stochastic dynamic environments. The variability and stochasticity of environmental conditions have a non-negligible impact on the failure behavior of engineering systems. This article develops a reliability modeling and assessment framework for systems operating under a Markovian dynamic environment. The stochastic dynamic environment is characterized by a continuous-time Markov chain. Using the cumulative exposure principle, the stochastic time scale, resulting from the cumulative effect of the Markovian dynamic environment, is computed via a Markov reward model. Based on the above settings, the system reliability model under the Markovian dynamic environment is developed. The maximum likelihood estimates and confidence intervals for the model parameters, including the transition rate matrix of the Markov chain, the reward rates of the Markov reward model, and the parameters of the baseline lifetime distribution, are obtained by utilizing the collected environment and lifetime data. The system reliability is then assessed with the estimated parameters. The effectiveness of the proposed framework are validated using simulation and through an application to a long-term storage system. The results show that the unknown reliability model parameters can be accurately estimated, and the proposed model with the consideration of the cumulative effect of the Markovian dynamic environment can provide a more accurate reliability estimate than that without such a consideration.