Reliability Analysis of Systems with n-Stage Shock Process and m-Stage Degradation

As two major types of damage, natural degradation and random shocks usually emerge in a system simultaneously and may exhibit some complex dependencies. An interesting and not negligible phenomenon is that systems at different health levels have differing resistance to these two damage processes. This study presents a multistate model to capture the main characteristics of a system with dependencies of both damage processes on the current damage level. In the case of multistage damage-level dependencies, the proposed model can be seen as an extension of existing multistage models, i.e., a composite model of n-stage shock process and m-stage degradation. The reliability and probability of system states at time t are derived under the framework of the Markov renewal process. We also use a Monte Carlo simulation to mimic the system lifespan and improve the multistate model. Finally, a study case of microelectromechanical systems is provided to demonstrate the application of the proposed methodology.