A reliability model for load-sharing K-out-of-N systems subject to soft and hard failures with dependent workload and shock effects

A component in a k-out-of-n system may experience soft and hard failures resulting from exposure to natural degradation and random shocks. Due to load-sharing characteristics, once a component fails, the surviving components share an increased workload, which increases their own degradation rates. Moreover, under the larger workload, random shocks may cause larger abrupt degradation increments and larger shock sizes. Therefore, the system experiences the dependent workload and shock effects (DWSEs). Such dependence will cause the load-sharing system to fail more easily, though it is often not considered in existing methods. In this paper, to evaluate the system reliability more accurately, we develop a novel reliability model for load-sharing k-out-of-n systems with DWSEs. In the model, the joint probability density function of shock effects to soft and hard failures is developed to describe the DWSEs on a component. To derive an analytical expression of system reliability with load-sharing characteristics and DWSEs, conditional probability density function is used to model the random component failure times. A load-sharing MicroElectro-Mechanical System (MEMS) is then utilized to illustrate the effectiveness of the reliability model.