Reliability assessment for a generalized k-out-of-n: F system under a mixed shock model with multiple sources

It is inevitable for the engineering systems subject to the damages resulted from random shocks and different parts of the systems may suffer the shocks from different sources due to their inherent differences or diverse functions. Nevertheless, the existing research has not delved into the operation process of a complex system with heterogeneous components impacted by the shocks from multiple sources and the case that components in different types are subject to the shocks from various sources. To fill the gaps in current research, this paper investigates the reliability of a generalized k-out-of-n: F system with heterogeneous components under a mixed shock model with multiple sources. A shock impact vector is defined to represent the situation that different types of components in the system can be affected by the shocks from disparate shock sources. For each type of components, they may fail due to the shocks from diverse sources with corresponding failure mechanisms where the mixed shock models combining cumulative, run and extreme criteria are proposed. Moreover, the breakdown of the entire system is caused by the total number or the sparsely successive number of the failed components reaching a critical value. This study combines finite Markov chain imbedding method and phase-type distribution to derive the reliability indicators for each type of components and the entire system both in discrete shock length and continuous time. Numerical examples are provided to prove the applicability of the proposed model and the validity of the methodology.