Reliability assessment for coherent systems operating under a generalized mixed shock model with multiple change points of the environment

The operating environment of some industrial systems is complex and may change several times. However, the latest literature about shock models only considered the case that the shock environment may change only one time at most, which cannot accord with the reality of shock environment changing multiple times. To bridge the research gaps, this paper evaluates the reliability of two coherent systems, series-parallel and parallel-series systems, which operate under a generalized mixed shock model with multiple change points. Two distinct shock environments are considered, where the shock impact mechanisms on two coherent systems are completely different. The cases that the system initially runs in environment I or II are both investigated. The shock environment may change multiple times. After one successful shift of the environment, the system continues to run in the other environment. The proposed shock model is a generalization of many existing shock models, and when the parameters of the proposed model take specific values, some previous shock models can be obtained. Reliability indices of two coherent systems are derived by a multi-phase finite Markov chain imbedding approach. An application of target system is presented to demonstrate validity of the proposed model and the effectiveness of the method.