Mixed shock model for multi-state weighted k-out-of-n: F systems with degraded resistance against shocks

In previous studies of shock models, the probability of shocks causing damage to the system during operation is always constant. However, it is more practical for the system to become more vulnerable to shocks under a severe condition and the probabilities of subsequent shocks causing damage to the system increase. Furthermore, few studies have focused on the shock environment of weighted k-out-of-n: F systems. To fill these research gaps, this paper proposes a novel mixed shock model for a multi-state weighted k-out-of-n: F system with a consideration of its resistance against shocks. The components in the system operate in a two-stage process and different weights are taken for their different states. The system has multiple states determined by the total system weight/performance. System failure results from the competing failure criteria of insufficient system weight/performance and from reaching the critical number of failed components. A combination of finite Markov chain imbedding approach, universal generating function technique and phase-type distribution is adopted to analyze the probabilistic indices of the components and entire system. Numerical illustrations based on a power-generating plant are presented to demonstrate the applicability of new shock model and the effectiveness of proposed method.