Reliability Analysis of the Multi-State <i>k</i>-out-of-<i>n</i>: F Systems with Multiple Operation Mechanisms

Abstract

Modern engineering systems are designed and utilized to realize complicated functions, and their operation mechanisms are becoming more complex. Nevertheless, prior related research mainly focused on the reliability evaluations of the systems with a single operation mechanism, which are not appropriate to depict the operation process of systems with multiple operation mechanisms. Faced with the research gaps and practical needs, this paper establishes a new reliability model for the multi-state k-out-of-n: F system composed of n subsystems, which runs under multiple interactive operation mechanisms, including performance sharing, balanced requirement, and protection strategy. The units in each subsystem can share the performance via a common bus, with the purpose of regulating the performance of all equal units. A new triggering criterion of the protection device in each subsystem is proposed based on the total performance of the units. Due to the protection from the device, the degradation rate of the units between two adjacent states decreases to a lower rate. Each subsystem breaks down when the total performance of the units reaches a critical value. According to the number of failed subsystems, the state of the entire system can be divided into multiple states. The Markov process imbedding method combined with the finite Markov chain imbedding approach is developed to obtain the probabilistic indexes of each subsystem and the entire system. The applicability of the proposed model and the effectiveness of the method can be sufficiently demonstrated by illustrative examples and sensitivity analyses.

Keywords

• multi-state <i>k</i>-out-of-<i>n</i>: F system
• multiple operation mechanisms
• reliability analysis
• Markov process imbedding approach
• finite Markov chain imbedding approach