Reliability analysis of multi-state systems with lag-dependent components

Abstract

In a multi-state system (MSS) with dependent components, the performance distributions of low priority components (LPCs) depend on the states of high priority components (HPCs). However, the relationship between LPCs and HPCs is usually considered as the instantaneous dependency (instant-dependency). In practice, the dependency between them is lagging due to the electronic circuits, i.e, the performance distributions of LPCs would be changed after a certain transmission time when one state of HPCs transfers to another. In this paper, the lag-dependency between LPCs and HPCs in a MSS is considered. At the beginning of transfer of each state for HPCs, three kinds of lag threshold values are set to quantify the transmission time from HPCs to corresponding LPCs. Due to the lag-dependency, the sojourn time and probabilities of states of HPCs are reanalyzed. As an important method of reliability analysis, the universal generating function is utilized to analyze the reliability of a MSS with lag-dependent components. The effectiveness of the proposed methods is proved via a comparative analysis of MSSs with instant-dependent components and lag-dependent components. The results show that the reliability of MSS would be underestimated if the lag-dependency is not considered.