Reliability Model of Consecutive $(2, k)$ -Out-of-( $2, n$ ) :F Systems With Local Load-Sharing

Most previous reliability models of consecutive k-out-of-n system assume that the components are independent or their reliabilities are equal. The system reliability can be obtained according to the configuration of <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> consecutive failed components. However, for consecutive <inline-formula> <tex-math notation="LaTeX">$(2,k)$ </tex-math></inline-formula>-out-of-<inline-formula> <tex-math notation="LaTeX">$(2,n)$ </tex-math></inline-formula> systems with local load-sharing, workloads on failed components will be equally shared by both vertically and horizontally adjacent components. Consequently, the component failure probability density function (FPDF) may be unequal and dependent on the actual load (both original and sharing load), which is determined by the states of adjacent components. Furthermore, the component FPDF may be time-varying with the failure sequences of adjacent components. Therefore, reliability modeling must consider the component dynamic process determined by the failure sequences of adjacent components, instead of the static configuration determined by failure states of adjacent components in the traditional models. To solve the above issues, this paper develops a new reliability model for consecutive <inline-formula> <tex-math notation="LaTeX">$(2,k)$ </tex-math></inline-formula>-out-of-<inline-formula> <tex-math notation="LaTeX">$(2,n)$ </tex-math></inline-formula> systems with local load-sharing. The system and component dynamic processes are automatically searched and combined into a set of state transition paths. In each path, the component load-varying process can be confirmed, by considering the influence of adjacent failures on its shared load. Based on the state transition paths, the component and system reliability models are further derived, according to the confirmed load processes of each component. Finally, we present graphical illustrations of the reliability evaluation of cable-strut systems in long-span suspension bridges.

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