1-out-of-N multi-state standby systems with state-dependent random replacement times

Abstract

Research on analysis of replacement time in standby systems has focused on systems with binary-state standby components. However, when the standby components are multi-state, the replacement time depends on the state of the standby component when it is activated for replacement. This article considers the impacts of state-dependent random replacement times on 1-out-of-N systems consisting of multi-state standby components. Numerical algorithms for evaluating the multi-state standby system's instantaneous availability, expected availability over system mission time and the expected mission completion time are proposed. A Markov state transition model is used to describe the component behaviour in standby mode. The time-to-failure of the operating component and the replacement time of the standby component can obey arbitrary types of distributions. Illustrative examples are provided to demonstrate the proposed numerical algorithms. The effects of the number of standby components, different replacement time distributions and activation sequences are also discussed.

Optimization of Multilayer Standby Mechanisms in Continuous Chemical Processes

“…Yun and Cha 21 analyzed the effects of switching time to the availability of a two-component warm standby system based on three different switch models. Levitin et al 22 incorporated random replacement times into the design of 1-out-of-N warm standby systems. Zhong and Jin 23 used semi-Markov theory to analyze cold standby availability using a preventive maintenance policy.…”

Reliability analysis of standby systems with multi‐state elements subject to constant transition rates

“…Furthermore, the case with the optimal activation sequence for maximizing the reliability of heterogeneous standby systems is provided in this paper. We also assume here that elements in both standby and operation modes can be multi‐state, whereas in the previous model only binary‐state operating elements were considered. Moreover, Levitin et al focused on state‐dependent random replacement times while this paper considers multi‐state elements subject to constant transition rates.…”

“…We also assume here that elements in both standby and operation modes can be multi‐state, whereas in the previous model only binary‐state operating elements were considered. Moreover, Levitin et al focused on state‐dependent random replacement times while this paper considers multi‐state elements subject to constant transition rates. The iterative methods for reliability assessment of standby systems with different characteristics utilized in Levitin et al have been developed with specific numerical procedures to efficiently analyze the considered standby systems.…”

“…Moreover, Levitin et al 33 focused on state-dependent random replacement times while this paper considers multi-state elements subject to constant transition rates. The iterative methods for reliability assessment of standby systems with different characteristics utilized in Levitin et al 31,33 have been developed with specific numerical procedures to efficiently analyze the considered standby systems. This paper makes contributions by considering standby systems consisting of multi-state elements with absorbing states to represent total failure of the element, which can be represented by Markov state transition diagrams.…”