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This paper presents a consecutive k$k$‐out‐of‐n$n$: F$F$ balance system in a shock environment, where the state transition of component is induced by external shocks. If a predetermined threshold number of effective shocks are applied to component in a critical state, the component will fail. The state of the system is defined by the number of consecutive failing component groups in the system, which leads to system failure when a critical number of consecutive failing components is reached. To minimize maintenance costs, we propose a preventive maintenance method with an optimization model. We use finite Markov chain imbedding and Phase‐type distribution to calculate component group failure rates and associated probability functions in discrete and continuous time, respectively. The validity and accuracy of the model are confirmed by numerical examples and Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

The balanced system often performs key missions in many fields, such as aerospace, new energy storage, and the military. However, the failure of the system can cause major losses. Therefore, the mission needs to be aborted when the risk of system failure is higher. In this paper, the optimal mission abort policy for a k‐out‐of‐n: F balanced system is studied. The system with a restricted mechanism consists of m sectors and there are n components in each sector, in which the components fail due to two situations: internal failure or external shocks. If the number of working components in m sectors is the same, the system is balanced. If one component fails, the system will force down or resume a component with a probability to keep balance. The model of the mentioned system is established, and the Markov process imbedding approach is used for deriving the reliability indices. Two optimization models are established according to two competitive abort criteria. Finally, an unmanned aerial vehicle performing a mission is discussed to illustrate the proposed mission abort policy. [ABSTRACT FROM AUTHOR]

Cascading failure is a phenomenon that minor disturbances trigger a chain reaction failure of the system, causing the disaster to quickly spread in the system and causing part or all of the system to collapse. Traditional cascading models that based on the assumption that the propagation time of cascading failures can be ignored are inadequate for modeling and analyzing all the practical cascading failure systems. It is necessary to develop a general methodology for the cascading failure systems with cascading failure propagation speed and different load effects. This paper derives new models which extend the load effect mode and consider the propagation speed of cascading failure. In the models, the time of the cascading failure propagation is considered. Three load effect modes are proposed that consider the number of remaining working components, the influence range of the failed parts, and the distance between the failed parts and the unfailed components. Additionally, the reliability of the systems with different types of cascading failures is analyzed, and formulas computing reliability indexes are derived. Numerical examples are provided to demonstrate the application of the proposed methodology. [ABSTRACT FROM AUTHOR]

Based on the extended geometric process, a repair replacement model of a degradation system is studied, in which the delayed repair time depends on the working time after the last repair. Replacement and repair thresholds describe when the system will be replaced and when the system can be repaired, respectively. Two kinds of replacement policies are studied. One policy is jointly determined by the moment of the Nth failure and the first hitting time of the working time after the last repair for the replacement threshold, and the system is replaced, whichever occurs first; the other is the special case of the first policy, and the system is replaced when the working time after the last repair first hits the replacement threshold. The exact expressions of the long-run average cost rate are obtained. The optimal policies exist and can be ascertained by numerical methods. Finally, numerical examples are presented to demonstrate the application of the results obtained in the paper. [ABSTRACT FROM AUTHOR]

In this article, by considering both a limited number of failure replacements and a limited number of random working cycles as warranty terms, a hybrid warranty (HW) is designed from the manufacturer's point of view to warrant the product that does successive projects at random working cycles. The warranty cost produced by HW is derived and analyzed. By defining that HW warrants the product, two types of post-warranty replacement models are investigated from the consumer's point of view to ensure the reliability of the product through HW, i.e., customized post-warranty replacement and uniform post-warranty replacement. Depreciation expense is integrated into each post-warranty replacement. The expected cost rate model is presented for each post-warranty replacement and some special cases are obtained by setting parameters in the expected cost rate. Finally, sensitivities on both HW and post-warranty replacements are analyzed in numerical experiments. It is shown that when a limited number of failure replacements or/and a limited number of random working cycles are introduced to a warranty, the warranty cost can be reduced; and the performance of the uniform post-warranty replacement is superior to the customized post-warranty replacement. [ABSTRACT FROM AUTHOR]

We study a model of a two-stage degradation process in a dynamic environment. The two stages, the normal stage and the defective stage, are separated by the first hitting time of the alarm threshold by the degradation level. Wiener processes with piecewise linear drift are used in each stage to describe the degradation level in a dynamic environment. System failure is triggered in two ways: the system degradation level reaches the defect-based failure threshold; the duration in the defective stage is larger than the duration-based failure threshold. Explicit expressions for the system reliability for different duration-based failure thresholds are obtained. These include when the duration-based failure threshold is zero, when it is a positive constant and when it tends to infinity. A simulation procedure is described for the case in which the duration-based failure threshold is a random variable. Finally, some numerical examples are presented to illustrate the proposed reliability assessment method. The modelling method and the results can be used for reliability evaluation, residual life prediction and maintenance decision optimization of a system with two-stage degradation in a dynamic environment. [ABSTRACT FROM AUTHOR]

This paper develops reliability and maintenance models for a single‐unit system subject to hard failures under random environment of external shocks. Motivated by the observations of shot‐noise process in practice, the impact of shock damage on system failure behavior is characterized by random hazard rate increments. To remove such negative impact, imperfect preventive repair is performed periodically, and preventive replacement is performed after several repairs. Considering the joint effects of both random shocks and imperfect repair on the system hazard rate, we derive recursive equations for the system reliability function. Furthermore, we investigate the optimal maintenance policy that minimizes the expected cost per unit time of the system. The applicability of the reliability and maintenance model is validated by a case study on a wind turbine system. [ABSTRACT FROM AUTHOR]

This article studies the asymptotic behavior of a stochastic Chemostat model with Lotka–Volterra food chain in which the dilution rate was influenced by white noise. The long-time behavior of the model is studied. Using Lyapunov function and Itô's formula, we show that there is a unique positive solution to the system. Moreover, the sufficient conditions for some population dynamical properties including the boundedness in mean and the stochastically asymptotic stability of the washout equilibrium were obtained. Furthermore, we show how the solutions spiral around the predator-free equilibrium and the positive equilibrium of deterministic system. Besides, the existence of the stationary distribution is proved for the considered model. Numerical simulations are introduced finally to support the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a simple chemostat model with inhibitory exponential substrate uptake and a time delay. A detailed qualitative analysis about existence and boundedness of its solutions and the local asymptotic stability of its equilibria are carried out. Using Lyapunov-LaSalle invariance principle, we show that the washout equilibrium is global asymptotic stability for any time delay. Using the fluctuation lemma, the sufficient condition of the global asymptotic stability of the positive equilibrium is obtained. Numerical simulations are also performed to illustrate the results. [ABSTRACT FROM AUTHOR]