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Discrete repairable degradation systems can be modeled by a homogeneous discrete-time second-order semi-Markov chain with finite state space for theoretical and practical sake. In the present paper, the state space can be divided into three subclasses, namely excellent states, good states (middle states) and failure states. The transitions among states may be driven by degradations and inside shocks of the system, repair actions, self-healings, energy supplement and other recovery ways. The Z-transform is used to give distributions for some interesting problems such as distributions of an I-period (oscillation & working time) and a gap between I-periods, and instantaneous and steady availabilities of the system. Finally, some numerical examples are given to illustrate the results obtained in the paper. The work may be used in reliability and maintenance analysis of discrete time repairable systems. [ABSTRACT FROM AUTHOR]

Multi-state system models are more practical and valuable when describing complex engineering structures than binary-state system models. Modelling of linear consecutive- (k , l) -out-of- n : F systems with shared components under non-homogeneous Markov dependence is discussed in this work. The proposed model is an extension of both "consecutive- k -out-of- n : F system" and "consecutive- k -out-of- n : F system with shared components between adjacent subsystems". All the components in the system are assumed to have three states and are non-homogeneous Markov-dependent. Using the method of sum of disjoint products (SDP), the system reliability formula is derived by summing the reliability values for all disjoint cases. The well-known finite Markov chain imbedding approach (FMCIA) is used for deriving the reliability formula for each disjoint case. For the special cases of systems with homogeneous Markov-dependent or independent components, the corresponding results are deduced. Finally, some numerical examples are presented to illustrate all the results developed here. • Consecutive-(k,l)-out-of-n: F systems with shared components are modelled. • Using the method of SDP and FMCIA, the system reliability formula is derived. • The method is also fit for homogeneous Markov-dependent or independent cases. • Numerical examples demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Reliability analysis of balanced system has become a key factor for the safe operation of some important equipment and the perfect completion of some important missions. As some real systems consisting of several subsystems with different levels of performance and under degradation processes when in operations are relatively common, they have received widely concerned in the recent years, but are rarely in the new reliability research field of balanced systems, the researches on the balanced systems by considering multi-state are rare, and even few researches are in combination with degradation processes. In this paper, a new balanced system for the multi-state system under degradation processes by considering new failure criteria is put forth. The system consists of two subsystems and fails when either subsystem enters into absorbing states, a new model is proposed and applied to two special cases by assuming that the thresholds of the sojourn time in upcoming unbalanced subsets are constant and random variables respectively, and this paper is the first to extend balanced systems into competing risks. The related expressions of the reliability indexes are derived by employing the theory of aggregated stochastic processes. Finally, numerical examples are presented and some future research topics are also discussed. [ABSTRACT FROM AUTHOR]

• Two Markov renewal shock models with multiple failure mechanisms are developed. • The reliability indexes for systems under two proposed models are analyzed. • Limiting behavior of mean time to failure of system under two models is discussed. In this article, two Markov renewal shock models with multiple failure mechanisms are developed based on the extreme shock model and cumulative shock model respectively. The shock size and interarrival time dependency is studied by assuming the sizes and interarrival times of shocks are governed by an absorbing Markov chain with finite state space. Under the competing risk extreme shock model, the system fails when a single shock of a large size occurs or when it enters the absorbing state whichever occurs first. Under the competing risk cumulative shock model, the system fails when it transfers to the absorbing state, or when the accumulation of sizes of the previous shocks exceeds a prespecified critical level, whichever occurs first. The methods to calculate the reliability functions and other reliability indexes under the proposed two Markov renewal shock models are provided. A special case that the shock arrival process is independent of the current state of the system is considered. The limiting behavior of the mean time to failure of the system under two models is discussed. Finally, a study case of lithium-ion battery systems is conducted to illustrate the proposed models and obtained results. [ABSTRACT FROM AUTHOR]

• A competing risk model with restriction on transition times is developed. • Some reliability indexes of the proposed semi-Markov system are given. • A nonlinear integer programming with corresponding solution algorithm is presented. In this paper, a competing risk model with a restriction on transition times for semi-Markov multi-state repairable systems is proposed. The states of semi-Markov systems can be divided into three categories: a normal working subset, a defective working subset and a breakdown subset which contains an absorbing state where the system cannot escape once entering it. If the number of transitions between the normal and defective working subsets exceeds a given value, the system will be abandoned due to the high maintenance costs. The theory of aggregated stochastic process is employed to obtain the closed-form formulas of the probabilities of competing risks, distributions of survival times and point-wise availabilities. An integer nonlinear programming is presented which enables the system to satisfy the prescribed performance requirements and control its economic cost. A corresponding algorithm for solving the integer nonlinear programming is provided to find the optimal number of transition times. Two numerical examples including Markov process and semi-Markov process are conducted to illustrate the obtained results and proposed methods finally. [ABSTRACT FROM AUTHOR]

Motivated by many networked computing systems used in data centers, Grid or Cloud computing infrastructures, and spatially distributed wireless sensor networks configured in aerospace and military industries, this paper considers a multi-state series-parallel system where n heterogeneous components can possess multiple states with different performance rates. Performability is concerned with the probability of such a system performing at a cumulative system performance W characterized in terms of the minimum of all cumulative subsystem performance G j (1 ≤  j  ≤  m ), G j is the sum of the performance rates of components belonging to the j th subsystem. This paper proposes a multi-valued decision diagram (MDD)-based approach to model and evaluate the concerned performability. A single compact MDD model is constructed by sharing all isomorphic model structures involved in different cumulative system performance. The MDD model can be reused when different versions of component state probability distributions are evaluated, thus it can facilitate solutions to further problems that require executing numerous iterations of performability evaluations, for example, the redundancy and/or reliability optimization problems. [ABSTRACT FROM AUTHOR]

A multi-state linear consecutive- k -out-of- n : F system, MLC( k,n ) consists of n components ordered in a line, which fails if at least k consecutive components have failed. It abounds in real-world applications such as wireless sensor networks, microwave station networks, and oil pipeline systems. Performability of an MLC( k,n ) system is concerned with probability that the system performs at a performance state characterized in terms of the largest number of consecutive failed components. This paper proposes a multi-valued decision diagram (MDD)-based approach to model and evaluate performability of an MLC( k,n ) system with heterogeneous components following arbitrary lifetime distributions. The proposed approach encompasses a novel and efficient MDD model generation procedure. Both complexity analysis and illustrative examples are provided to show efficiency of the proposed MDD approach. As demonstrated through examples, the proposed MDD approach is also applicable to MLC( k,n ) systems with non-identical reparable components and component importance analysis. [ABSTRACT FROM AUTHOR]