Maintenance optimization for a multi-stage system characterized by multiple mechanisms

As an excellent tool for reliability system research, the finite Markov chain imbedding (FMCI) approach can be used not only to evaluate the system reliability, but also to do other research in reliability systems such as generating functions, waiting time, and optimal arrangement problems. But the computation for system reliability based on the FMCI approach becomes difficult if the number of components in the system is comparatively large, because there would be more matrices that need to be multiplied. To overcome this drawback, the accelerated scan finite Markov chain imbedding (AS-FMCI) approaches with fixed step length, and alterable step, are introduced in this paper to decrease the complexity of computation for system reliability through decreasing the number of the matrixes that need to be multiplied. A numerical example is presented, and the results show that the new method can save computational time.

Most studies on k-out-of-n systems are in the binary context. The k-out-of-n system has failed if and only if at least k components have failed. The generalised multi-state k-out-of-n: G and F system models are defined by Huang et al. [Huang, J., Zuo, M.J., and Wu, Y.H. (2000), ‘Generalized Multi-state k-out-of-n: G Systems’, IEEE Transactions on reliability, 49, 105–111] and Zuo and Tian [Zuo, M.J., and Tian, Z.G. (2006), ‘Performance Evaluation of Generalized Multi-state k-out-of-n Systems’, IEEE Transactions on Reliability, 55, 319–327], respectively. In this article, by using the finite Markov chain imbedding (FMCI) approach, we present a unified formula with the product of matrices for evaluating the system state distribution for generalised multi-state k-out-of-n: F systems which include the decreasing multi-state F system, the increasing multi-state F system and the non-monotonic multi-state F system. Our results can be extended to the generalised multi-state k-out-of-n: G system. Three numerical examples are presented to illustrate the results.

Based on some real backgrounds, a new balanced system structure, a consecutive k-out-of- m: F system with a symmetry line, is proposed in this paper. Considering different state numbers of a subsector, the new balanced system is analyzed under two situations respectively: the subsector with binary-state and the subsector with multi-state, while the multi-state balanced systems have not been studied in the previous research. Besides, two models are developed in terms of assumptions for the two situations, respectively. For this system, several methods, such as the finite Markov chain imbedding approach, the order statistics technique and the phase-type distributions, are used on the models. In addition to system reliability formulas, the means and variances of the system lifetimes under two models for different situations are given. Finally, numerical examples are presented to illustrate the results obtained in this paper.

In this article, a performance sharing system with transmission loss and a shock operation environment is studied. Such systems are widely found in power distribution systems, distributed computing systems, data transmission systems, communication systems, and so on. The system consists of n components and each of them works to satisfy its demand and shares its performance surplus with others through a common bus. When the system operates, it may suffer a variety of stresses from its operating environment, which can be regarded as random external shocks, and the transmission loss is also wildly seen in engineering systems. Therefore, the random shocks and transmission loss are considered in this article. The performance level of a component is affected by three types of random external shocks – invalid shocks, valid shocks and extreme shocks. The system fails if at least one component cannot satisfy its demand. A finite Markov chain imbedding approach and phase-type distributions are used to estimate the performance level for each component and the universal generating function technique is applied to analyze system reliability. Analysis of a power distribution system is given to show the application of the model under study and the effectiveness of the proposed method.

Mixed shock model for multi-state weighted k-out-of-n: F systems with degraded resistance against shocks

Reliability assessment for a k-out-of-n: F system supported by a multi-state protective device in a shock environment

This paper presents an integrated inspection and failure model of equipment for asset management. The model combines both repairable and aging failure modes with maintenance activities. Based on this model, an optimization approach for determining equipment inspection interval is proposed. The proposed approach can optimize the inspection interval by minimizing the total cost including maintenance, failure loss, repair, replacement, and patrol costs. The proposed method is applied to a mixed set of equipment consisting of breakers and transformers in two regions. The results indicate that the optimal inspection interval for each region can be effectively obtained using the proposed method. Equipment aging failures have significant impacts on the optimal inspection interval. The optimal inspection interval gradually becomes shorter over years due to the equipment aging process. The optimal inspection interval is different for different regions depending on the equipment aging status and other factors in each region. Therefore, it is recommended to have a region-specific inspection strategy for each area.

1 - Analysis for a qualification test procedure with FMCIA (finite Markov chain imbedding approach)

Reliability modelling for linear and circular [formula omitted]-out-of-[formula omitted]: F systems with shared components

The reliability of various systems under shock models has been explored extensively in the literature, where the constant mechanism of shock impact has always been studied. Nevertheless, engineering systems operate in a more complicated shock environment due to developments, and it is worth studying the reliability of such multi-component systems in a variable shock environment. Driven by the research gaps and practical situations, this paper constructs a reliability model of multi-component systems under a generalized mixed shock model with a change point. The multi-state components operate in the shock environment I initially and it may continue to run in the shock environment II after the random change point of the environment. Two novel shock impact mechanisms of the variable environment are put forward, where a series of failure criteria based on shocks are included. Four different structures of multi-component systems are considered in this paper. It can be proved that the proposed mixed shock model is a generalization of some transformed models. A multi-stage finite Markov chain imbedding approach is established to derive the probabilistic indices of the components and entire systems. Based on the engineering applications, illustrative examples are provided to verify the effectiveness of the proposed model.

In 1986, Fu proposed the finite Markov chain imbedding approach. Since then, it has played an important role in the analyses of system reliability, such as on reliability computations, importance analyses of components, failure rate function computations, the birth of new reliability system models, and analyses of new reliability tests. We present a survey on the developments and applications of this approach in the reliability field.

Reliability forecast of the sleeper system is very important for minimizing the maintenance cost. Generally, there are two kinds of failure criteria for sleeper system. In this paper, by using the finite Markov chain imbedding approach, the reliability of sleeper system based on the two kinds of failure criteria is given. Numerical example show that the proposal method is efficient not only for the special case that was studied in other literature, but also for the generalized case that was not studied until now.

This article extends the finite Markov chain imbedding approach to evaluate the system reliability of a dynamic k-out-of- n:F system operating under two cyclic alternating conditions, and this article presents a method to obtain the optimal replacement interval of the system according to age-based replacement policy. In terms of the “dynamic k-out-of- n:F” model, we regard the system as two distinct k-out-of- n:F systems with different values of k while the system is operating under each condition. We apply the proposed model to analyze the reliability of a wireless sensor network, whose sensors switching into sleep state to save energy and shifting into listen state to detect the information alternatively. We also obtain the optimal replacement interval to redeploy the wireless sensor networks.

Optimal inspection interval for a k-out-of-n system with non-identical components

A shock model for multi-component system considering the cumulative effect of severely damaged components