A general model for consecutive-k-out-of-n: F repairable system with exponential distribution and (k−1)-step Markov dependence

In this paper, a general model for consecutive-k-out-of-n: F repairable system with exponential distribution and (k−1)-step Markov dependence is introduced. The lifetime of a component is an exponential random variable, its parameter depends on the number of consecutive failed components that precede the component. The repair time is also an exponential random variable. A priority repair rule on the basis of the system failure risk is adopted. Then the transition density matrix of the system is determined. Some reliability indices, including the system availability, rate of occurrence of failures and reliability are evaluated accordingly. For the demonstration of the model and methodology, a linear system example and a circular system example are investigated.     

Synchronization analysis through coupling mechanism in realistic neural models

Synchronization which relates to the system’s stability is important to many engineering and neural applications. In this paper, an attempt has been made to implement response synchronization using coupling mechanism for a class of nonlinear neural systems. We propose an OPCL (open-plus-closed-loop) coupling method to investigate the synchronization state of driver-response neural systems, and to understand how the behavior of these coupled systems depend on their inner dynamics. We have investigated a general method of coupling for generalized synchronization (GS) in 3D modified spiking and bursting Morris–Lecar (M-L) neural models. We have also presented the synchronized behavior of a network of four bursting Hindmarsh–Rose (H-R) neural oscillators using a bidirectional coupling mechanism. We can extend the coupling scheme to a network of N neural oscillators to reach the desired synchronous state. To make the investigations more promising, we consider another coupling method to a network of H-R oscillators using bidirectional ring type connections and present the effectiveness of the coupling scheme.     

Optimizing Markovian modeling of chaotic systems with recurrent neural networks

In this paper, we propose a methodology for optimizing the modeling of an one-dimensional chaotic time series with a Markov Chain. The model is extracted from a recurrent neural network trained for the attractor reconstructed from the data set. Each state of the obtained Markov Chain is a region of the reconstructed state space where the dynamics is approximated by a specific piecewise linear map, obtained from the network. The Markov Chain represents the dynamics of the time series in its statistical essence. An application to a time series resulted from Lorenz system is included.     

Age-usage semi-Markov models

This paper presents a non-homogeneous age-usage semi-Markov model with a measurable state space. Several probability functions useful to assess the system’s reliability are investigated. They satisfy the same family of equations we call indexed Markov renewal equations. Sufficient conditions to assure the existence and uniqueness of their solutions are provided. The numerical analysis of these equations is executed through the construction of a process discrete in time and space, which is shown to converge to the continuous one in the Skorohod topology. An algorithm useful for solving the discretized system of equations is presented by using a matrix representation.     

Sub-stochastic matrix analysis for bounds computation—Theoretical results

Performance evaluation of complex systems is a critical issue and bounds computation provides confidence about service quality, reliability, etc. of such systems. The stochastic ordering theory has generated a lot of works on bounds computation. Maximal lower and minimal upper bounds of a Markov chain by a st-monotone one exist and can be efficiently computed. In the present work, we extend simultaneously this last result in two directions. On the one hand, we handle the case of a maximal monotone lower bound of a family of Markov chains where the coefficients are given by numerical intervals. On the other hand, these chains are sub-chains associated to sub-stochastic matrices. We prove the existence of this maximal bound and we provide polynomial time algorithms to compute it both for discrete and continuous Markov chains. Moreover, it appears that the bounding sub-chain of a family of strictly sub-stochastic ones is not necessarily strictly sub-stochastic. We establish a characterization of the families of sub-chains for which these bounds are strictly sub-stochastic. Finally, we show how to apply these results to a classical model of repairable system. A forthcoming paper will present detailed numerical results and comparison with other methods.     

Imperfect debugging in software reliability: A Bayesian approach

The objective of studying software reliability is to assist software engineers in understanding more of the probabilistic nature of software failures during the debugging stages and to construct reliability models. In this paper, we consider modeling of a multiplicative failure rate whose components are evolving stochastically over testing stages and discuss its Bayesian estimation. In doing so, we focus on the modeling of parameters such as the fault detection rate per fault and the number of faults. We discuss how the proposed model can account for “imperfect debugging” under certain conditions. We use actual inter-failure data to carry out inference on model parameters via Markov chain Monte Carlo methods and present additional insights from Bayesian analysis.     

An analytical methodology for assessment of smart monitoring impact on future electric power distribution system reliability

Smart grid is referred to a modernized power grid which can mitigate fault detection and allow self‐healing of the system without the intervention of operators. This article proposes an innovative analytical formulation using Markov method to evaluate electric power distribution system reliability in smart grids, which incorporates the impact of smart monitoring on the overall system reliability. An accurate reliability model of the main network components and the communication infrastructure have been also considered in the methodology. The proposed approach was applied to a well‐known test bed (Roy Billinton Test System) and various reliability case studies with monitoring provision and monitoring deficiency are analyzed. This article involves the developing possibilities of communication technologies and next‐generation control systems of the entire smart network based on the real‐time monitoring and modern control system to achieve a reliable, economical, safe, and high efficiency of electricity. The implementations indicate that using an appropriate set of the smart grid monitoring devices for power system components can virtually influence all the reliability indices although the amount of improvement varies between techniques. The proposed approach determined that smart monitoring for which components of the electric power distribution systems are tailored and deduce to major economical benefits. The described approach also reveals which reliability indices drastically influenced using monitoring. © 2014 Wiley Periodicals, Inc. Complexity 21: 99–113, 2015     

Reliability assessment of multi-state phased mission system with non-repairable multi-state components

Phased mission systems (PMSs) like satellites and spacecraft perform their functions over non-overlapping mission periods, called phases. One of the challenges in assessing reliability of PMSs comes from considering the s-dependence among phases, and the consideration on the multi-state behavior of components and systems makes the reliability analysis even more difficult. To effectively address this problem, a multi-state multivalued decision diagram algorithm for PMS and a multi-state multi-valued decision diagram model for phased mission system (PMS-MMDD) method is developed for the reliability modelling of non-repairable multi-state components. Based on the Semi-Markov process, a Markov renewal equation-based method is developed to deal with non-exponential multi-state components and a numerical method, the trapezoidal integration method, is used to compute the complex integrals in the path probability evaluation. A case study of a multi-state attitude and orbit control system in a spacecraft is analyzed to illustrate the proposed PMS-MMDD model and the Markov renewal equation-based evaluation method. The accuracy and computation efficiency of the proposed method are verified by the Monte Carlo simulation method.     

The augmented semi‐Markov system and its asymptotic behaviour

This paper suggests a generalized semi‐Markov model for manpower planning, which could be adopted in cases of unavailability of candidates with the desired qualifications/experience, as well as in cases where an organization provides training opportunities to its personnel. In this context, we incorporate training classes into the framework of a non‐homogeneous semi‐Markov system and we introduce an additional, external semi‐Markov system providing the former with potential recruits. For the model above, referred to as the Augmented Semi‐Markov System, we derive the equations that reflect the expected number of persons in each grade and we also investigate its limiting population structure. An illustrative example is provided. Copyright © 2010 John Wiley & Sons, Ltd.     

基于智能控制的高速线材轧机水冷控制系统优化

针对武汉钢铁集团公司大型轧钢厂当前在高速线材生产线中存在的水冷控制系统可靠性差,轧线温度波动范围大等问题,应用智能计算理论及方法对上述工业控制系统进行系统辨识、建模以及优化.分析比较了基于梯度下降搜索BP算法、径向基函数网络、Levenberg Marquardt BP算法的前馈神经网络对SMS水冷系统的逼近精度、训练速度.研究了采用Levenberg-Marquardt BP算法的前馈神经网络在样本集和测试集上的表现,建立了基于Levenberg-Marquardt BP算法的前馈神经网络水冷控制系统模型.解决了高速线材水冷控制系统可靠性,温度控制精度问题.     

Reliability analysis of k-out-of-n: F balanced systems with multiple functional sectors

In this paper, new concepts of balanced systems are proposed based on real engineering problems. The system under study consists of l groups and each group has n functional sectors. The conception of balance difference is proposed for the first time. It is assumed that unbalanced systems are rebalanced by either forcing down some working units into standby or resuming some standby units into operation. In addition, a case that the forced-down units are subject to failure during standby is studied in this paper. Based on different balanced cases and system failure criteria, two reliability models for balanced systems are developed. The proposed systems have widespread applications in aerospace and military industries, such as wing systems of airplane and unmanned aerial vehicles with balanced engine systems. Markov process imbedding method is used to analyze the number of working units in each sector for each model. Finite Markov chain imbedding approach and universal generating function technique are used to obtain the system reliability for different models. Several case studies are finally presented to demonstrate the new models.     

Uncertain and negative evidence in continuous time Bayesian networks

The continuous time Bayesian network (CTBN) enables reasoning about complex systems by representing the system as a factored, finite-state, continuous-time Markov process. Inference over the model incorporates evidence, given as state observations through time. The time dimension introduces several new types of evidence that are not found with static models. In this work, we present a comprehensive look at the types of evidence in CTBNs. Moreover, we define and extend inference to reason under uncertainty in the presence of uncertain evidence, as well as negative evidence, concepts extended to static models but not yet introduced into the CTBN model.     

Interval reliability for aggregated Markov repairable system with repair time omission

In this paper, Markov models of repairable systems with repair time omission are considered whose finite state space is grouped into two sets, the set of working states, W, and the set of failed states, F. If the system enters failed states from a working state at any instance, and sojourns at the failed states F less than a given nonnegative critical value τ, then the repair interval can be omitted from downtime records. Otherwise, If the system enters failed states from a working state at any instance, and sojourns at the failed states F more than the given nonnegative critical value τ, then the repair interval cannot be omitted from downtime records. In terms of the assumption, a new model is developed. The focus of attention is the new model’s availability, interval reliability and interval unreliability. Several results are derived for these reliability indexes for the new model. Some special cases and numerical examples are given to illustrate the results obtained by using Maple software in the paper.     

基于BP神经网络的航空公司机队可靠性评价模型

机队作为航空公司运输能力的关键,其安全性与可靠性直接影响到航空公司的经济效益.根据航空公司机队可靠性统计和数据采集方式以及实际应用情况,建立了航空公司机队可靠性评价指标体系.鉴于机队可靠性受多种复杂因素影响及各指标体系非线性等特点,结合人工神经网络基本原理和特性,提出了BP神经网络机队可靠性评价模型.最后应用该模型对航空公司机队可靠性进行了实例分析,得出了评价等级.结果表明,基于BP神经网络机队可靠性评价模型是可行的,该方法能够实现动态的评价,对提高航空公司机队可靠性评价技术水平具有现实的意义.     

一类随机时延网络控制系统的神经网络自适应容错控制

针对一类随机时延网络控制系统,提出一种基于RBF神经网络自适应动态补偿的容错控制策略.该方法通过在线估计时延将系统建模为随机切换系统,并在模型参考自适应方法的基础上设计RBF神经网络动态补偿容错控制器,利用Lyapunov稳定性理论给出神经网络补偿器的在线权值学习算法,以保证网络控制系统在故障情况下的跟踪性能和状态一致最终有界稳定.最后通过仿真验证了该方法的有效性.     

Approximation of Solutions of Fractional-Order Delayed Cellular Neural Network on $$\varvec{[0,\infty )}$$

In this paper, we study a class of fractional-order cellular neural network containing delay. We prove the existence and uniqueness of the equilibrium solution followed by boundedness. Based on the theory of fractional calculus, we approximate the solution of the corresponding neural network model over the interval \([0,\infty )\) using discretization method with piecewise constant arguments and variation of constants formula for fractional differential equations. Furthermore, we conclude that the solution of the fractional-delayed system can be approximated for large t by the solution of the equation with piecewise constant arguments, if the corresponding linear system is exponentially stable. At the end, we give two numerical examples to validate our theoretical findings.     

Discrete time queueing networks with product form steady state. Availability and performance analysis in an integrated model

For a discrete time network of generalized Bernoulli servers with unreliable nodes we derive the steady state probabilities for the joint queue length vector for all nodes and the availability status of the network. This allows us to assess the performance behavior and the reliability, resp. availability, of the network in an integrated model. Because our result exhibits a product form for the steady state distribution it opens the path to fast algorithmic evaluation of the desired performance and reliability indices.     

Bayesian estimation of system reliability in Brownian stress-strength models

A stress-strength system fails as soon as the applied stress,X, is at least as much as the strength,Y, of the system. Stress and strength are time-varying in many real-life systems but typical statistical models for stress-strength systems are static. In this article, the stress and strength processes are dynamically modeled as Brownian motions. The resulting stress-strength system is then governed by a time-homogeneous Markov process with an absorption barrier at O. Conjugate as well as non-informative priors are developed for the model parameters and Markov chain sampling methods are used for posterior inference of the reliability of the stress-strength system. A generalization of this model is described next where the different stress-strength systems are assumed to be exchangeable. The proposed Bayesian analyses are illustrated in two examples where we obtain posterior estimates as well as perform model checking by cross-validation.     

Spare routing problem with p minimal paths for time-based stochastic flow networks

A time-based stochastic flow network (TBSFN), in which each arc has several possible capacities/states and a lead time, is addressed to discuss the system reliability of spare routing for a computer network. The minimum transmission time to send a given amount of data through a single minimal path is uncertain. Although the transmission time will be shortened even if the data are sent through p (p > 1) disjoint minimal paths simultaneously, it is still variable in a TBSFN. This paper is concerned with evaluating the probability that a specified amount of data can be sent through p minimal paths simultaneously within a time threshold. Such a probability is named the system reliability, which can be treated as a performance index for measuring the transmission ability. We present an efficient methodology to assess the system reliability. Furthermore, a spare routing for boosting the system reliability is established in advance to indicate the main and spare p minimal paths. Subsequently, the system reliability of the spare routing can be computed easily, which shows the contribution of the spare design. From the viewpoint of decision support, we may conduct the sensitive analysis to find out the most important arc which will increase/decrease the system reliability most significantly.     

Replacement times and costs in a degrading system with several types of failure: The case of phase-type holding times

A reliability system submitted to external and internal failures, that can be repairable or non-repairable, with degradation levels, and with sojourn times phase-type distributed, is considered. Repair is not as good as new, and the repair of internal failure follows policy N, that is, after N completed repairs the system is replaced by a new one to the following failure, repairable or not. For this system, a Markov model is constructed, and the stationary probability vector is calculated. It is shown that the distribution of the time between two consecutive replacements follows a phase-type distribution, whose representation is determined. The costs of these periods are calculated. An optimization problem involving the costs, the availability, and the number of internal repairs is illustrated by a numerical example.