共查询到20条相似文献,搜索用时 15 毫秒
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Farhad Kianfar 《Applied mathematics and computation》2005,170(2):924-940
The simultaneous planning of the production and the maintenance in a flexible manufacturing system is considered in this paper. The manufacturing system is composed of one machine that produces a single product. There is a preventive maintenance plan to reduce the failure rate of the machine. This paper is different from the previous researches in this area in two separate ways. First, the failure rate of the machine is supposed to be a function of its age. Second, we assume that the demand of the manufacturing product is time dependent and its rate depends on the level of advertisement on that product. The objective is to maximize the expected discounted total profit of the firm over an infinite time horizon. In the process of finding a solution to the problem, we first characterize an optimal control by introducing a set of Hamilton–Jacobi–Bellman partial differential equations. Then we realize that under practical assumptions, this set of equations can not be solved analytically. Thus to find a suboptimal control, we approximate the original stochastic optimal control model by a discrete-time deterministic optimal control problem. Then proposing a numerical method to solve the steady state Riccati equation, we approximate a suboptimal solution to the problem. 相似文献
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A novel optimal preventive maintenance policy for a cold standby system consisting of two components and a repairman is described herein. The repairman is to be responsible for repairing either failed component and maintaining the working components under certain guidelines. To model the operational process of the system, some reasonable assumptions are made and all times involved in the assumptions are considered to be arbitrary and independent. Under these assumptions, all system states and transition probabilities between them are analyzed based on a semi-Markov theory and a regenerative point technique. Markov renewal equations are constructed with the convolution of the cumulative distribution function of system time in each state and corresponding transition probability. By using the Laplace transform to solve these equations, the mean time from the initial state to system failure is derived. The optimal preventive maintenance policy that will provide the optimal preventive maintenance cycle is identified by maximizing the mean time from the initial state to system failure, and is determined in the form of a theorem. Finally, a numerical example and simulation experiments are shown which validated the effectiveness of the policy. 相似文献
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自保护技术作为自愈技术的一种,能够使系统在环境或工况条件变化的干扰下以较高可靠性运行。本文构建了一个新的具有相依主要部件和辅助部件的系统可靠性模型,其中主要部件的退化速率与工作中的辅助部件的数量有关。此外,基于定期检测和预防维修策略,本文利用半再生过程技术求解了系统的长期运行平均成本,并以长期运行平均成本最小化为目标给出了系统的最优预防维修策略。最后,以镗刀系统为例,利用所提方法给出了预防更换阈值和检测周期的最优值,以期望为实际维修行为决策提供理论参考。 相似文献
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S. Shakuntla A.K. LalS.S. Bhatia Jai Singh 《Applied mathematics and computation》2011,218(8):3981-3992
The purpose of this paper is to compute reliability of Polytube manufacturing plant having four units using supplementary variable technique. The failure and repair rates of the sub-systems are variable. The mathematical equations are derived using Chapman-Kolmogorov differential equations which are formed using mnemonic rule from the transition diagram of Polytube manufacturing plant. The system of partial differential equations obtained has been solved using Lagrange’s method and reliability of the system for the various choices of constant transition rates is solved numerically using Runge-Kutta fourth order. A sensitive analysis of subsystem is finally carried out to improve overall availability. 相似文献
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This paper considers a competing risk (degradation and sudden failure) maintenance situation. A maintenance model and a repair cost model are presented. The degradation state of the units is continuously monitored. When either the degradation level reaches a predetermined threshold or a sudden failure occurs before the unit reaches the degradation threshold level, the unit is immediately repaired (renewed) and restored to operation. The subsequent repair times increase with the number of renewals. This process is repeated until a predetermined time is reached for preventive maintenance to be performed. The optimal maintenance schedule that maximizes the unit availability subject to repair cost constraint is determined in terms of the degradation threshold level and the time to perform preventive maintenance. 相似文献
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研究具有初始应力的小垂度粘弹性索的非线性动态响应及振动主动控制。在假定索材料的本构关系为一般微分本构类型的基础上,建立小垂度粘弹性索的运动微分方程;应用Galerkin方法将其转化为可用Runge-Kutta数值积分方法求解的一系列三阶非线性常微分方程。在仅考虑面内的横向振动及忽略非线性的情况下得到了连续状态空间中的状态方程,将状态方程离散为差分方程形式,并用矩阵指数来逐步近似状态转移矩阵;基于二次性能指标的最小化得到了最优的控制力与状态向量。最后通过数值仿真研究说明了粘性参数对索动态响应的影响。 相似文献
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研究由两个部件串联组成的系统的预防维修策略, 当系统的工作时间达到T时进行预防维修, 预防维修使部件恢复到上一次故障维修后的状态. 当部件发生故障后进行故障维修, 因为各种原因可能会延迟修理. 部件在每次故障维修后的工作时间形成随机递减的几何过程, 且每次故障后的维修时间形成随机递增的几何过程. 以部件进行预防维修的间隔T和更换前的故障次数N组成的二维策略(T,N)为策略, 利用更新过程和几何过程理论求出了系统经长期运行单位时间内期望费用的表达式, 并给出了具体例子和数值分析. 相似文献
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A. Csenki 《商业与工业应用随机模型》1994,10(4):279-293
Consider a repairable system at the time instants t and t + x, where t, x ≥0. The joint availability of the system at these time instants is defined as the probability of the system being functional in both t and t + x. A set of integral equations is derived for the joint availability of a system modelled by a finite semi–Markov process. The result is applied to the semi–Markov model of a two–unit system with sequential preventive maintenance. The method used for the numerical solution of the resulting system of integral equations is a two–point trapezoidal rule. The system of implementation is the matrix computation package MATLAB on the Apple Macintosh SE/30. The numerical results obtained by this method are shown to be in good agreement with those from simulation. 相似文献
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Sophie Bloch‐Mercier 《商业与工业应用随机模型》2000,16(3):219-234
We consider a reparable system with a finite state space, evolving in time according to a semi‐Markov process. The system is stopped for it to be preventively maintained at random times for a random duration. Our aim is to find the preventive maintenance policy that optimizes the stationary availability, whenever it exists. The computation of the stationary availability is based on the fact that the above maintained system evolves according to a semi‐regenerative process. As for the optimization, we observe on numerical examples that it is possible to limit the study to the maintenance actions that begin at deterministic times. We demonstrate this result in a particular case and we study the deterministic maintenance policies in that case. In particular, we show that, if the initial system has an increasing failure rate, the maintenance actions improve the stationary availability if and only if they are not too long on the average, compared to the repairs ( a bound for the mean duration of the maintenance actions is provided). On the contrary, if the initial system has a decreasing failure rate, the maintenance policy lowers the stationary availability. A few other cases are studied. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
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首先,我们给出了引入伴随方程(组)扩充原方程(组)的策略使给定偏微分方程(组)的扩充方程组具有对应泛瓯即,成为Lagrange系统的方法,以此为基础提出了作为偏微分方程(组)传统守恒律和对称概念的一种推广-偏微分方程(组)扩充守恒律和扩充对称的概念;其次,以得到的Lagrange系统为基础给定了确定原方程(组)扩充守恒律和扩充对称的方法,从而达到扩充给定偏微分方程(组)的首恒律和对称的目的;第三,提出了适用于一般形式微分方程(组)的计算固有守恒律的方法;第四,实现以上算法过程中,我们先把计算(扩充)守恒律和对称问题均归结为求解超定线性齐次偏微分方程组(确定方程组)的问题.然后,对此关键问题我们提出了用微分形式吴方法处理的有效算法;最后,作为方法的应用我们计算确定了非线性电报方程组在内的五个发展方程(组)的新守恒律和对称,同时也说明了方法的有效性. 相似文献
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A. M. de Roos 《Numerical Methods for Partial Differential Equations》1988,4(3):173-195
A numerical integration method is introduced for the class of hyperbolic partial differential equations that occur in physiologically structured population models. These equations describe the time evolution of the population density-function over the individual state-space Ω. Exploiting the biological interpretation of the equation, this density-function is represented by a set of moments over a collection of subdomains in Ω, moving along the characteristics of the partial differential equation (PDE). These moments are readily interpreted as numbers of individuals in a cohort, mean individual state in a cohort, etc. The numerical method consists of approximating the differential equations. The method appears to be very efficient for this special type of PDE. It combines such desirable properties as as lack of dispersion and dissipation and a preservation of monotonicity of the density function along the characteristics with a strong relation to the biological background of the equations for these moments to arrive at a closed system of ordinary differential equations. The method also allows one to incorporate the usual type of nonlinearities that occur in physiologically structured population models. A numerical example is presented as an illustration of the application of the method. 相似文献
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This paper deals with a GALERKIN-based multi-scale time integration of a viscoelastic rope model. Using HAMILTON's dynamical formulation, NEWTON's equation of motion as a second-order partial differential equation is transformed into two coupled first order partial differential equations in time. The considered finite viscoelastic deformations are described by means of a deformation-like internal variable determined by a first order ordinary differential equation in time. The corresponding multi-scale time-integration is based on a PETROV-GALERKIN approximation of all time evolution equations, leading to a new family of time stepping schemes with different accuracy orders in the state variables. The resulting nonlinear algebraic time evolution equations are solved by a multi-level NEWTON-RAPHSON method. Realizing this transient numerical simulation, we also demonstrates a parallelized solution of the viscous evolution equation in CUDA©. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Hamid Reza Marzban Hamid Reza Tabrizidooz 《Communications in Nonlinear Science & Numerical Simulation》2012,17(1):100-109
The hybrid function approximation method for solving Hutchinson’s equation which is a nonlinear delay partial differential equation, is investigated. The properties of hybrid of block-pulse functions and Lagrange interpolating polynomials based on Legendre-Gauss-type points are presented and are utilized to replace the system of nonlinear delay differential equations resulting from the application of Legendre pseudospectral method, by a system of nonlinear algebraic equations. The validity and applicability of the proposed method are demonstrated through two illustrative examples on Hutchinson’s equation. 相似文献
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** Corresponding author. Email: romulo.zequeira{at}utt.fr*** Email: christophe.berenguer{at}utt.fr In this paper, we study the determination of optimal inspectionpolicies when three types of inspections are available: partial,perfect and imperfect. Perfect inspections diagnose withouterror the system state. The system can fail because of threecompeting failure types: I, II and III. Partial inspectionsdetect without error type I failures. Failures of type II canbe detected by imperfect inspections which have non-zero probabilityof false positives. Partial and imperfect inspections are madeat the same time. Type III failures are detectable only by perfectinspections. If the system is found failed in an inspection,a repair is made which renders the system in a good-as-new condition.The system is preventively maintained following an age-basedpolicy. Preventive maintenance actions return the system toa good-as-new condition. We consider cost contributions of inspections,repairs, preventive maintenance and periods of unavailability.The model presented permits to determine the optimal (constant)inter-inspection period for partial, imperfect and perfect inspectionsand the optimal times of preventive maintenance actions. 相似文献