Scheduling flexible maintenance activities subject to job-dependent machine deterioration

This paper considers single machine scheduling that integrates machine deterioration. The current maintenance state of the machine is determined by a maintenance level which drops by a certain, possibly job-dependent, amount while jobs are processed. A maintenance level of less than zero is associated with the machine??s breakdown and is therefore forbidden. Consequently, maintenance activities that raise the maintenance level again may become necessary and have to be scheduled additionally. In what follows, two general types of maintenance activities are distinguished. In the full maintenance case, maintenance activities are always executed until the machine has reached the maximum maintenance level. In contrast to this, the schedule in the partial maintenance case has to additionally determine the duration of maintenance activities. By combining both cases with regular objective functions such as minimization of maximum tardiness, minimization of the sum of completion times, or minimization of the number of tardy jobs, we obtain a new set of specific single-stage scheduling problems. Besides motivating and introducing these problems, we shall also analyze the computational complexity of general and specific cases.     

Approximation schemes for scheduling on a single machine subject to cumulative deterioration and maintenance

We consider a scheduling problem on a single machine to minimize the makespan. The processing conditions are subject to cumulative deterioration, but can be restored by a single maintenance. We link the problem to the Subset-sum problem (if the duration of maintenance is constant) and to the Half-Product Problem (if the duration of maintenance depends on its start time). For both versions of the problem, we adapt the existing fully polynomial-time approximation schemes to our problems by handling the additive constants.     

Optimal cycle production of a manufacturing system subject to deterioration

A single part type, single machine, fluid model manufacturing system is considered. The machine is subject to a deterministic deterioration process, which depends on the operation rate. The objective is to minimize a long term average cost index which penalizes inventory surplus and backlog. The optimal policy determined presents some similarities with the policy conjectured optimal in the past for a similar Markovian formulation. The considered problem can be applied to several real contexts, and not just from the manufacturing domain, as briefly discussed in the paper.     

An age reduction approach for finite horizon optimization of preventive maintenance for single units subject to random failures

We consider a single unit working in a continuous mode of operation characterized by an increasing failure rate. We determine the optimal number of preventive maintenance activities to be scheduled within a time horizon of interest, the required extent of the preventive maintenance by means of an age reduction of the unit and the corresponding optimal value of the expected profit. We assume that any breakdown occuring is minimally repaired, the repair is performed instantaneously, and the repair cost is the same for any repair. On the other hand, the cost associated with a preventive maintenance activity may vary as well as its duration.     

Optimal maintenance policies for systems subject to a Markovian operating environment

Many stochastic models of repairable equipment deterioration have been proposed based on the physics of failure and the characteristics of the operating environment, but they often lead to time to failure and residual life distributions that are quite complex mathematically. The first objective of our study is to investigate the potential for approximating these distributions with traditional time to failure distribution. We consider a single-component system subject to a Markovian operating environment such that the system’s instantaneous deterioration rate depends on the state of the environment. The system fails when its cumulative degradation crosses some random threshold. Using a simulation-based approach, we approximate the time to first failure distribution for this system with a Weibull distribution and assess the quality of this approximation. The second objective of our study is to investigate the cost benefit of applying a condition-based maintenance paradigm (as opposite to a scheduled maintenance paradigm) to the repairable system of interest. Using our simulation model, we assess the cost benefits resulting from condition-based maintenance policy, and also the impact of the random prognostic error in estimating system condition (health) on the cost benefits of the condition-based maintenance policy.     

A modern approach to industrial process control

The history of industrial process computer control now spans over 10 years. During this time control theory has transgressed from the frequency domain to the time domain, and yet few applications of these modern methods to industrial processes can be found in the literature. This paper attempts to temper the current state of computer process control with some historical perspective and then goes on to describe an application of modern control techniques to the basic oxygen steel-making process. This application of adaptive filtering and nonlinear state estimation is used to illustrate that modern methods can be used to compensate for a lack of process knowledge. The point of emphasis is that these modern methods can replace the extensive modeling and simulation phases which historically have retarded the success of many on-line computer control projects. The paper is intended to stimulate more applications of modern control methods to industrial processes.     

一类带有加速度约束的非线性系统最优滑模控制

针对加速度受约束的非线性时变系统,设计了一种全局最优滑模控制算法.首先引入全程滑态因子,保证滑模面一开始就在零值附近,然后选取位置跟踪误差绝对值的积分为指标函数,通过求解该指标函数的最小值来确定滑模面方程的相关参数,最后设计了基于指数趋近律的滑模控制算法.仿真结果表明了该方法的有效性和强鲁棒性.     

Generalized sequential preventive maintenance policy of a system subject to shocks

The paper proposes and analyses a generalized sequential preventive maintenance policy of a system subject to shocks. The shocks arrive according to a non-homogeneous Poisson process {N i (t); t S 0 }, whose intensity function r i (t) varies with the number of maintenance actions (i - 1 ) that have already been carried out, and the time (t) that has elapsed since the last maintenance action. Upon the arrival of the k th shock, the system is maintained or repaired minimally with probability θ i , k and q i , k respectively depending on the number of maintenance actions (i - 1 ) that have already occurred and the ordinal number of the arriving shock (the k th ) since the last maintenance. In addition, a planned maintenance is carried out as soon as T i time units have elapsed since the (i - 1 ) th maintenance action. If i = N, the system is replaced rather than maintained. The objective is to determine the optimal plan (in terms of N and T i ) that minimizes the expected cost per unit of time. It is shown that under certain reasonable assumptions, a sequential preventive maintenance policy has unique solutions. Various special cases are considered.     

Adaptive neural control for uncertain systems subject to actuator failure

In this paper, the design of controller based on neural network is investigated for a class of uncertain systems subject to actuator failures. An adaptive neural controller is designed by utilizing the approximation technique of neural network. The key feature in this work is to remove the requirement on the boundedness of unknown nonlinear functions that is usually encountered in the existing works. Moreover, sufficient conditions are derived such that the closed-loop system is robustly stable. Finally, numerical simulation results are given.     

A stochastic control approach to Slotted-ALOHA random access protocol

ALOHA random access protocols are distributed protocols based on transmission probabilities, that is, each node decides upon packet transmissions according to a transmission probability value. In the literature, ALOHA protocols are analysed by giving necessary and sufficient conditions for the stability of the queues of the node buffers under a control vector (whose elements are the transmission probabilities assigned to the nodes), given an arrival rate vector (whose elements represent the rates of the packets arriving in the node buffers). The innovation of this work is that, given an arrival rate vector, it computes the optimal control vector by defining and solving a stochastic control problem aimed at maximising the overall transmission efficiency, while keeping a grade of fairness among the nodes. Furthermore, a more general case in which the arrival rate vector changes in time is considered. The increased efficiency of the proposed solution with respect to the standard ALOHA approach is evaluated by means of numerical simulations.     

A practical method for assessing the performance of control loops subject to random load changes

A method is described for detecting load changes and characterizing subsequent responses in single-input-single-output (SISO) feedback control loops. The method is computationally simple and suitable for on-line implementation in a controller. Load changes are detected using a statistical change detection procedure that uses zero-crossings information to account for autocorrelation. Responses are characterized by a normalized index that can be related to a damping ratio in a second-order model. Results are presented from applying the method to data from a simulated control loop and two temperature control loops in a large office building.     

Leader localization in multi-agent systems subject to failure: A graph-theoretic approach

In this paper, structural controllability of a leader–follower multi-agent system with multiple leaders is studied. A graphical condition for structural controllability based on the information flow graph of the system is provided. The notions of p-link and q-agent controllability in a multi-leader setting are then introduced, which provide quantitative measures for the controllability of a system subject to failure in the agents and communication links. The problem of leader localization is introduced, which is concerned with finding the minimum number of agents whose selection as leaders results in a p-link or q-agent controllable network. Polynomial-time algorithms are subsequently presented to solve the problem for both cases of undirected and directed information flow graphs.     

A preventive maintenance policy for a standby system subject to internal failures and external shocks with loss of units

In many situations, serious damage and considerable financial losses are caused by non-repairable failures of a system. Redundant systems and maintenance policies are commonly employed to improve reliability. This paper is focused on the modelling of a complex cold standby system by analysing the effectiveness and costs of preventive maintenance, always in an algorithmic form. The online unit of the system is subject to wear failures and external shocks. The online unit can go through an indeterminate number of degradation levels before failure. This one is observed when inspections occur. Inspections are performed at random intervals, and when one takes place, the unit is taken to the preventive maintenance facility if it is necessary. The preventive maintenance time and cost is different depending on the degradation level observed. If only one unit is performing, a minimal maintenance policy is adopted in order to optimise system behaviour. Reliability measures such as the conditional probability of failure are worked out in a well-structured and algebraic form in transient and stationary regimes by using algorithmic methods. The stationary distribution is calculated using matrix analytic methods, and rewards are included in the model. An optimisation example shows the versatility of the model presented.     

基于分布参数控制理论的可变质产品最优经营策略

应用分布参数控制理论,研究了零售企业对于可变质产品的最优经营管理问题.通过建立可变质产品的最优经营管理的分布参数控制系统模型,得出了零售企业每个瞬间每种可变质产品的最优经营管理策略,并对空间伴随函数和控制变量给出了明确的经济学解释.该模型更合理地描述了可变质产品的实际经营特性,具有一定的现实意义和实用价值.     

A generalised maintenance policy with age-dependent minimal repair cost for a system subject to shocks under periodic overhaul

A system is subject to shocks that arrive according to a non-homogeneous Poisson process. As shocks occur, the system has two types of failures: type 1 failure (minor failure) is removed by a minimal repair, whereas type 2 failure (catastrophic failure) is removed by overhaul or replacement. The cost of minimal repair depends on age. A system is overhauled when the occurrence of a type 2 failure or at age T, whichever occurs first. At the N-th overhaul, the system is replaced rather than overhauled. A maintenance policy for determining optimal number of overhauls and optimal interval between overhauls which incorporate minimal repairs, overhauls and replacement is proposed. Under such a policy, an approach which using the concept of virtual age is adopted. It is shown that there exists a unique optimal policy which minimises the expected cost rate under certain conditions. Various cases are considered.     

Optimal control of the linear regulator subject to disturbances

An optimal control problem for linear regulators with external disturbances is formulated. It is shown that if some a priori knowledge of the disturbance is incorporated into the design procedure the optimal control is not an explicit function of the disturbance and, for polynomial disturbances, can be implemented as a linear function of the state of the system.     

Optimum preventive maintenance policies for systems subject to random working times,replacement, and minimal repair

This paper proposes, from the economical viewpoint of preventive maintenance in reliability theory, several preventive maintenance policies for an operating system that works for jobs at random times and is imperfectly maintained upon failure. As a failure occurs, the system suffers one of two types of failure based on a specific random mechanism: type-I (repairable) failure is rectified by a minimal repair, and type-II (non-repairable) failure is removed by a corrective replacement. First, a modified random and age replacement policy is considered in which the system is replaced at a planned time T, at a random working time, or at the first type-II failure, whichever occurs first. Next, as one extended model, the system may work continuously for N jobs with random working times. Finally, as another extended model, we might consider replacing an operating system at the first working time completion over a planned time T. For each policy, the optimal schedule of preventive replacement that minimizes the mean cost rate is presented analytically and discussed numerically. Because the framework and analysis are general, the proposed models extend several existing results.     

Optimal maintenance policy for multi-component systems under Markovian environment changes

In this paper, we study multi-component systems, which environmental conditions and opportunistic maintenance (OM) involve. Environmental conditions will exert an influence on deterioration processes of the components in the system. For each component, the worse the environmental conditions are, the faster its deterioration speed is. We want to determine when to preventively maintain each component under such environmental influence. Our purpose is to minimize its long-run average maintenance cost. We decompose such a multi-component system into mutually influential single-component systems, and formulate the maintenance problem of each component as a Markov decision process (MDP). Under some reasonable assumptions, we prove the existence of the optimal (n_r, N_r) type policy for each component. A policy iteration method is used to calculate its optimal maintenance policy. Based on the method, we develop an iterative approximation algorithm to obtain an acceptable maintenance policy for a multi-component system. Numerical examples find that environmental conditions and OM pose significant effects on a maintenance policy.     

Optimal control theory for ambient pollution

We study optimal control of systems of distributed parameters applied to problems of ambient pollution. The model consists of a parabolic partial differential equation that models the transport of a pollutant in an incompressible viscous fluid, with boundary conditions and initial value, that is in our model we consider the velocity that the pollutant propagates in the environment. The developed mathematical modelling allows us to calculate the pollution concentration that is poured in a region of the space in such a way that at time t?=?T, the pollution concentration is as close as possible to the acceptable maximum concentration in the environment. We characterise the optimal control to obtain an optimality system that allows the numerical calculation of the problem and show the convergence of the method. As application, we study the case of the contamination of a river with mercury (Hg) in water without movement and with movement. We present some numerical experiments.