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.     

An age replacement policy via the Bayesian method

This article aims to estimate the probability of item replacement on an age replacement policy. An item is replaced until time T, or until a first non-repairable catastrophic failure occurs – whichever comes first. Because the sample size is relatively small under the replacement policy, we use a Bayesian approach to estimate probability. A prior choice is undoubtedly closely related to the problem under consideration. Here, we consider the (Jeffreys (1961 Jeffreys, H. 1961. Theory of Probability, Oxford: Clarendon Press.  [Google Scholar]), Theory of Probability, Oxford: Clarendon Press) prior and the conjugate prior that are justified to some extent. We also derive some approximations of the posterior and discuss certain special cases. Our objective is to determine an optimal replacement policy in which the long-run average cost per unit time is minimised. We also assume that some catastrophic failures can be repaired. On the spectrum of long-run average costs per unit time, our cost is smaller than others. Here, we use numerical examples to illustrate some known models, and make some comparisons as well.     

An optimal replacement policy for repairable cold standby system with priority in use

In this article, a cold standby repairable system consisting of two nonidentical components and one repairman is studied. It is assumed that component 2 after a repair is “as good as new” while component 1 after a repair is not, but component 1 is given priority in use. Under these assumptions, by using the geometric process repair model, we consider a replacement policy N based on the number of failures of component 1 under which the system is replaced when the number of failures of component 1 reaches N. Our problem is to determine an optimal policy N* such that the long-run average cost per unit time (i.e. the average cost rate) of the system is minimized. The explicit expression of the average cost rate of the system is derived and the corresponding optimal replacement policy N* can be determined numerically. Finally, a special system with Weibull-distributed working time and repair time of component 1 is given to illustrate the theoretical results in this article.     

Extended optimal replacement policy for a two-unit system with failure rate interaction and external shocks

This study presents an extended replacement policy for a two-unit system which is subjected to shocks and exhibits failure rate from interaction. The external shocks that affect the system are of two types. A type I shock causes a minor failure of unit-A and the damage that is caused by such a failure affects unit-B, whereas a type II shock causes a total failure of the system (catastrophic failure). All unit-A failures can be recovered by making minimal repairs. The system also exhibits the interaction between the failure rates of units: a failure of any unit-A causes an internal shock that increases the failure rate of unit-B, whereas a failure of a unit-B causes instantaneous failure of unit-A. The goal of this study is to derive the long-run cost per unit time of replacement by introducing relative costs as a factor in determining optimality; then, the optimal replacement period, T*, and the optimal number of unit-A failures, n*, which minimise that cost can be determined. A numerical example illustrates the method.     

A multi-criteria optimal replacement policy for a system subject to shocks

A system is subject to shocks that arrive according to a non-homogeneous Poisson process. As these shocks occur, the system experiences one of two types of failures: a type-I failure (minor), rectified by a minimal repair; or a type-II failure (catastrophic) that calls for a replacement. In this study, we consider a multi-criteria replacement policy based on system age, nature of failure, and entire repair-cost history. Under such a policy, the system is replaced at planned life time T, or at the nth type-I failure, or at the kth type-I failure (k < n) at which the accumulated repair cost exceeds the pre-determined limit, or at the first type-II failure, whichever occurs first. An optimal policy over the control parameters is studied analytically by showing its existence, uniqueness, and structural properties. This model is a generalization of several existing models in the literature. Some numerical examples are presented to show several useful insights.     

Number-dependent replacement model with random lead-time for systems under maintenance continuously

This article considers a number-dependent replacement policy where a system has two types of failures and is replaced at the nth type I failure (minor failure) or first type II failure (catastrophic failure), whichever occurs first where type I and type II failures are age dependent. Type I failures can be removed by restoration without any cost, since the maintenance work is executed continuously during the operation of the system. However, type II failure can be removed only through a replacement at a replacement cost. A spare unit for replacement can be delivered upon order and is available only when the random lead-time is finished. A model is developed for the average cost per unit time and is based on the stochastic behaviour of the assumed system and reflects the cost of storing a spare as well as system downtime. The optimal number for a minimum-cost policy is described and discussed. It is shown that the optimal number n* which minimises the cost rate is given by a unique solution of the equation under certain conditions.     

Window‐LRFU: a cache replacement policy subsumes the LRU and window‐LFU policies

Replacement algorithms have been widely used as key technologies for cache management in areas such as file systems or database management. A replacement algorithm determines which page to be evicted when the cache is full and a new page is referenced. Because replacement policies considering only recency or frequency such as LRU (Least Recently Used) and LFU (Least Frequently Used) do not perform well, replacement polices that take both recency and frequency into account have been intensively studied. As a classical replacement policy, LRFU (Least Recently/Frequently Used) policy subsumes the LRU and LFU policy. However, because LFU is not able to adapt to the change of page accessing pattern and it is hard to select a suitable λ for each certain trace, LRFU cannot always guarantee a good performance. In this paper, we propose a Window‐LRFU policy, to subsume the LRU and Window‐LFU policies. Experimental results show that the Window‐LRFU policy outperforms LRFU and has at least competitive performance than other classical algorithms. Copyright © 2015 John Wiley & Sons, Ltd.     

基于Web访问特性的缓存替换策略

在分析Web轨迹的基础上,找出用户访问Web内容的访问特性:访问再次到达的概率和访问内容大小分布,并建立相应的代价公式,利用这些代价作为计算Web内容价值的要素.根据这些特性判断用户访问内容被再次访问的可能性,提出内容分发网络缓存替换策略.最后通过数值仿真计算与现有替换策略进行比较,说明了该替换策略的优越性.     

Optimal replacement policy for a repairable system with multiple vacations and imperfect fault coverage

The present investigation deals with the reliability analysis of a repairable system consisting of single repairman who can take multiple vacations. The system failure may occur due to two types of faults termed as major and minor. When the system has failed due to minor faults, it is perfectly recovered by the repairman. If the system failure is due to major faults, there are some recovery levels/procedures that recover the faults imperfectly with some probability. However, the system cannot be repaired in ‘as good as new’ condition. It is assumed that the repairman can perform some other tasks when either the system is idle or waiting for recovery from the faults. The life time of the system and vacation time of the repairman are assumed to be exponential distributed while the repair time follows the general distribution. By assuming the geometric process for the system working/vacation time, the supplementary variable technique and Laplace transforms approach are employed to derive the reliability indices of the system. We propose the replacement policy to maximize the expected profit after a long run time. The validity of the analytical results is justified by taking numerical illustrations.     

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.     

An economic production quantity model for deteriorating items with preventive maintenance policy and random machine breakdown

In recent years, many researches on economic production quantity (EPQ) models with machine breakdown and preventive maintenance have been developed, but few of them have developed integrated models for deteriorating items. In this study, we develop EPQ models for deteriorating items with preventive maintenance, random machine breakdown and immediate corrective action. Corrective and preventive maintenance times are assumed to be stochastic and the unfulfilled demands are lost sales. Two EPQ models of uniform distribution and exponential distribution of corrective and maintenance times are developed. An example and sensitivity analysis is given to illustrate the models. For the exponential distribution model, it is shown that the corrective time parameter is one of the most sensitive parameters to the optimal total cost.     

Optimum random and age replacement policies for customer-demand multi-state system reliability under imperfect maintenance

This paper proposes the generalised random and age replacement policies for a multi-state system composed of multi-state elements. The degradation of the multi-state element is assumed to follow the non-homogeneous continuous time Markov process which is a continuous time and discrete state process. A recursive approach is presented to efficiently compute the time-dependent state probability distribution of the multi-state element. The state and performance distribution of the entire multi-state system is evaluated via the combination of the stochastic process and the Lz-transform method. The concept of customer-centred reliability measure is developed based on the system performance and the customer demand. We develop the random and age replacement policies for an aging multi-state system subject to imperfect maintenance in a failure (or unacceptable) state. For each policy, the optimum replacement schedule which minimises the mean cost rate is derived analytically and discussed numerically.     

Service networks with multichannel nodes in a random environment

Service networks with multichannel nodes of semi-Markovian type are considered. The parameters of a source of demands depend on the state of the Markovian random environment. For the process of servicing demands, the conditions of existence of a stationary mode are found, and the properties of stationary distribution in terms of spectral characteristics of the routing matrix are investigated. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 167–172, January–February, 2000.     

Optimal imperfect preventive maintenance policies for a used system

In some practical situations, it may be more economical to work a used system than do a new one. From this viewpoint, this article considers three basic preventive maintenance (PM) policies for a used system: the system with initial variable damage Y ₀ begins to operate at time 0, and suffers damage due to shocks. It fails when the total damage exceeds a failure level K and corrective maintenance is made immediately. To prevent such failure, it undergoes PM at a planned time T, a shock number N and a damage level k, but maintenances are imperfect. However, failure rate of a used system maybe higher than that of a new one, so some maintenance is applied to the policies at each shock in the extended models. Using the theory of cumulative processes, expected cost rate models are obtained, optimal policies which minimise them are derived analytically and discussed numerically.     

数控机床功能部件可靠度建模与维护预警系统开发*

为了提高机床可靠性,深入分析了机床功能部件故障数据,研究了采用两重威布尔分段模型建立机床功能部件可靠度分布模型的方法与极大似然方法确定模型参数的过程。提出了基于可靠性分析的机床维护预警系统开发,阐述了预警系统原理设计过程与功能模块设计方法。系统的实例应用表明,该方法对机床预防维护非常合理有效。     

Integrated scheduling and flexible maintenance in deteriorating multi-state single machine system using a reinforcement learning approach

This paper studies an integrated optimization problem of production scheduling and flexible preventive maintenance (PM) in a multi-state single machine system with deteriorating effects. A flexible PM strategy is proposed to proactively cope with machine failures while ensuring relatively regular PM intervals, which is composed of time-based PM (TBPM) and condition-based PM (CBPM). TBPM is conducted within every flexible time window and CBPM is implemented immediately after the most deteriorated yet still functional state. An illustrative case is presented using the enumeration approach to demonstrate the integration of production scheduling and machine maintenance. Then, Q-learning-based solution framework (QLSF) is further designed with proper state and action sets and reward functions to facilitate the determination of appropriate production scheduling rule under the constraint of the flexible maintenance. Numerical experiments show that the proposed QLSF outperforms the other four state-of-the-art scheduling rules in different scenarios. Moreover, the performance of the proposed flexible PM strategy is also examined and validated in comparison with three candidate maintenance strategies, i.e., run-to-failure corrective maintenance (CM), combination of TBPM and CM, and CBPM. The proposed flexible maintenance and solution approach can enrich the relevant academic knowledge base, and provide managerial insights and guidance in practical production systems.     

基于密文策略属性基加密系统访问机制的缓存替换策略

为提高基于密文策略属性基加密（CP-ABE）系统的数据缓存性能,针对CP-ABE加密的数据,提出一种有效的缓存替换算法--最小属性价值（MAV）算法。该算法结合CP-ABE加密文件的访问策略并统计高频属性值的个数,利用余弦相似度方法和高频属性值统计表来计算属性相似度;同时结合属性相似度和文件大小计算缓存文件的属性值价值,并替换属性值价值最小的文件。在与最近最少使用（LRU）、最不经常使用（LFU）、Size缓存替换算法的对比实验中,针对CP-ABE加密后的数据,MAV算法在提高加密文件请求命中率和字节命中率方面具有更好的性能。     

Preventive maintenance and replacement scheduling for repairable and maintainable systems using dynamic programming

This paper presents mathematical models and a solution approach to determine the optimal preventive maintenance schedules for a repairable and maintainable series system of components with an increasing rate of occurrence of failure (ROCOF). The maintenance planning horizon has been divided into discrete and equally-sized periods and in each period, three possible actions for each component (maintain it, replace it, or do nothing) have been considered. The optimal decisions for each component in each period are investigated such that the objectives and the requirements of the system can be achieved. In particular, the cases of minimizing total cost subject to a constraint on system reliability, and maximizing system reliability subject to a budgetary constraint on overall cost have been modeled. As the optimization methodology, dynamic programming combined with branch-and-bound method is utilized and the effectiveness of the approach is presented through the use of a numerical example. Such a modeling approach should be useful for maintenance planners and engineers tasked with the problem of developing recommended maintenance plans for complex systems of components.     

Efficient learning using a virtual learning environment in a university class

This study examines a blended learning setting in an undergraduate course in psychology. A virtual learning environment (VLE) complemented the face-to-face lecture. The usage was voluntary and the VLE was designed to support the learning process of the students. Data from users (N = 80) and non-users (N = 82) from two cohorts were collected. Control variables such as demographical data, attitude towards the learning subject, computer literacy, motivation, learning effort and available infrastructure were captured by means of a self-report. As a learning outcome, the grade in the final exam was included. For the VLE-users, the mean performance in the VLE was taken as a predictor for success in the final exam. Two different groups of VLE-users were observed and classified into ’light and ’heavy’ users. The results showed that among those students who had spent two or more hours per week for pre- and post processing of the lectures, ‘heavy’ VLE-users performed better than non-users in the final exam. Additionally, the ‘heavy’ users’ performance in the VLE was the best predictor for the grade in the final exam. We discuss the results in the context of self-regulated learning competence.     

Optimal routing policy of a stochastic-flow network

Under the assumption that each arc’s capacity of the network is deterministic, the quickest path problem is to find a path sending a given amount of data from the source to the sink such that the transmission time is minimized. However, in many real-life networks such as computer systems, telecommunication systems, etc., the capacity of each arc is stochastic due to failure, maintenance, etc. Such a network is named a stochastic-flow network. Hence, the minimum transmission time is not fixed. We try to evaluate the probability that d units of data can be sent through the stochastic-flow network within the time constraint according to a routing policy. Such a probability is named the system reliability, which is a performance index to measure the system quality. This paper mainly finds the optimal routing policy with highest system reliability. The solution procedure is presented to calculate the system reliability with respect to a routing policy. An efficient algorithm is subsequently proposed to derive the optimal routing policy.