Two-Stage Replacement Strategies

The following replacement problem is considered. N items, which are subject to failure, can be divided into two groups distinguished by the fact that the individual replacement cost in one group is higher than in the other. A strategy is required to minimize replacement costs. In some cases the cheapest policy is to replace each item, when it fails, by a new item. However, the paper shows that this policy can usually be improved upon by what is called a two-stage policy. In a two-stage policy the failures in one group are replaced by new items; those in the other group are replaced by items already operating in the first group. Under some circumstances it is shown to be worth while to create a second group. Formulae are given for calculating the optimum two-stage strategies for any life distribution, but the emphasis is on the formulation of general conditions under which two-stage schemes are preferable to simple replacement. Some extensions and generalizations are briefly indicated.     

工作时间受限的单部件可修系统的维修策略

基于几何过程理论,研究了一类工作时间受限的单部件可修系统的最优更换策略问题.假定系统的维修时间和工作时间都服从一般分布,当工作时间低于预先给定的阈值φ,或当系统的维修次数达到N时,不再维修,而是更换上全新系统.利用更新过程理论,得到了系统平均故障频度和平均可用度等可靠性指标,并给出了系统长期运行单位时间期望效益函数的表达式,最后通过数值模拟讨论了下限阈值和工作次数对最优策略的影响.     

修理工可单重休假的预防维修更换策略

本文研究了一个修理工带有单重休假的单部件可修系统.为了延长系统的使用寿命,在系统故障前考虑了预防维修,且假定预防维修能够“修复如新”,而故障维修为“修复非新”时,以系统的故障次数N为更换策略.通过更新过程和几何过程理论,得出系统经长期运行单位时间内期望费用的明显表达式,并对预防维修的定长间隔时间T及更换策略N进行了讨论,最后,通过实例分析,求出最优策略N’,使得目标函数取得最优值.     

Optimal replacement policy for obsolete components with general failure rates

Identical components are considered, which become obsolete once new‐type ones are available, more reliable and less energy consuming. We envision different possible replacement strategies for the old‐type components by the new‐type ones: either purely preventive, where all old‐type components are replaced as soon as the new‐type ones are available; either purely corrective, where the old‐type ones are replaced by new‐type ones only at failure; or a mixture of both strategies, where the old‐type ones are first replaced at failure by new‐type ones and next simultaneously preventively replaced after a fixed number of failed old‐type components. To evaluate the respective value of each possible strategy, a cost function is considered, which represents the mean total cost on some finite time interval [0, t]. This function takes into account replacement costs, with economical dependence between simultaneous replacements, and also some energy consumption (and/or production) cost, with a constant rate per unit time. A full analytical expression is provided for the cost function induced by each possible replacement strategy. The optimal strategy is derived in long‐time run. Numerical experiments conclude the paper. Copyright © 2008 John Wiley & Sons, Ltd.     

On a scheme for predictive maintenance

An operating system contains a replaceable unit whose wear (i.e. accumulated amount of damage) can be observed over time. When the wear reaches a certain level the unit is no longer able to function satisfactorily and needs to be replaced. Although units are produced to the same nominal specification there is still some random variation among them in their wear rates. This will be expressed by incorporating a random effect, or frailty term, in the model for individual degradation. There are costs for observing the wear on a unit, for replacing a unit, and for allowing a unit to fail before being replaced. When the last cost is comparatively large replacement before failure is preferable. For some standard examples of wear processes the lifetime distributions are obtained and the cost consequences of particular maintenance schemes are investigated.     

Bivariate lifetime distributions and optimal replacement

The assumption that components which are part of a technical system work independently seems not appropriate in a number of applications. A lot of multivariate extensions of the univariate exponential distribution have been suggested as lifetime distributions. But only the models of J. E. Freund and of A. W. Marshall and I. Olkin seem to be physically motivated. A combination of these approaches yields a bivariate lifetime distribution which is investigated in some detail. Applications of this bivariate lifetime model are considered in preventive maintenance. In a two-component parallel system the optimal replacement time shall be determined with respect to the total expected discounted cost criterion. Results of the theory of stochastic processes are used to obtain the optimal strategy for different information levels. Some numerical examples based on a two-component parallel system with dependent component lifetimes show how the optimal replacement policy depends on the different information levels and on the degree of dependence of the components.     

Leader-follower strategy via a sliding mode approach

In this paper, the decision making problem in continuoustime dynamic systems is considered for the situation with two decision makers and a hierarchical decision structure. The leader-follower strategy is studied. To implement the leader's strategy, we propose to use a sliding mode approach, which allows the leader to constrain the state of the system within some manifold of the state space and forces the follower to choose the strategy preferable for the leader. The corresponding sliding manifolds are derived from the classical variational problem formulation for a class of systems whose right-hand side is affine with respect to the two control inputs. Numerical examples are considered with simulations to illustrate the technique.The authors wish to express their thanks to Dr. Vadim Utkin for his helpful discussions.     

Dialogue strategy for horizontal communication in MAS organization

A multi agent organization model defines the structure, roles, interaction ways and coordination styles of a multi agent system. Multi agent organizations may constrain the communication between included members. Organizations’ communication is the process of sending or receiving all the messages through a group of agents in order to achieve common goals. In a dialogue, agents follow some rules that define the permissive speech acts called dialogue protocol. Aiming for common goals, the dialogue strategy is the policy of agents to choose a particular speech act among the allowed ones by the protocol. In this paper a formal model for dialogue strategy for a group of agents in an organization is proposed in order to choose the most preferable speech acts. The argumentation theory is applied to the proposed method to define the values of plausible speech acts and to rank them. The algorithm finds the best option to utter and also it decreases the volume of exchanging messages. The proposed dialogue strategy is illustrated via a deliberation dialogue example in a group of agents.     

基于消费者异质性社交能力的推荐奖励策略

从消费者社交性的视角优化推荐奖励策略。文章基于效用理论,分析消费者的购买和推荐行为。构建了当期利润最大化基本模型和纳入远期利益的扩展模型,优化产品价格和折扣,给出高低折扣策略的适用空间,并探讨消费者社交能力对企业利润和社会绩效的影响。结果显示,消费者的社交能力差异较小时适合采取高折扣策略,否则适宜低折扣策略。当企业考虑远期利益的时候,企业的最优策略是免费策略。随着环境参数变化,最优奖励策略由高折扣调整为低折扣时会带来福利损失,但低折扣策略并不必定导致社会福利的损失。此外,还给出了实践中某些商品价格虚高的经济解释。本研究能够为企业实施推荐计划制定奖励策略提供依据。     

On the asymptotics of fault probability in least‐recently‐used caching with Zipf‐type request distribution

We consider the least‐recently‐used cache replacement rule with a Zipf‐type page request distribution and investigate an asymptotic property of the fault probability with respect to an increase of cache size. We first derive the asymptotics of the fault probability for the independent‐request model and then extend this derivation to a general dependent‐request model, where our result shows that under some weak assumptions the fault probability is asymptotically invariant with regard to dependence in the page request process. In a previous study, a similar result was derived by applying a Poisson embedding technique, where a continuous‐time proof was given through some assumptions based on a continuous‐time modeling. The Poisson embedding, however, is just a technique used for the proof and the problem is essentially on a discrete‐time basis; thus, it is preferable to make assumptions, if any, directly in the discrete‐time setting. We consider a general dependent‐request model and give a direct discrete‐time proof under different assumptions. A key to the proof is that the numbers of requests for respective pages represent conditionally negatively associated random variables. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

A unified treatment of single component replacement models

In this paper we discuss a general framework for single component replacement models. This framework is based on the regenerative structure of these models and by using results from renewal theory a unified presentation of the discounted and average finite and infinite horizon cost models is given. Finally, some well-known replacement models are discussed, and making use of the previous results an easy derivation of their cost functions is presented.     

Evaluating Recruitment Strategies Using Fuzzy Set Theory in Stochastic Manpower Planning

Abstract

One aspect of Manpower Planning is the investigation of wastage and internal transitions for homogeneous groups of employees in a Manpower system. In the relevant literature, the attainability of a desired stock vector was studied under control by recruitment for time-discrete Markov models. These approaches allow choosing a proper recruitment strategy, resulting in an attainable vector most similar to a desired one. In this article, this problem will be discussed under stochastic assumptions for attainability after one step. Based on fuzzy set theory, a procedure is introduced that allows evaluating and comparing recruitment strategies, resulting in the determination of a most preferable strategy.     

Modified Two-Point Stepsize Gradient Methods for Unconstrained Optimization

For unconstrained optimization, the two-point stepsize gradient method is preferable over the classical steepest descent method both in theory and in real computations. In this paper we interpret the choice for the stepsize in the two-point stepsize gradient method from the angle of interpolation and propose two modified two-point stepsize gradient methods. The modified methods are globally convergent under some mild assumptions on the objective function. Numerical results are reported, which suggest that improvements have been achieved.     

Morita equivalence for infinite matrix rings

In this paper, weak distinguished subcategory and distinguished subcategory of modules are introduced. Left(right) local unital rings are particularly considered. Also, representable equivalent functors between categories. By using the replacement techniques of modules, a general theory of Morita equivalence for infinite matrix rings is established. This theory not only extends the classical Morita theory of equivalence from finite matrix rings to infinite matrix rings and also contains some new results which are useful in studying the algebraic structures for infinite matrix rings. Some results of classical Morita theory are included as its special cases.     

基于截断δ-冲击模型的不完全维修更换策略

本文在截断δ-冲击模型的基础上,考虑了因系统劣化而导致的冲击失效门限值与维修时间的变化,扩充失效状态,从而提出一种新的截断δ-冲击模型。以最小费用为目标,稳态可用度为约束条件,建立N型更换策略的不完全维修更换策略模型,并给出三种常用冲击到达间隔分布的期望寿命。最后通过算例验证模型的有效性,并对参数进行灵敏度分析。     

Limit theorems for triangular urn schemes

We study a generalized Pólya urn with balls of two colours and a triangular replacement matrix; the urn is not required to be balanced. We prove limit theorems describing the asymptotic distribution of the composition of the urn after a long time. Several different types of asymptotics appear, depending on the ratio of the diagonal elements in the replacement matrix; the limit laws include normal, stable and Mittag-Leffler distributions as well as some less familiar ones. The results are in some cases similar to, but in other cases strikingly different from, the results for irreducible replacement matrices.     

Optimal maintenance strategy for non‐renewing replacement–repair warranty

In this paper, we study the maintenance policy following the expiration of the non‐renewing replacement–repair warranty (NRRW). For such purposes, we first define the non‐renewing free replacement–repair warranty and the non‐renewing pro rata replacement–repair warranty. Then the maintenance model following the expiration of the NRRW is discussed from the user's point of view. As the criterion to determine the optimal maintenance strategy, we formulate the expected cost rate per unit time from the user's perspective. All system maintenance costs incurred after the warranty is expired are paid by the user. Given the cost structures during the life cycle of the system, we determine the optimal maintenance period following the expiration of the NRRW. Finally, a few numerical examples are given for illustrative purposes. Copyright © 2012 John Wiley & Sons, Ltd.     

基于优惠合同的在线租赁策略设计

近年来租赁行业竞争日益激烈,租赁企业为了吸引客户有时会开展一些优惠活动。针对这一现状,本文讨论了存在优惠合同时承租方的在线租赁决策问题,其中假设该优惠合同 给予承租方一次以比较优惠的价格连续租赁设备多期的机会。首先,分析了存在优惠合同时的最优离线策略。其次,利用在线算法和竞争比理论分别设计了承租方放弃优惠合同和签订优惠 合同两种情形下的最优在线策略及最优竞争比。最后,通过汽车租赁优惠的数值算例说明选择签订优惠合同是更好的策略,进一步给出了签订优惠合同和购买设备的最佳时间。     

修理设备可更换且修理延迟的两相同部件冷储备可修系统(Ⅱ)

在文[1]的基础上,本文研究了修理有延迟和修理设备可更换的两单元冷储备可修系统.在假定单元的寿命服从指数分布、修理时间和延迟时间服从一般分布、修理设备的寿命和故障后的更换时间服从指数分布下,通过定义修理设备的"广义忙期",使用更新过程理论和全概率分解技术,提出一种新的分析技巧,讨论了修理设备的一些可靠性指标,获得了如修理设备的可用度和故障次数等可靠性结果.