The Optimum Repair Limit Replacement Policies

This paper considers a single unit system which is first repaired if it fails. If the repair is not completed up to the fixed repair limit time then the unit under repair is replaced by a new one. The cost functions are introduced for the repair and the replacement of the failed unit. The optimum repair limit replacement time minimizing the expected cost per unit of time for an infinite time span is obtained analytically under suitable conditions. Two special cases where the repair cost functions are proportional to time and are exponential are discussed in detail with numerical examples.     

Optimal Repair Limit Replacement Policies with Imperfect Repair

This paper considers the repair limit replacement policies with imperfect repair. The repair is imperfect in the sense that the mean life of a repaired system is less than the mean life of a new system. Furthermore, we examine the repair limit replacement policy for the case in which there are two types of repair-local and central repair. The local repair is imperfect whilst the central repair is perfect (i.e. the system is as good as new after central repair). The optimal policies are derived to minimize the expected cost per unit of time for an infinite time span. Analytical results are presented along with numerical examples.     

A Note on the Repair Limit Replacement Policy

In this note we show that the results of Nakagawa and Osaki are optimal over both deterministic and random repair limit policies.     

A Combined Block and Repair Limit Replacement Policy

This paper considers a combined block and repair limit replacement policy. The policy is defined as follows:

• (i) The unit is replaced preventively at times kT(k=1, 2…
• (ii) For failures in [(k - 1)T, kT) the unit undergoes minimal repair if the estimated repair cost is less than x. Otherwise it is replaced by a new one.

The optimal policy is to select T* and x* to minimize the expected cost per unit time for an infinite time span. A numerical example is given to illustrate the method.     

Utilizing Weibull Failure Rates in Repair Limit Analysis for Equipment Replacement/Preventive Maintenance Decisions

Repair limit analysis was originally proposed as a methodology for determining whether to repair or to replace an operating unit. The approach structures the problem as a Markov or semi-Markov decision process in which state-dependent repair limits trigger the replacement decision. Such a basic framework can easily be applied to more general equipment repair/overhaul environments in which typical maintenance condition monitoring information can serve as the overhaul trigger. One unnecessary limitation of repair limit analysis found in the literature is the use of a constant force of mortality within each state of the model. The purpose of this paper is to extend the repair limit analysis by incorporating a changing force of mortality as the unit ages. In this way, the analysis is more flexible in the parameter estimation phase and it is argued here more appealing since a changing (and usually increasing) force of mortality is utilized in equipment maintenance environments.     

Replacement Policies under Minimal Repair

In many situations where system failures occur the concept of ‘minimal repair’ is important. A minimal repair occurs when the failed system is not treated so as to return it to ‘as new’ condition but is instead returned to the average condition for a working system of its age. Examples include complex systems where the repair or replacement of one component does not materially affect the condition of the whole system.For a system with decreasing reliability it will become increasingly expensive to maintain operation by minimal repairs, and the question then arises as to when the entire system should be replaced. We consider cases where the failure distribution can be modelled by the Weibull distribution. Two policies have been suggested for this case. One is to replace at a fixed time and the other is to replace at a fixed number of failures. We consider a third policy, to replace at the next failure after a fixed time, and show that it is optimal.Expressions to decide the replacement point and the cost of this policy are derived. Unfortunately these do not give rise to explicit representations, and so they are used to provide extensive numerical comparisons of the policies in a search for effective explicit approximations. Conclusions are drawn from these comparisons regarding the relative effectiveness of the policies and approximations.     

Optimal Continuous Policies for Repair and Replacement

This paper investigates the problem of finding optimal replacement policies for equipment subject to failures with randomly distributed repair costs, the degree of reliability of the equipment being considered as a state of a Markov process. Algorithms have been devised to find optimal combined policies both for preventive replacement and for replacement in case of failure by using repair-limit strategies.First a simple procedure to obtain an optimal discrete policy is described. Then an algorithm is formulated in order to calculate an optimal continuous policy: it is shown how the optimal repair limit is the solution to an ordinary differential equation, and how the value of the repair limit determines the optimal preventive replacement policy.     

Costing a Finite Minimal Repair Replacement Policy

In this paper an integral equation technique is used to evaluate the expected cost for the period (0, t] of a policy involving minimal repair at failure with replacement after N failures. This cost function provides an appropriate criterion to determine the optimal replacement number N* for a system required for use over a finite time horizon. In an example, it is shown that significant cost savings can be achieved using N* from the new finite time horizon model rather than the value predicted by the usual asymptotic model.     

Repair Replacement Modelling over Finite Time Horizons

In this paper an integral equation approach is given for evaluating the expected cost of repair replacement policies over finite time horizons. An asymptotic estimate of this expected cost is also obtained. The policy involving imperfect repair on failure with replacement after N failures is taken as an illustrative example and optimal policies N* are found for both infinite and finite time horizons of use.     

Optimizing System Availability Under Minimal Repair with Non-Negligible Repair and Replacement Times

Availability measures are given for a repairable system under minimal repair with constant repair times. A new policy and an existing replacement policy for this type of system are discussed. Each involves replacement at the first failure after time T, with T representing total operating time in the existing model and total elapsed time (i.e. operating time + repair time) in the new model. Optimal values of T are found for both policies over a wide range of parameter values. These results indicate that the new and administratively easier policy produces only marginally smaller optimal availability values than the existing policy.     

待定无穷小方法在积分型极限中的应用

提出了一种利用待定无穷小求limn→∞∫π20 sinnxdx形式的极限的简单方法,该方法既不需要利用Lebesgue积分的性质,又避免了使用数列极限的ε-N定义,并给出了若干例子.     

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.     

The Stein--Tikhomirov Method and a Nonclassical Central Limit Theorem

We present a simplified version of the Stein--Tikhomirov method realized by defining a certain operator in the class of twice differentiable characteristic functions. Using this method, we establish a criterion for the validity of a nonclassical central limit theorem in terms of characteristic functions.     

变量重排优化Groebner基运算的研究

本文通过使用变量重排的方法,改变了多项式环中理想的Groebner基的计算过程,得到不同的过程的计算效率也不同,因此通过这种方法应该能够找出减少计算Groebner基时间的方法．     

Optimal Replacement Policy for a General Model with Imperfect Repair

A general model is considered which incorporates imperfect repair and repair cost which depends on time and on the number of repairs in the cycle. This model is an extension of models examined previously in the literature. The objective of this paper is to find the optimal replacement policy and compare it with the replacement policies considered earlier for some variants of this model. The form of the optimal replacement policy is found in the general case and the expected average cost per unit time is derived in two special cases. Numerical examples show that the optimal policy is considerably better than the optimal periodic policy. This paper generalizes and unifies previous research in the area.     

案例式中心极限定理教学研究

以案例教学法作为中心极限定理教学的主要手段,选取贴近实际生活的案例——合理规划用电问题和竞争问题,作为教学切入点,激发学生学习兴趣,引导学生从实际情景中发现问题解决问题.课堂实践表明,案例式教学加深了学生对中心极限定理的理解和应用,开阔了学生视野,并对促进课堂教学,课程建设,师生能力提高都有重要意义.     

A Generalized Block Replacement Policy with Minimal Repair and General Random Repair Costs for a Multi-unit System

A generalization of the block replacement policy (BRP) is proposed and analysed for a multi-unit system which has the specific multivariate distribution. Under such a policy an operating system is preventively replaced at times kT (k = 1, 2, 3,...), as in the ordinary BRP, and the replacement of the failed system at failure is not mandatory; instead, a minimal repair to the component of the system can be made. The choice of these two possible actions is based on some random mechanism which is age-dependent. The cost of the ith minimal repair of the component at age y depends on the random part C(y) and the deterministic part C_i(y). The aim of the paper is to find the optimal block interval T which minimizes the long-run expected cost per unit time of the policy.     

延误休假且修理延迟的可修系统的更换策略

研究了修理工多重延误休假且修理延迟的可修系统,假设系统故障后均不能"修复如新",系统在准备休假期间故障的概率为q,系统延迟修理的概率为1-P,以系统故障次数为更换策略,运用更新过程和几何过程理论,得出系统长期运行单位时间内平均停机时间的表达式,并通过数值例子验证了存在最优策略,使得平均停机时间最短.