Optimal number of minimal repairs before replacement based on a cumulative repair-cost limit policy

In this paper, we consider a replacement model with minimal repair based on a cumulative repair-cost limit policy, where the information of all repair costs is used to decide whether the system is repaired or replaced. As a failure occurs, the system experiences one of the two types of failures: a type-I failure (repairable) with probability q, rectified by a minimal repair; or a type-II failure (non-repairable) with probability p (=1 − q) that calls for a replacement. Under such a policy, the system is replaced anticipatively 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 threshold, or any type-II failure, whichever occurs first. The object of this paper is to find the optimal number of minimal repairs before replacement that minimizes the long-run expected cost per unit time of this polish. Our model is a generalization of several classical models in maintenance literature, and a numerical example is presented for illustration.     

Optimal number of minimal repairs before replacement of a deteriorating system with inspections

In this study, we propose a generalised replacement model for a deteriorating system with failures that could only be detected through inspection work. The system is assumed to have two types of failures and is replaced at the Nth type I failure (minor failure) or first type II failure (catastrophic failure), depending on whichever occurs first. The probability of type I and II failures depends on the number of failures since the last replacement. Such systems can be repaired upon type I failure, but are stochastically deteriorating, that is, the lengths of the operating intervals are stochastically decreasing, whereas the durations of the repairs are stochastically increasing. Then, the expected net cost rate is obtained. Some special cases are considered. Finally, a numerical example is provided.     

Optimal number of minimal repairs with cumulative repair cost limit for a two-unit system with failure rate interactions

A discrete replacement model is presented that includes a cumulative repair cost limit for a two-unit system with failure rate interactions between the units. We assume a failure in unit 1 causes the failure rate in unit 2 to increase, whereas a failure in unit 2 causes a failure in unit 1, resulting in a total system failure. If unit 1 fails and the cumulative repair cost till to this failure is less than a limit L, then unit 1 is repaired. If there is a failure in unit 1 and the cumulative repair cost exceeds L or the number of failures equals n, the entire system is preventively replaced. The system is also replaced at a total failure, and such replacement cost is higher than the preventive replacement cost. The long-term expected cost per unit time is derived using the expected costs as the optimality criterion. The minimum-cost policy is derived, and existence and uniqueness are proved.     

Some replacement policies with minimal repairs and repair cost limit

Some extended replacement policies based on the number of failures, incorporating the concept of repair cost limit are discussed. Three models are considered as follows: (a) a unit is replaced at the nth failure, or when the estimated minimal repair cost exceeds a particular limit c; (b) a unit has two types of failures and is replaced at the nth type 1 failure, or type 2 failure, or when the estimated repair cost of type 1 failures exceeds a predetermined limit c—type 1 failures are minimal; failures, type 2 failures are catastrophic failures and both occur with constant probability; (c) a unit has two types of failures and the type 1 and type 2 failures are age dependent—the unit is replaced at the nth type 1 failure, type 2 failure, or when the estimated repair cost due to type 1 failures exceeds a predetermined limit c. Introducing costs due to replacements, inspections, and minimal repairs, an optimal number of minimal repairs before replacement is obtained, which minimizes the expected cost rate. Some particular cases are also derived. Finally, the application of these models to computer science is discussed.     

Optimal number of repairs before replacement for a two-unit system subject to non-homogeneous pure birth process

We consider a discrete replacement model for a two-unit system subject to failure rate interaction and shocks. Two types of shocks occur according to a non-homogeneous pure birth process and can affect the two-unit system. Type I shock causes unit A to fail and can be rectified by a general repair, while type II shock results in a non-repairable failure and must be fixed by a replacement. Two-unit systems also exhibit failure rate interactions between the units: each failure of unit A causes some damage to unit B, while each failure of unit B causes unit A into an instantaneous failure. The occurrence of a particular type of shock is dependent on the number of shocks occurred since the last replacement. The objective of this paper is to determine the optimal number of minor failures before replacement that minimizes the expected cost rate. A numerical example is presented to illustrate application of the model.     

Optimal age-replacement time with minimal repair based on cumulative repair cost limit and random lead time

In this article, we consider an age-replacement model with minimal repair based on a cumulative repair cost limit and random lead time for replacement delivery. A cumulative repair cost limit policy uses information about a system's entire repair cost history to decide whether the system is repaired or replaced; a random lead time models delay in delivery of a replacement once it is ordered. A general cost model is developed for the average cost per unit time based on the stochastic behaviour of the assumed system, reflecting the costs of both storing a spare and of system downtime. The minimum-cost policy time is derived, its existence and uniqueness is shown, and structural properties are presented. Various special cases are included. Because the framework and analysis are general, the proposed model extends several existing results. Finally, a numerical example is provided for illustration.     

Optimal number of minor failures before replacement

This paper extends a replacement model based on failure number to include a repair-cost limit for general failure distributions. The stochastic behaviour of failures and repair costs are modelled by a non-homogeneous Poisson process. An efficient marginal analysis algorithm is presented for finding the optimal failure number for replacement that minimizes the average cost rate.     

A generalized model for jointly determining the optimal ordering point and the optimal number of minimal repairs before replacement

Many maintenance policies have assumed that whenever a unit is to he replaced, a new unit is immediately available. However, if the procurement lead time is not negligible, an ordering policy should be considered that determines when to order a spare and when to replace the operating unit after it has begun operating. A generalized model is presented to jointly determine the optimal ordering point and the optimal number of minimal repairs before replacement. By introducing costs due to ordering, repairs, shortage and holding, the expected cost per unit time in the long run is derived as a criterion of optimality, and the optimal ordering point and the optimal number of minimal repairs before replacement are sought by minimizing that cost. Various special cases are discussed. Finally, a numerical example is given.     

基于预测的Web缓存替换策略

为提高Web缓存性能，在缓存替换算法的基础上加入预测机制，提出了基于预测的Web替换策略P-Re。预测算法采用PPM上下文模型，当缓存空间不够用来存放新的对象时，P-Re选择键值较小且未被预测到的对象进行替换。实验表明，基于预测的Web缓存替换算法P-Re相对于传统替换算法而言具有较高的命中率和字节命中率。     

Optimal replacement policy for a deteriorating production system with preventive maintenance

This paper presents a new policy for determining the optimal replacement time of a deteriorating production system. The optimal replacement time is expressed in terms of the accumulated number of failures that the system has experienced. The provision of preventive maintenance is incorporated in the system model and the objective function is cost efficiency (i.e. the long-run average cost per unit working time). A numerical example is given in the paper. The basic concept used in this paper parallels the geometric process replacement policy N introduced by Lam in 1988. The work in this paper generalizes and modifies Lam's 1988 work.     

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.     

Preventive replacement policies with time of operations,mission durations,minimal repairs and maintenance triggering approaches

When a mission arrives at a random time and lasts for a duration, it becomes an interesting problem to plan replacement policies according to the health condition and repair history of the operating unit, as the reliability is required at mission time and no replacement can be done preventively during the mission duration. From this viewpoint, this paper proposes that effective replacement policies should be collaborative ones gathering data from time of operations, mission durations, minimal repairs and maintenance triggering approaches. We firstly discuss replacement policies with time of operations and random arrival times of mission durations, model the policies and find optimum replacement times and mission durations to minimize the expected replacement cost rates analytically. Secondly, replacement policies with minimal repairs and mission durations are discussed in a similar analytical way. Furthermore, the maintenance triggering approaches, i.e., replacement first and last, are also considered into respective replacement policies. Numerical examples are illustrated when the arrival time of the mission has a gamma distribution and the failure time of the unit has a Weibull distribution. In addition, simple case illustrations of maintaining the production system in glass factories are given based on the assumed data.     

Optimal number of hosts in a distributed system based on cost criteria

Redundant or distributed systems are increasingly used in system design so that the required reliability and availability can be easily achieved. However, such an approach requires additional resources that can be very costly. Hence, how to design and test such a system in the most cost-effective way is of concern to the developers. A general cost model and a solution algorithm are presented for the determination of the optimal number of hosts and optimal system debugging time that minimize the total cost while achieving a certain performance objective. During testing, software faults are corrected and the reliability shows an increasing trend, and hence system reliability increases. A general system model is constructed based on a Markov process with software reliability and availability obtained from software reliability growth models. The optimization problem is formulated based on the cost criteria and the solution procedure is described. An application example is presented.     

Optimal replacement policy for a two-dissimilar-component cold standby system with different repair actions

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. When failures occur, the repair of both component 1 and component 2 are not ‘as good as new’. The consecutive operating times of component 1 after repair constitute a decreasing geometric process, while the repair times of component 1 are independent and identically distributed. For component 2, its failure is rectified by minimal repair, and the repair time is negligible. Component 1 has priority in use when both components are good. The replacement policy N is based on the failure number of component 1. Under policy N, we derive the explicit expression of the long-run average cost rate C(N) as well as the average number of repairs of component 2 before the system replaced. The optimal replacement policy N*, which minimises the long-run average cost rate C(N), is obtained theoretically. If the failure rate r(t) of component 2 is increasing, the existence and uniqueness of the optimal policy N* is also proved. Finally, a numerical example is given to validate the developed theoretical model. Some sensitivity analyses are provided to show the influence of some parameters, such as the costs for replacement and repair, and the parameters of the lifetime and repair time distributions of both components, to the optimal replacement policy N* and corresponding average cost rate C(N*).     

Testing using a minimal number of instructions

A new technique to test microprocessor chips is presented in this article. The basic test philosophy adopted is to partition a microprocessor's instructions into several sets. Instructions which affect the identical modules inside the processor are grouped into the same set. The appropriate subset of each instruction set is exercised and if the results are satisfactory, then the microprocessor is assumed to be functioning correctly. The instruction subsets form a test sequence for the microprocessor. Stuck-at faults at the address lines, the data lines and at the output of some of the internal modules are also detected by the test sequence.     

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.     

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。     

命名数据网络中基于数据请求代价与流行度的动态替换策略

针对怎样高效地对命名数据网络(NDN)缓存中的数据进行替换的问题,提出了一种综合考虑数据流行度与数据请求代价的数据替换策略。该策略根据数据的请求时间间隔动态地分配数据流行度因子与数据请求代价因子的比重,使节点缓存高流行度与高请求代价的数据。当用户下次请求数据时能够从本节点获取,降低数据请求的响应时间并减少链路拥塞。仿真结果表明,本策略能够有效提高网内存储命中率,降低用户获取数据的时间以及缩短用户获取数据的距离。     

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.     

Controller design based on a limit criterion

Controller design and tuning are mostly aimed at minimization of the variance of the error signal. In many situations, however, one is more interested in keeping this signal within some (safety or quality) limits as long as possible. Using the classical Wiener filter theory, a controller design is presented that minimizes the expected number of crossings per unit time of some specified level. Results obtained by simulation are included.