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.     

Comparison of group replacement policies under minimal repair

Three replacement policies for a group of identical units are compared. ( 1 ) Units are periodically replaced all together. Between the periodic group replacements, minimal repairs are performed at failures. ( 2 ) The group replacement interval is divided into repair and waiting intervals. Minimal repairs are performed at failures during the repair interval, but no repair is made in the waiting interval, and the unit remains failed until the group replacement time comes. ( 3 ) Each unit undergoes minimal repair at failure during the repair interval. Beyond the interval, no repair is made until a number of failures. The expected cost rate expressions under each policy are derived. It is shown that the third policy is better economically than the other two policies. Numerical examples are given to demonstrate the results.     

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 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 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 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.     

Optimum repair limit policies with a time constraint

In this paper, we discuss the optimum repair limit policies with a time constraint. We apply the expected total discounted cost as a criterion and obtain the optimum policies which minimize it. We show that, under certain conditions, there exists a finite and unique optimum policy. Finally, we present a numerical example using a mixed Weibull distribution.     

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.     

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.     

Optimum ordering policies with age-dependent minimal repair and two types of lead times

Two ordering policies for a complex system with age-dependent minimal repair and two types of lead times are considered. Introducing costs due to ordering, repairs, shortage and holding, the expected cost per unit time is derived in the long run as a criterion of optimality and the optimum ordering policies found by minimizing that cost. We show that, under certain conditions, there exists a finite and unique optimum policy. Various special cases are discussed.     

Warranty strategy accounts for bathtub failure rate and random minimal repair cost

This investigation presents a novel repair-replacement warranty strategy. The strategy involves splitting the warranty period into two intervals in which only minimal repairs can be undertaken, separated by a middle interval in which no more than one replacement is allowed. The cost of the i^th minimal repair at age y depends on the random part C(y) and the deterministic part, c_i(y). Distribution functions of failure rates, with a bathtub shape over the lifetime of the product, are also considered. The form of the optimal repair-replacement strategy that minimizes the expected cost of servicing the warranty over the warranty period is discussed as well.     

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.     

Dynamic buffer management with extensible replacement policies

The objective of extensible DBMSs is to ease the construction of specialized DBMSs for nontraditional applications. Although much work has been done in providing various levels of extensibility (e.g., extensibility of data types and operators, query language extensibility, and query optimizer extensibility), there has been very limited research in providing extensibility at the buffer management level. Supporting extensibility at the buffer management level is important as it can contribute significantly to overall system performance. This paper addresses the problem of supporting extensibility of buffer replacement policies. The main contribution is the proposal of a framework for modeling buffer replacement policies. This work is novel in two aspects. First, by providing a uniform and generic specification of buffer replacement policies, the proposed framework unifies existing work in this area. Second, our work introduces a new level of extensibility. None of the existing extensible DBMSs, to our knowledge, provides extensibility at the buffer management level. The proposed framework provides a basis for the construction of an extensible buffer manager as part of a 100% Java-based storage manager. We conducted an extensive performance study to investigate the performance of the proposed framework. The experimental results demonstrate that the proposed framework is indeed feasible for existing DBMSs and improves system performance significantly without costing significant overhead. Edited by M. Kersten     

Optimal maintenance policies with lead times and repair

Maintenance policies with lead times and repair are discussed. We first discuss ordering policy with repair and refer to inspection-ordering policy. In each policy, as a criterion of optimality, we apply cost effectiveness which balances system effectiveness and cost, and obtain the optimal policies. It is shown that, under certain conditions, there exists a finite and unique optimal policy.     

Repair-limit risk-free warranty policies with imperfect repair

The current competitive market environment requires manufacturers to continuously provide better service and support. As a result, warranty considerations emerge as a significant instrument for increasing product marketability. In this paper, we propose a new warranty policy, the repair-limit risk-free warranty with a threshold point on the number of repairs, where replacement is deemed to be more cost effective thereafter. Consumers are better off with this than with a traditional free-repair policy since they could be compensated with a new product in case of premature failures. As for the manufacturers, it not only offers extra marketing incentives, but also reduces the possibility of high-cost lawsuits due to the products with "proven" bad quality. Some useful results of the warranty cost of imperfectly repaired products are derived through a censored quasi-renewal process.     

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.     

Influence maximization with limit cost in social network

Social networking service (SNS) applications are changing the way information spreads in online communities. As real social relationships are projected into SNS applications, word of mouth has been an important factor in the information spreading processes of those applications. By assuming each user needs a cost to accept some specific information, this paper studies the initial "seed user" selection strategy to maximize information spreading in a social network with a cost budget. The main contributions of this paper are: 1) proposing a graphic SEIR model (gSEIR) by extending the epidemic compartmental model to simulate the dynamic information spreading process between individuals in the social network; 2) proposing a formal definition for the influence maximization problem with limit cost (IMLC) in social networks, and proving that this problem can be transformed to the weighted set-cover problem (WSCP) and thus is NP-Complete; 3) providing four different greedy algorithms to solve the IMLC problem; 4) proposing a heuristic algorithm based on the method of Lagrange multipliers (HILR) for the same problem; 5) providing two parts of experiments to test the proposed models and algorithms in this paper. In the first part, we verify that gSEIR can generate similar macro-behavior as an SIR model for the information spreading process in an online community by combining the micro-behaviors of all the users in that community, and that gSEIR can also simulate the dynamic change process of the statuses of all the individuals in the corresponding social networks during the information spreading process. In the second part, by applying the simulation result from gSEIR as the prediction of information spreading in the given social network, we test the effectiveness and efficiency of all provided algorithms to solve the influence maximization problem with cost limit. The result show that the heuristic algorithm HILR is the best for the IMLC problem.     

Consistency and repair for XML write-access control policies

XML access control policies involving updates may contain security flaws, here called inconsistencies, in which a forbidden operation may be simulated by performing a sequence of allowed operations. This article investigates the problem of deciding whether a policy is consistent, and if not, how its inconsistencies can be repaired. We consider total and partial policies expressed in terms of annotated schemas defining which operations are allowed or denied for the XML trees that are instances of the schema. We show that consistency is decidable in PTIME for such policies and that consistent partial policies can be extended to unique least-privilege consistent total policies. We also consider repair problems based on deleting privileges to restore consistency, show that finding minimal repairs is NP-complete, and give heuristics for finding repairs. Finally, we experimentally evaluate these algorithms in comparison with an exact approach based on answer-set programming.     

代理缓存一致性策略和替换策略的研究

针对代理缓存的一致性策略和替换策略还没有很好地结合起来,从而影响了代理缓存系统的整体性能的现状,分别探讨了基于Internet的代理缓存一致性策略和替换策略的处理流程、性能评价指标和研究现状,进而给出将这两种策略结合起来的一致性一替换算法的处理流程,并提出陈旧命中比是其主要性能评价指标,能很好地衡量代理缓存的各种算法的优劣和代理缓存系统的整体性能。     

Optimal age and block replacement policies for a multi-component system with failure interaction

In this paper we consider a generalized age and block replacement policy for a multicomponent system with failure interaction. The i-th component (1 i N) has two types of failures. Type I and type II failures are age dependent. Type I failure (minor failure) is removed by a minimal repair, whereas type II failure (catastrophic failure) induces a total failure of the system (i.e. failure of all other components in the system) and is removed by an unplanned (or unscheduled) replacement of the system. For an age replacement maintenance policy, planned (or scheduled) replacements occur whenever an operating system reaches age T , whereas in the block replacement case, planned replacements occur every T units of time. The aim of this paper is to derive the expected long-run cost per unit time for each policy. The optimal T * which would minimize the cost rate is discussed. Various special cases are detailed. A numerical example is given to illustrate the method.