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1.
Nat Jack 《The Journal of the Operational Research Society》1991,42(9):759-766
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. 相似文献
2.
Summary This paper considers a repair limit replacement model for a single-unit system taking account of the lead time to replace a new unit. It discusses the optimum repair limit replacement policies minimizing the expected cost per unit time in the steady-state. Numerical examples of such optimum policies are also presented.
Zusammenfassung In dieser Arbeit wird für ein System, das aus einer Einheit besteht, ein Instandhaltungsmodell mit begrenzter Reparaturzeit betrachtet, das die Vorbereitungszeit zur Installation einer neuen Einheit berücksichtigt. Es wird die optimale reparaturzeitbegrenzte Instandhaltungspolitik diskutiert, die die erwarteten Kosten je Einheitszeit im Gleichgewichtszustand minimiert. Numerische Beispiele derartiger optimaler Politiken werden ebenfalls gegeben.相似文献
3.
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. 相似文献
4.
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. 相似文献
5.
R. I. Phelps 《The Journal of the Operational Research Society》1981,32(7):549-554
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. 相似文献
6.
J. C. Di Véroli 《The Journal of the Operational Research Society》1974,25(1):89-97
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. 相似文献
7.
Viliam Makis Andrew K. S. Jardine 《The Journal of the Operational Research Society》1992,43(2):111-120
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. 相似文献
8.
N. A. J. Hastings 《The Journal of the Operational Research Society》1969,20(3):337-349
In the repair limit replacement method when an item requires repair it is first inspected and the repair cost is estimated. Repair is only then undertaken if the estimated cost is less than the "repair limit". Dynamic programming methods are used in this paper as a general approach to the problem of determining optimum repair limits. Two problems are formulated and the cases of finite and infinite planning horizons and discounted and undiscounted costs are discussed. Methods are given for allowing for equipment availability and for the introduction of new types of equipment. An improved general formulation for finite time horizon, stochastic, dynamic programming problems is developed. 相似文献
9.
R. I. Phelps 《The Journal of the Operational Research Society》1983,34(5):425-427
The problem of replacement under minimal repair is considered. It is shown that a particular form of control limit policy is optimal in the space of all possible policies. This generalises a previous result. 相似文献
10.
《European Journal of Operational Research》1988,37(2):194-203
In this paper, a periodical replacement problem with a general repair is considered where a system is replaced at only scheduled times kT (k = 0,1,…) and is repaired whenever it fails. By general repair, we mean that repair brings the state of the system to a certain better state. A stochastic model to describe the operation in time of a repairable system which is maintained by a general repair is developed. The model contains the minimal repair case in which repair restores a system to its functioning condition just prior to failure. The sensitivity of replacement policies under a general repair to derivation from the minimal repair assumption is numerically examined. It will be seen that the policies are insensitive when the deterioration of the system is not fast and the replacement cost is high relative to the repair cost. The minimal repair assumption is then justified for such situations. 相似文献
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13.
《European Journal of Operational Research》2006,174(3):1706-1722
The series system is one of the most important and common systems in reliability theory and applications. This paper investigates availability, maintenance cost, and optimal maintenance policies of the series system with n constituting components under the general assumption that each component is subject to correlated failure and repair, imperfect repair, shut-off rule, and arbitrary distributions of times to failure and repair. Imperfect repair is modeled through the basic idea of the quasi renewal processes introduced by H. Wang, H. Pham, A quasi renewal process and its applications in imperfect maintenance, International Journal of Systems Science 27(10) (1996) 1055–1062; 28(12) (1997) 1329. System availability, mean time between system failures, mean time between system repairs, asymptotic fractional down time of the system, etc., are derived, and a numerical example is presented to compare with the existing models by R.E. Barlow, F. Proschan, Satistical Theory of Reliability of Life Testing, Holt, Renehart & Winston, NY, 1975. Then two classes of maintenance cost models are proposed and system maintenance cost rates are modeled. Finally, properties of system availability and maintenance cost rates are studied. Optimization models to optimize system availability and/or system maintenance costs are developed, and optimum system maintenance policies are discussed through a numerical example. 相似文献
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研究了修理设备可更换的k/n(G)表决可修系统,其中修理设备在修理故障部件时可能发生失效.假定部件和修理设备的寿命服从负指数分布,故障部件的修理时间和修理设备的更换时间服从一般分布的条件下,利用马尔可夫更新过程理论和拉普拉斯变换(Laplace-Stieltjes变换),分别讨论了系统首次故障前的平均时间,可用度,故障频度及修理设备的不可用度和失效频度,获得了相关指标的递推表达式.在此基础上,给出了1/2(G)表决可修系统和(n-1)/n(G)表决可修系统相关可靠性指标的表达式. 相似文献
16.
This paper presents a replacement model with age-dependent failure type based on a cumulative repair-cost limit policy, whose concept uses the information of all repair costs to decide whether the system is repaired or replaced. As failures occur, the system experiences one of the 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. A critical type-I failure means a minor failure at which the accumulated repair cost exceeds the pre-determined limit for the first time. The system is replaced at the nth type-I failure, or at a critical type-I failure, or at first type-II failure, whichever occurs first. The optimal number of minimal repairs before replacement which minimizes the mean cost rate is derived and studied in terms of its existence and uniqueness. Several classical models in maintenance literature are special cases of our model. 相似文献
17.
修理设备可更换且有修理延迟的N部件串联系统分析 总被引:3,自引:0,他引:3
假定部件的寿命服从指数分布,修理延迟时间和修理时间均服从任意分布,并且修理设备的寿命服从指数分布,其更换时间服从任意分布的情况下,利用马尔可夫更新过程理论和拉普拉斯变换工具,研究了修理有延迟且修理设备可更换的n部件串联可修系统,求得了系统的可用度和(0,t]时间内的平均故障次数.进一步,在定义修理设备“广义忙期”下,利用全概率分解,提出了一种新的分析技术,讨论了修理设备的可靠性指标,得到修理设备的一些重要可靠性结果. 相似文献
18.
Tadashi Dohi Akira Ashioka Naoto Kaio Shunji Osaki 《Mathematical and Computer Modelling》2003,38(11-13):1169
In this paper, we consider a simple repair-time limit replacement problem with imperfect repair, and focus on the problem of determining the optimal repair-time limit which minimizes the expected cost per unit time in the steady-state. Applying the Lorenz transform, we develop a nonparametric method to estimate the optimal repair-time limit from the empirical repair-time data. Numerical examples are considered to calculate the optimal policy and to examine the asymptotic properties of the estimator. 相似文献
19.
Under the generalized age replacement policy, the system is replaced either at the predetermined age or upon failure if its corresponding repair time exceeds the threshold, whichever comes first. In this paper, we investigate the optimal choice of the pre‐determined preventive replacement age for a nonwarranted system, which minimizes the expected cost rate during the life cycle of the system from the customer's perspective under certain cost structures. Furthermore, we discuss several properties of such a generalized age replacement policy in comparison with the traditional age replacement policy. An efficiency, which represents the fractional time that the system is on, is defined under the proposed generalized age replacement policy and its monotonicity properties are investigated as well. The main objective of this study is to investigate the advantageous features of the generalized age replacement policy over the traditional age replacement policy with regard to the availability of the repairable system. Assuming that the system deteriorates with age, we illustrate our proposed optimal policies numerically and observe the impact of relevant parameters on the optimal preventive replacement age. 相似文献
20.
In this paper, 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 behavior
of the assumed system, reflecting the costs of both storing a spare and of system downtime. The optimal age for preventive
replacement minimizing that cost rate is derived, its existence and uniqueness is shown, and structural properties are presented.
Various special cases are included, and a numerical example is given for illustration. Because the framework and analysis
are general, the proposed model extends several existing results. 相似文献