Age replacement of components during IFR delay time

This paper proposes two alternative policies for preventive replacement of a component, which shows sign of occurrence of a fault, and operates for some random time with degraded performance, before its final failure. The time between fault occurrence and component failure is termed as delay time. The first policy, namely age replacement during delay time policy (ARDTP), recommends replacement of a faulty component on failure or preventive replacement of the same after a fixed time during its delay time. It considers the performance degradation during delay time to develop an age replacement policy. It is also shown that the policy is a feasible proposition for a component that has positive (nonnegative) performance degradation during its CFR (IFR) delay time. The second policy, OARDTP, extends ARDTP to opportunistic age replacement policy where a faulty component is replaced at the first available randomly occurring maintenance opportunity, after a fixed time from occurrence of fault, or on failure. The time between opportunities (TBO) is considered to be exponentially distributed. This policy reduces the number of forced shutdowns, which is essential to ARDTP. It is shown that the second policy is superior to the first policy if the cost of a preventive replacement with forced shutdown is more than the preventive replacement cost during an opportunity. The policies are appropriate for complex process plants, where the tracking of the entire service life of each component is difficult. Their implementation requires tracking of components' delay time only, and estimation of mean time to occurrence of faults. The policies are relatively insensitive to estimation error in failure replacement cost. As their implementation requires immediate capturing of fault occurrence information, they are particularly attractive to organizations where operators are involved in the maintenance of machines.     

(τ, k) block replacement policy with idle count

The authors propose a new block replacement policy for a group of nominally identical units. Each unit is individually replaced on failure during a specified time interval. Beyond the failure replacement interval, failed units are left idle until a specified number of failures occur, then a block replacement is performed. The average cost rate for this two-phase block replacement policy is derived and analyzed. The policy yields lower cost rate than two block replacement policies published previously. Numerical examples demonstrate the results     

Calculation of Age-Replacement with Weibull Failure Times

An age-replacement policy with Weibull failure times is considered. It is troublesome to compute an optimum replacement time numerically. Upper and lower bounds of an optimum time are given in simple terms of replacement costs and parameters of a Weibull distribution. A numerical example shows that the approximation can be used when the ratio of the replacement cost for a failed unit to that for a nonfailed unit is large. The approximation is best when the optimum age of replacement is small.     

Cost limit replacement policy under minimal repair

This paper presents a policy for either repairing or replacing a system that has failed. When a system 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 cost limit”. However, the repair cannot return the system to “as new” condition but instead returns it 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. A Weibull distribution of time to failure and a negative exponential distribution of estimated repair cost are assumed for analytic amenability. An optimal “repair cost limit” policy is developed that minimizes the average cost per unit time for repairs and replacement. It is shown that the optimal policy is finite and unique.     

Improvement, deterioration, and optimal replacement underage-replacement with minimal repair

Improvement and deterioration for a repairable system are studied, in particular in terms of the effect of ageing on the distribution of the time to first failure under a nonhomogeneous Poisson process. For a repairable system undergoing minimal repair, the optimal replacement time under the age replacement policy is discussed     

A geometric-process repair-model with good-as-new preventive repair

This paper studies a deteriorating simple repairable system. In order to improve the availability or economize the operating costs of the system, the preventive repair is adopted before the system fails. Assume that the preventive repair of the system is as good as new, while the failure repair of the system is not, so that the successive working times form a stochastic decreasing geometric process while the consecutive failure repair times form a stochastic increasing geometric process. Under this assumption and others, by using geometric process we consider a replacement policy N based on the failure number of the system. Our problem is to determine an optimal replacement policy N such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. The explicit expression of the average cost rate is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. And the fixed-length interval time of the preventive repair in the system is also discussed. Finally, an appropriate numerical example is given. It is seen from that both the optimal policies N** and N* are unique. However, the optimal policy N** with preventive repair is better than the optimal policy N* without preventive repair     

Continuous-time predictive-maintenance scheduling for adeteriorating system

A predictive-maintenance structure for a gradually deteriorating single-unit system (continuous time/continuous state) is presented in this paper. The proposed decision model enables optimal inspection and replacement decision in order to balance the cost engaged by failure and unavailability on an infinite horizon. Two maintenance decision variables are considered: the preventive replacement threshold and the inspection schedule based on the system state. In order to assess the performance of the proposed maintenance structure, a mathematical model for the maintained system cost is developed using regenerative and semi-regenerative processes theory. Numerical experiments show that the s-expected maintenance cost rate on an infinite horizon can be minimized by a joint optimization of the replacement threshold and the a periodic inspection times. The proposed maintenance structure performs better than classical preventive maintenance policies which can be treated as particular cases. Using the proposed maintenance structure, a well-adapted strategy can automatically be selected for the maintenance decision-maker depending on the characteristics of the wear process and on the different unit costs. Even limit cases can be reached: for example, in the case of expensive inspection and costly preventive replacement, the optimal policy becomes close to a systematic periodic replacement policy. Most of the classical maintenance strategies (periodic inspection/replacement policy, systematic periodic replacement, corrective policy) can be emulated by adopting some specific inspection scheduling rules and replacement thresholds. In a more general way, the proposed maintenance structure shows its adaptability to different possible characteristics of the maintained single-unit system     

Joint optimization of block-replacement and periodic-review spare-provisioning policy

This paper considers the problem of joint optimization of "preventive maintenance" and "spare-provisioning policy" for system components subject to wear-out failures. A stochastic mathematical model is developed to determine the jointly optimal "block replacement" and "periodic review spare-provisioning policy." The objective function of the model represents the s-expected total cost of system maintenance per unit time, while the preventive replacement interval and the maximal inventory level are chosen as the decision variables. The objective function of the model is in an analytic form with parameters easily obtainable from field data. The model has been tested using field data on electric locomotives in Slovenian Railways. The calculated optimal values of the model decision variables are realistic. "Sensitivity analysis of the model" shows that the model is relatively insensitive to moderate changes of the parameter values. The results of testing and of sensitivity analysis of the model prove that a trade-off exists between the replacement related cost and the inventory related cost. The jointly optimal preventive replacement interval defined by this model differs appreciably from the corresponding interval determined by the conventional model where only replacement related costs are considered. Also, the results of the sensitivity analysis show that even minor modification of the value of each model decision variable (without the appropriate adjustment of the value of the other decision variable) can lead to important increase of the s-expected total cost of system maintenance. This indicates that separate optimization of preventive maintenance policy and spare-provisioning policy does not ensure minimal total cost of system maintenance. This model can be readily applied to optimize maintenance procedures for a variety of industrial systems, and to upgrade maintenance policy in situations where block replacement preventive maintenance is already in use.     

A geometric-process maintenance model for a deteriorating system under a random environment

This paper studies a geometric-process maintenance-model for a deteriorating system under a random environment. Assume that the number of random shocks, up to time t, produced by the random environment forms a counting process. Whenever a random shock arrives, the system operating time is reduced. The successive reductions in the system operating time are statistically independent and identically distributed random variables. Assume that the consecutive repair times of the system after failures, form an increasing geometric process; under the condition that the system suffers no random shock, the successive operating times of the system after repairs constitute a decreasing geometric process. A replacement policy N, by which the system is replaced at the time of the failure N, is adopted. An explicit expression for the average cost rate (long-run average cost per unit time) is derived. Then, an optimal replacement policy is determined analytically. As a particular case, a compound Poisson process model is also studied.     

An Optimal Inspection and Replacement Policy

An optimal inspection and replacement policy is discussed for a unit which assumes any one of several Markov states. The policy evaluation function is the s-expected cost-per-unit-time over an infinite time span. The problem is formulated as a semi-Markov decision process with a modified policy-improvement routine. Some properties of the optimal policy are discussed, for example, the control limit rule holds and the inspection time interval becomes shorter as degradation progresses.     

An Age-Based Inspection and Replacement Policy for Heterogeneous Components

This paper considers a hybrid maintenance policy for a single component from a heterogeneous population. The component is placed in a socket, and the component and socket together comprise the system. The $s$-population of components consists of two sub-populations with different failure characteristics. By supposing that a component may be in a defective but operating state, so that there exists a delay time between defect arrival and component failure, we consider a novel maintenance policy that is a hybrid of inspection and replacement policies. There are similarities in this approach with the concept of “burn-in” maintenance. The policies are investigated in the context of traction motor bearing failures. Under certain circumstances, particularly when the mixture parameter is large, and the distribution of lifetimes for the two component types are well separated, the hybrid policy has significant cost savings over the standard age-based replacement policy, and over the pure inspection policy. In addition to the cost metric, the mean time between operational failures of the system under the hybrid policy can be used to guide decision-making. This maintenance policy metric is calculated using simulation, and using an approximation which assumes that operational failures occur according to a Poisson process with a rate that can be calculated in a straightforward way. The simulation results show good agreement with the approximation.      

Optimal maintenance-policies for deteriorating systems undervarious maintenance strategies

This paper presents algorithms for deriving optimal maintenance policies to minimize the mean long-run cost-rate for continuous-time Markov deteriorating systems. The degree of deterioration (except failure) of the system is known only through inspection. The time durations of inspection and replacement are nonnegligible. The costs are for inspection, replacement, operation, and downtime (idle). In particular, the replacement time, replacement cost, and operating cost-rate increase as the system deteriorates. Five maintenance strategies are considered-failure replacement, age replacement, sequential inspection, periodic inspection, and continuous inspection. Iterative algorithms are developed to derive the optimal maintenance policy and the corresponding cost rate for each strategy. Under sufficient conditions, structural optimal policies are obtained     

A maintenance model for two-unit redundant system

In this paper, a maintenance model for two-unit redundant system with one repairman is studied. At the beginning, unit 1 is operating, unit 2 is the standby unit. The costs include the operating reward, repair cost and replacement cost, besides, a penalty cost is incurred if the system breaks down. Two kinds of replacement policy, based on the number of failures for two units and the working age, respectively are used. The long-run average cost per unit time for each kind of replacement policy is derived. Also, a particular model in which the system is deteriorative, two units are identical and the penalty cost rate is high, is thoroughly studied.     

Comparison of Age, Block, and Failure Replacement Policies

Two widely used preventive replacement policies are the age replacement policy (ARP) and the block replacement policy (BRP). Another replacement policy is the failure replacement policy (FRP) in which no preventive replacements are made at all. In this paper we give a rule for choosing the least costly of the above three policies under conditions specified in the paper. The implementation of this rule is illustrated for two special cases, where the distribution of item life times is uniform, or 2-stage Erlang.     

Optimal ordering policies and optimal number of minimal repairs before replacement

Many maintenance policies in the literature have assumed that whenever a unit is to be replaced, a new unit is immediately available. However, if the procurement lead time is not negligible an odering policy should determine when to order a spare and when to replace the operating unit. This paper presents a model for determining the optimal ordering point and the optimal number of minimal repairs before replacement which include the optimal number of minimal repairs before replacement of Park as a special case. We derive the expected cost per unit time in the steady-state as a criterion of optimality and seek the optimum policy by minimizing that cost. Finally, we present the numerical examples for illustration.     

Replacement models with inspection and preventive maintenance

This paper considers the maintenance policy where a unit is inspected and maintained preventively at periodic intervals, and as the effectiveness, the age after maintenance becomes younger. The mean time to failure and the expected number of maintenances before failure are obtained. Two replacement models are considered and an optimum policy for each model is discussed.     

Analytical characterization of cache replacement policy impact on content delivery time in information‐centric networks

Information‐centric networking (ICN) has emerged as a promising candidate for designing content‐based future Internet paradigms. ICN increases the utilization of a network through location‐independent content naming and in‐network content caching. In routers, cache replacement policy determines which content to be replaced in the case of cache free space shortage. Thus, it has a direct influence on user experience, especially content delivery time. Meanwhile, content can be provided from different locations simultaneously because of the multi‐source property of the content in ICN. To the best of our knowledge, no work has yet studied the impact of cache replacement policy on the content delivery time considering multi‐source content delivery in ICN, an issue addressed in this paper. As our contribution, we analytically quantify the average content delivery time when different cache replacement policies, namely, least recently used (LRU) and random replacement (RR) policy, are employed. As an impressive result, we report the superiority of these policies in term of the popularity distribution of contents. The expected content delivery time in a supposed network topology was studied by both theoretical and experimental method. On the basis of the obtained results, some interesting findings of the performance of used cache replacement policies are provided.     

Age Replacement In Simple Systems With Increasing Loss Functions

Some age replacement policies are investigated and conditions for the unique existence of an optimum policy are derived. The optimum policy is the one which minimizes the expected cost per unit time over an infinite time span or maximizes the proportion of time during which the system is in operation. Losses have been expressed through increasing operating cost, if the objective is to minimize the expected total cost per unit time and through increasing renewal times if the objective is to maximize the availability of the system.     

Bounds of age replacement time

An age replacement policy with a planned replacement time t₀ is considered. Five approximations which give upper or lower bounds of an optimum time t₀¹ and are computed more easily than t₀¹ are derived. A numerical example shows, when the failure time has a Weibull distribution, that some approximations are fairly good.