Repair Replacement Policy Research Articles

A repair-replacement policy for a system subject to missions of random types and random durations

A repair-replacement policy for a system subject to missions of random types and random durations

A REPAIR REPLACEMENT PROBLEM FOR COLD STANDBY SYSTEM USING ALPHA SERIES AND GEOMETRIC PROCESS

The present paper studies a cold standby repairable system consisting of two identical components namely component 1, component 2 and onerepairman is studied. Assume that each component after repair is not 'as good as new' and also the successive working times form a decreasing a-series process, the successive repair time's form an increasing geometric process and both the processes are exposing to exponential failure law. Under these assumptions we study an optimal replacement policy N in which we replace the system when the number of failures of component 1 reaches N. It can be determined that an optimal repair replacement policy N* such that the long run average cost per unit time is minimized. It can also be derived an explicit expression of the long-run average cost and the corresponding optimal replacement policy N* can be determined analytically. Numerical results are provided to support the theoretical results

A hybrid repair-replacement policy in the proportional hazards model

Cox's proportional hazards model is widely used to describe the hazard rate of a system deteriorating with age and diagnostic covariates. Existing maintenance in the proportional hazards model was primarily concerned with replacement, resulting in excessive maintenance for many repairable systems. This paper develops a novel hybrid repair-replacement model in the proportional hazards model with a stochastically increasing Markovian covariate process. Preventive repair reduces both age and covariate, and the reduction rate decreases as the number of repairs increases. At an inspection epoch where the system age, covariate state, and repair number are available, the decision-maker considers three possible actions, i.e., no maintenance, preventive repair, and preventive replacement. The objective is to derive the optimal policy that minimizes the long-run average maintenance cost rate. The optimization problem is formulated in the semi-Markov decision process (SMDP) framework. The structural properties of the optimal policy are examined to reduce the policy space. Then a policy-iteration algorithm with a backward policy-improvement step is developed for efficiently finding the optimization results. A practical numerical example with sensitivity analysis is conducted to illustrate the effectiveness of the proposed approach. A comparison with two heuristic policies confirms the superiority of the proposed policy in reducing maintenance costs.

Cataloging Of Unit Replacement Based On Long Run Repair Average Cost Rate (Acr) Based On Weibull Distribution Model

Large amounts of money are lost each year in the real-estate industry because of poor schedule and cost control, In Industry the investigated failure and repair pattern, reliabilities of generators, compressors, turbines, using simple statistical tools and simulation techniques. The repair duration is divided into the 1)Major repair 2)Minor repair ,In major repair having(repair hour greater than a threshold valve)and Minor repair having(repair hour less than (or)equal to threshold valve).This approach is mainly for Weibull distribution method. In Weibull analysis is a common method for failure analysis and reliability engineering used in a wide range of applications. In this paper, the applicability of Weibull analysis for evaluating and comparing the reliability of the schedule performance of multiple projects is presented, while the successive performance of multiple projects is presented ,while the successive repair times are increasing and are exposing to Weibull distribution ,under these assumptions ,an optimal replacement policy ‘T’ in which we replace the system ,when the repair time reaches T. It can be determined that an optimal repair replacement policy T* such that long run average cost and the corresponding optimal replacement policy T* can be determined analytically.

Determination of Optimal Warranty Period with Preventive Maintenance Actions for Items from Heterogeneous Populations

In this study, we develop an optimal maintenance policy with replacement service and minimal repair service for items from heterogeneous populations and determine the optimal warranty length and repair time threshold. We consider the information-based repair-replacement policy model and develop the formula to evaluate the expected cost rate during the product life cycle. A general formulation is derived for the expected cost rate under a warranty policy for items of heterogeneous populations. When a replacement service and minimal repair service are provided for a failed item, then an item from a weak population has the property of an item from a weak population after service. Similarly, an item from a strong population has the property of an item from a strong population after service. We define the optimal maintenance strategies to minimize the expected cost rate with failure time and repair time for items with heterogeneous reliability characteristics. The effects of parameters of the intensity function for the failure times on the optimal length of the warranty period are studied numerically. Assuming that the product deteriorates, we illustrate the proposed approach using numerical applications and observe the impacts of relevant parameters on the optimal length of the warranty period.

Identification of Unit Replacement Based on Long-Run Repair Average Cost Rate (Acr) Based on Truncated Exponential Failure Model

Earlier, authors presented [1] and published [2] investigated failure nature, repair pattern and reliabilities of hydro power generators, using simple statistical tools and simulation techniques respectively. It is identified that analysis of hydro power generators require a special approach by dividing the repair into two categories based on the repair duration. That is i) Minor repairs (Repair hours less than or equal a threshold value T) and ii) Major Repairs (Repair hours greater than a threshold value T).This approach is specially introduced by authors [1, 2] and obtained good fit of “truncated exponential failure model”. Through this proposed model reliabilities are estimated and conclusions were drawn. In the above work, we have assumed that the system after repair is ‘as good as new’. On the basic assumption that the system after repair is not ‘as good as new’ and also the successive working times are stochastically decreasing while, the successive repair time's are stochastically increasing and are exposing to exponential truncated failure law. Under these assumptions, an optimal replacement policy T in which we replace the system when the repair time (working time) reaches T. It can be determined that an optimal repair replacement policy T* such that the long run average cost per unit time is minimized. It can also be derived an explicit expression of the long-run average cost and the corresponding optimal replacement policy T* can be determined analytically. Numerical results are provided to support the theoretical results.

A Bivariate Replacement Policy for a Cold Standby System Under Poisson Shocks

SYNOPTIC ABSTRACT This study considers a repair-replacement problem for a repairable cold standby system that is composed of two similar components with preventive maintenance. The system may fail because of intrinsic or extrinsic factors such as shocks. The shocks arrive according to a Poisson process. Whenever the magnitude of a shock exceeds a prespecified threshold of the operating component, the operating component fails. We assume that the intrinsic lifetime, the threshold, and the repair time of the operating component are geometric processes. A bivariate repair-replacement policy ( T,N) is adopted for the system, where T is the interval length between preventive maintenances and N is the number of failures of component 1. The explicit expression of the expected long-run cost-per-unit time is derived and the corresponding optimal bivariate policy ( T,N) can be determined analytically or numerically. Finally, three numerical examples are given to validate the theoretical results of the proposed model.

Optimal repair–replacement policies for a system with two types of failures

In this paper, the optimal replacement problem is investigated for a system with two types of failures. One type of failure is repairable, which is conducted by a repairman when it occurs, and the other is unrepairable, which leads to a replacement of the system at once. The repair of the system is not “as good as new”. The consecutive operating times of the system after repair form a decreasing geometric process, while the repair times after failure are assumed to be independent and identically distributed. Replacement policy N is adopted, where N is the number of repairable failures. The system will be replaced at the Nth repairable failure or at the unrepairable failure, whichever occurs first. Two replacement models are considered, one is based on the limiting availability and the other based on the long-run average cost rate of the system. We give the explicit expressions for the limiting availability and the long-run average cost rate of the system under policy N, respectively. By maximizing the limiting availability A(N) and minimizing the long-run average cost rate C(N), we theoretically obtain the optimal replacement policies N∗ in both cases. Finally, some numerical simulations are presented to verify the theoretical results.

OPTIMAL GEOMETRIC PROCESS REPLACEMENT POLICIES BASED ON NUMBER OF DOWN TIMES

We consider two repair-replacement policies for a cold standby system consisting of two components with a single repairman. It is assumed that each component after repair is not "as good as new". With this assumption by using geometric process we developed two replacement policies based on the number of down times of the component-1. Our problem is to choose optimal replacement policy (k) such that the long run expected reward per unit time of the system maximized. The mathematical expressions for the long run expected reward per unit time are evaluated and corresponding optimal replacement policies are obtained theoretically with numerical example and by simulation study. Also we have discussed Newton–Raphson method to find optimal k.

A bivariate optimal replacement policy for a cold standby repairable system with preventive repair

In this paper, the repair–replacement problem for a deteriorating cold standby repairable system is investigated. The system consists of two dissimilar components, in which component 1 is the main component with use priority and component 2 is a supplementary component. In order to extend the working time and economize the running cost of the system, preventive repair for component 1 is performed every time interval T, and the preventive repair is “as good as new”. As a supplementary component, component 2 is only used at the time that component 1 is under preventive repair or failure repair. Assumed that the failure repair of component 1 follows geometric process repair while the repair of component 2 is “as good as new”. A bivariate repair–replacement policy ( T, N) is adopted for the system, where T is the interval length between preventive repairs, and N is the number of failures of component 1. The aim is to determine an optimal bivariate policy ( T, N) ∗ such that the average cost rate of the system is minimized. The explicit expression of the average cost rate is derived and the corresponding optimal bivariate policy can be determined analytically or numerically. Finally, a Gamma distributed example is given to illustrate the theoretical results for the proposed model.

Hybrid minimal repair and age replacement policy for two-dimensional warranted products

In this paper, we investigate a hybrid minimal repair and age replacement policy for a repairable product sold with a two-dimensional non-renewing failure replacement warranty. We first model product failures using the one-dimensional approach and then use a more appropriate formulation to model the effect of age and usage to the product degradation. Under this policy, for a given usage rate y, the product is directly repaired minimally when it fails in (0, Sy] and replaced with the new one on the first failure in (Sy, ?y] or when its age reaches ?y, whichever occurs first. We obtain the global optimal solution of Sy, for a given ?y which minimises the expected cost per unit time to the buyer. We present numerical examples to illustrate the properties of the optimal solution.

An optimal repair–replacement policy for a cold standby system with use priority

In this paper, the maintenance problem for a cold standby system consisting of two dissimilar components and one repairman is studied. Assume that both component 1 and component 2 after repair follow geometric process repair and component 1 is given priority in use when both components are workable. Under these assumptions, using geometric process repair model, we consider a replacement policy N under which the system is replaced when the number of failures of component 1 reaches N. Our purpose is to determine an optimal replacement policy N∗ such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit expression for the average cost rate of the system is derived and the corresponding optimal replacement policy N∗ can be determined analytically or numerically. Finally, a numerical example is given to illustrate some theoretical results and the model applicability.

A deteriorating cold standby repairable system with priority in use

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. In this system, it is assumed that the working time distributions and the repair time distributions of the two components are both exponential and component 1 is given priority in use. After repair, component 2 is “as good as new” while component 1 follows a geometric process repair. Under these assumptions, using the geometric process and a supplementary variable technique, some important reliability indices such as the system availability, reliability, mean time to first failure (MTTFF), rate of occurrence of failure (ROCOF) and the idle probability of the repairman are derived. A numerical example for the system reliability R( t) is given. And it is considered that a repair-replacement policy based on the working age T of component 1 under which the system is replaced when the working age of component 1 reaches T. Our problem is to determine an optimal policy T ∗ such that the long-run average cost per unit time of the system is minimized. The explicit expression for the long-run average cost per unit time of the system is evaluated, and the corresponding optimal replacement policy T ∗ can be found analytically or numerically. Another numerical example for replacement model is also given.

A geometrical process repair model for a repairable system with delayed repair

In this paper, a repairable system consisting of one component and a single repairman (i.e. a simple repairable system) with delayed repair is studied. Assume that the working time distribution, the repair time distribution and the delayed repair time distribution of the system are all exponential. After repair, the system is not “as good as new”. Under these assumptions, by using the geometrical process and the supplementary variable technique, we derive some important reliability indices such as the system availability, rate of occurrence of failures (ROCOF), reliability and mean time to first failure (MTTFF). A repair replacement policy N under which the system is replaced when the number of failures of the system reaches N is also studied. The explicit expression for the average cost rate (i.e. the long-run average cost per unit time) of the system is derived, and the corresponding optimal replacement policy N ∗ can be found analytically or numerically. Finally, a numerical example for policy N is given.

Replacement problems for a cold standby repairable system

In this paper, a cold standby repairable system consisting of two identical components and one repairman is studied. Assume that each component after repair is not “as good as new”, by using a geometric process, we consider two kinds of repair replacement policy, one based on the working age T of component 1 under which the system is replaced when the working age of component 1 reaches T, and the other based on the failure number N of component 1 under which the system is replaced when the failure number of component 1 reaches N. Our problem is to choose optimal replacement policies T* and N* respectively such that the long-run average cost per unit time of the system is minimized. And we can prove under some mild conditions that the optimal policy N* is better than the optimal policy T*. Finally, a numerical example for policy N is given.

Some results on comparison of maintenance policies

In this paper, we study the stochastic comparisons of minimal repair replacement policies in repairable case. We give some results on comparisons of the same unit for different policies and on comparisons of the same policies for different units.

An optimal geometric process model for a cold standby repairable system

In this paper a cold standby repairable system consisting of two identical components and one repairman is studied. Assume that each component after repair is not `as good as new'. Under this assumption, by using a geometric process, we consider a replacement policy N based on the number of repairs of component 1. Our problem is to determine an optimal replacement policy N* such that the long-run expected reward per unit time is maximized. The explicit expression of the long-run expected reward per unit time is derived and the corresponding optimal repair replacement policy can be determined analytically or numerically. Finally, a numerical example is given.

An optimal inspection–repair–replacement policy for standby systems

In this paper, an optimal maintenance model for standby systems is studied. An inspection–repair–replacement policy is employed. Assume that the state of the system can only be determined through an inspection which may incorrectly identify the system state. After each inspection, if the system is identified as in the down state, a repair action will be taken. It will be replaced some time later by a new and identical one. The problem is to determine an optimal policy so that the availability of the system is high enough at any time and the long-run expected cost per unit time is minimized. An explicit expression for the long-run expected cost per unit time is derived. For a geometric model, a simple algorithm for the determination of an optimal solution is suggested.

An optimal inspection–repair–replacement policy for standby systems

In this paper, an optimal maintenance model for standby systems is studied. An inspection–repair–replacement policy is employed. Assume that the state of the system can only be determined through an inspection which may incorrectly identify the system state. After each inspection, if the system is identified as in the down state, a repair action will be taken. It will be replaced some time later by a new and identical one. The problem is to determine an optimal policy so that the availability of the system is high enough at any time and the long-run expected cost per unit time is minimized. An explicit expression for the long-run expected cost per unit time is derived. For a geometric model, a simple algorithm for the determination of an optimal solution is suggested.

Repair replacement policies

In this paper we introduce the concept of repair replacement. Repair replacement is a maintenance policy in which items are preventively maintained when a certain time has elapsed since their last repair. This differs from age replacement where a certain amount of time has elapsed since the last replacement. If the last repair was a complete repair, repair replacement is essentially the same as age replacement. It is in the case of minimal repair that these two policies differ. We make comparison between various types of policies in order to determine when and under which condition one type of policy is better than another.