Periodic replacement when minimal repair costs depend on the age and the number of minimal repair for a multi-unit system

A policy of periodic replacement with minimal repair at failure is considered for the multi-unit system which have the specific multivariate distribution. Under such a policy the system is replaced at multiples of some period T while minimal repair is performed at any intervening component failures. The cost of a minimal repair to the component is assumed to be a function of its age and the number of minimal repair. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the component. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited.     

Periodic replacement with minimal repair at failure and general random repair cost for a multi-unit system

A policy of periodic replacement with minimal repair at failure is considered for the multi-unit system which have the specific multivariate distribution. Under such a policy an operating system is completely replaced whenever it reaches age T (T > 0) at a cost c₀ while minimal repair is performed at any intervening component failures. The cost of the j-th minimal repair to the component which fails at age y is g(C(y),c_j(y)), where C(y) is the age-dependent random part, c_j(y) is the deterministic part which depends on the age and the number of the minimal repair to the component, and g is an positive nondecreasing continuous function. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the component. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited.     

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.     

An age replacement policy with minimal repair and general random repair cost

An age replacement policy is introduced which incorporates minimal repair, replacement, and general random repair costs. If an operating unit fails at age y<T, it is either replaced by a new unit with probability p(y) at a cost c₀, or it undergoes minimal repair with probability q(y) = 1−p(y). Otherwise, a unit is replaced when it fails for the first time after age T. The cost of the i-th minimal repair of an unit at age y depends on the random part C(y) and the deterministic part c_i(y). The aim of the paper is to find the optimal T which minimizes the long run expected cost per unit time of the policy. Various special cases are considered.     

An economic discrete replacement policy for a shock damage model with minimal repairs

A discrete replacement model for a repairable system which is subject to shocks and minimal repairs is discussed. Such shocks can be classified, depending on its effect to the system, into two types: Type I and Type II shocks. Whenever a type II shock occurs causes the system to go into failure, such a failure is called type II failure and can be corrected by a minimal repair. A type I shock does damage to the system in the sense that it increases the failure rate by a certain amount and the failure rate also increases with age due to aging process without external shocks; furthermore, the failure occurred in this condition is called type I failure. The system is replaced at the time of the first type I failure or the n-th type Il failure, whichever occurs first. Introducing costs due to replacement and mininal repairs, the long-run expected cost per unit time is derived as a criterion of optimality and the optimal number n∗ found by minimizing that cost. It is shown that, under certain conditions, there exists a finite and unique optimal number n∗.     

A note on a multi-unit system with r repair facility

This paper deals with a system consisting of (n + m) identical units; n units are needed for the system to function and the remaining m units are warm standby supported by r repair facility. The online and standby units have different but constant failure rates; the repair time distribution for the standby unit is taken to be a constant and the distribution for the online unit is arbitrary. Functions describing the behaviour of all the other units when one unit is undergoing online repair are studied and an earlier result is recovered as a special case.     

Cost-benefit analysis of a one-server two-unit cold standby system with repair and age replacement

This paper deals with the cost-benefit analysis of a one-server two-identical-unit cold standby system with repair and preventive maintenance (PM). The PM is of the age replacement type, where, if a unit has been in operation for a certain period of time, which may be a random variable, and if the other unit is in standby, the operating unit is taken off for PM. The expected net revenue in the interval [0,t) is obtained using two different approaches. The first approach is more general and allows nonlinearities in the revenue and costs. It is assumed that the revenue obtained by operating a unit for an uninterrupted interval of time is some function of the length of that interval. Similarly, the cost of a repair or PM action is function of the length of the repair or PM time, respectively, for that action. The second approach assumes that the revenue, repair cost and PM cost vary linearly with time. The pointwise availability is derived. The busy period of the server is divided into time spent in performing repair and time spent on PM. The expected net revenue in [0,t) is obtained. Both techniques make use of regeneration points. It is finally shown that the results of the first approach under assumptions of linear revenue and cost functions reduce to those of the second approach.     

Estimated costs of system maintenance and repair

This paper presents a practical model to estimate the system cost of maintenance and repair. The model considers all time and cost factors. An application to the model is presented. The relationships between cost and each of scheduled time for maintenance and mean time between failures are given.     

Profit evaluation of a two-unit system with internal and external repairs, inspection and post repair

In practice, systems do not always fail with a major breakdown, needing a heavy repair from some external source. Quite often, systems have a minor fault for which an immediate internal repair is more appropriate, in terms of availability of the system and economy, than calling a repairman from some external repair facility, waiting idly for his arrival or making a call with a higher cost. The present work discusses two non-identical unit systems with two types of repair, the internal and the external one. The external repair is called only when the internal staff fail to do the job. In the case of external repair, there is a provision of inspection, wherein if the repair is found unsatisfactory, it is sent for post repair. Using the regenerative point technique, various reliability characteristics of system effectiveness have been obtained.     

Cost-benefit analysis of a system with inspection, replacement and two types of repair

This paper investigates a mathematical model of a system composed of two units—one operative and the other in cold standby. There is a single repair facility which serves the triple role of inspection, repair and replacement of a failed unit. After inspection, the unit goes to minor (major) repair with probability p(q = 1 − p). Whenever the failed unit goes to major repair, an order is immediately placed for a new unit to replace the unit under major repair. Failure, inspection and delivery time distributions are negative exponential, whereas repair time distribution is arbitrary. The system is analysed in detail using the regenerative point technique and several reliability characteristics of interest to system designers and operation managers are obtained. Earlier results are verified in particular cases.     

A dual burn-in policy for defect-tolerant memory products using the number of repairs as a quality indicator

In most existing studies on the optimization of burn-in for semiconductor products, all chips are treated equally and subjected to burn-in of the same duration (i.e. a single burn-in (SBI) policy is employed). However, the quality levels of chips before burn-in are not the same in general, and therefore, it may be more advantageous to treat chips differently at the burn-in process based on appropriate quality indicators. This paper considers defect-tolerant memory products and develops a dual burn-in (DBI) policy in which the chips submitted to burn-in are classified into two groups according to the number of repairs, a quality indicator that can be obtained from the wafer probe test results, and different burn-in durations are applied to different groups of chips. Then, cost models are developed for the SBI and DBI policies, and their relative performances are compared in terms of the expected total cost per chip. The effectiveness of the proposed DBI policy is demonstrated using the actual data for a certain type of 256M DRAM products.     

Analysis of a two-unit system subject to repair and preventive maintenance with non-linear revenue and costs

The cost-benefit analysis of a one-server two-identical-unit cold standby system subject to repair and preventive maintenance (PM) with non-linear revenue and costs is presented in this paper. Initially, one unit is in operation and the other is cold standby. When a unit fails, it is taken up for repair or waits for repair if the server is busy. The latter results in a system breakdown. If a unit returns from service (repair or PM) and the other unit is operating, the operating unit is taken up for PM. The revenue obtained by operating a unit for an uninterrupted interval of time is some function of the length of the interval. Similarly, the cost of a repair or PM action is a function of the length of the repair or PM time, respectively, for that action. With the help of regeneration point technique, the expected net revenue over an interval (0,t] is obtained. It is shown that the results for the special case when the revenue and cost function are linear agree with previously obtained results.     

Optimum policy of one-unit system with two types of maintenance and minimal repair

This paper deals with a one-unit system with minimal repair. Two policies (new Policy IV and Policy IV′) are considered. Under these policies, the Laplace transform of the point-wise availability and the stationary availability of the system are obtained using not the renewal theory but the supplementary variable method. And under new Policy IV, the optimum policy in the sense of the availability is discussed.     

基于WEB的房屋维修系统设计与实现

房屋报修困难,维修更困难的现象经常出现。为了解决目前房屋维修存在较多问题的现状,通过系统分析、系统体系结构设计、系统功能设计、数据库设计等详细的设计后,使用当前较为先进的JSP技术开发实现了基于WEB的房屋维修系统。经使用测试具有较好的性能,较大降低了维修成本,提升了维修效率及用户满意度。     

Cost benefit analysis of a complex system with correlated failures and repairs

This paper studies the cost benefit analysis of a complex system consisting of two subsystems, say A and B, connected in series. Subsystem A consists of two identical units, whereas subsystem B has only one unit. The system operates if one of the two units of subsystem A and the subsystem B are operative. Assuming a bivariate exponential density for the joint distribution of failure and repair times of the units, some reliability characteristics useful to system managers have been obtained. Explicit results have also been obtained for the case when failure and repair times are uncorrelated.     

Optimal replacement policy (N, n) for a parallel system with common cause failure and geometric repair time

The purpose of this article is to present an improved replacement model for a parallel system of N identical units, by bringing in common cause failure (CCF), maintenance cost and repair cost per unit time additionally, and to develop a procedure to obtain the optimal redundant units N^* and optimal number of repairs n^* with the conditions that the system is allowed to undergo at most a prefixed number of repairs before to be replaced and the successive reapir times after failures constitute a non-decreasing Geometric process. Several conditions for the existence of the optimal N^* and n^* is stated and the results are illustrated by a numerical example.