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.     

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.     

Optimal replacement policies for systems with multiple standbycomponents

The authors consider two new preventive replacement policies for a multiple-component cold-standby system. The failure rate of the component in operation is constant. The system is inspected at random points over time to determine whether it is to be replaced. The replacement decision is based on the number of failed components at the time of inspection. There are two replacement options if the complete system fails during operation: (i) replace the system if an inspection reveals that it has failed (system failure is not self-announcing), and (ii) replace the system the instant it fails (system failure is self-announcing). There is a threshold value on the number of failed components (at the time of inspection) which minimizes the mean total cost. The authors develop a simple efficient procedure to find the optimal threshold value. They compare the cost of operating a system that is inspected at random points in time, with the cost of operating a system that is monitored continuously through an attached monitoring device, and discuss cost tradeoffs     

All opportunity-triggered replacement policy for multiple-unitsystems

A model is presented for a system which consists of n i.i.d units. Hazard rates of these units are increasing in time. A unit is replaced at failure or when the age of a unit exceeds T, whichever occurs first. When a unit is replaced, all the operating units with their age in the interval (T-w,T) are replaced. Both failure replacement and active replacement create the opportunities to replace other units preventively. This policy allows joint replacements and avoids the disadvantages resulting from replacement of new units, down time, and unrealistic assumptions for distributions of unit life. An algorithm is developed to compute the steady-state cost rate. Optimal T&W are obtained to minimize the mean total replacement cost rate. Application and analysis of results are illustrated through a numerical example     

Optimal number of uses for an intermittently-used system

This paper studies an intermittently-used system which fails by continuous deterioration with age or by discrete deterioration with use. The system is replaced before failure at number N of uses. The optimal number N^* to minimize the expected cost rate is discussed for three particular cases. The case where the system deteriorates with both operating time and use time is considered.     

Extended block replacement policy of a system subject to shocks

A generalization of the block replacement (BR) policy is proposed and analyzed for a system subject to shocks. Under such a policy, an operating system is preventively replaced by new ones at times i·T (i=1,2,3,...) independently of its failure history. If the system fails in: (a) ((i-1)·T, (i-1)·T+T₀), it is either replaced by a new one or minimally repaired; or (b) ((i-1)·T+T₀, i·T), it is either minimally repaired or remains inactive until the next planned replacement. The choice of these two actions is based on some mechanism (modeled as random) which depends on the number of shocks since the latest replacement. The average cost rate is obtained using the results of renewal reward theory. The model with two variables is transformed into a model with one variable and the optimum policy is discussed. Various special cases are considered. The results extend many of the well-known results for BR policies     

Optimal strategies for scheduling checkpoints and preventivemaintenance

At checkpoints during the operation of a computer, the state of the system is saved. Whenever a machine fails, it is repaired and then reset to the state saved at the latest checkpoint. In the present work, save times are known constants and repair times are random variables; failures are the epochs of a given renewal process. In scheduling the checkpoints, the cost of saves must be traded off against the cost of work lost when the computer fails. It is shown how to schedule checkpoints to minimize the mean total time to finish a given job. Similar optimization results are obtained for the tails of the distribution of the finishing time. Two variants of the basic model are considered. In one of the computer receives maintenance during each save; in the other it does not. Applications to the M/G/1 queuing system are touched on     

Reliability analysis and optimization applications of a two-unit standby redundant system with spare units

Consider a two-unit standby redundant system with two main units, one repair facility, and n spare units. When the main unit has failed and the other is under repair, a spare unit takes over the operation and if it fails, it is replaced by a new one until the repair of the failed unit is completed. The system fails when the last spare unit fails while one main unit is under repair and the other has failed. In this paper, we derive expressions for 1) the distribution function of the first time to system failure, 2) the probability that the total number of failed spare units during the time interval (0,t] is n and 3) the mean of the total number of failed spare units in (0,t] and its asymptotic behaviour. Introducing costs incurred for each failed main unit and each failed spare unit, the expected cost per unit of time of the system was also derived. Finally an optinmization problem is discussed in order to compare the expected cost of the system with both main units and spare units with that of spare units only, and particular cases are considered.     

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.     

Sequential imperfect preventive maintenance policies: A case study

In this paper, two preventive maintenance (PM) policies for the bus engines of a transport network have been considered. Based on the mean time to failure (MTTF) data of the engines of a particular make and model, maintenance policies are developed where the failure rate of the engines does not exceed the pre-determined level of maximum failure rate. In policy I, the system has a different failure distribution (Weibull) between PMs, and in policy II, each PM reduces the effective age of the system. The number of PM interventions and their schedule times, which minimize the expected mean cost rate over an infinite time horizon for both the policies, have been discussed. Finally, numerical illustrations and the effect of cost factors on the number of PM interventions and the expected cost rates have been presented.     

Optimum Age Replacement in the Bivariate Exponential Case

An age replacement policy is considered for pairs of units which operate in parallel and which have lifetimes displaying a bivariate exponential distribution. Both units are to be replaced at the same time. The limiting expected cost per unit time is the optimization criterion. The results state that no replacements should be made until at least one of the units in the pair fails. Both units shoould then be replaced either when one fails or when both fail, depending on which procedure involves the smaller limiting expected cost per unit time.     

Cost analysis of a two-unit cold standby system with two types of operation and repair

This paper deals with the cost analysis of a single-server two-identical unit cold standby system and two types of repair—minor and major. The unit requires minor repair if it fails for the first time. The major repair is required only when the unit fails after the minor repair. Upon minor repair the unit does not work as a normal unit but as a quasi-normal unit which has a different (increased) failure rate from that of a new one. Upon major repair the unit works as good as new (normal unit). Failure time distributions are negative exponential whereas repair time distributions are general. Using regeneration point technique the system characteristics of interest to system designers and operations managers have been obtained.     

传统室分错层单支路泄漏实现MIMO双流效果

随着移动网络的迅速发展,用户对下载速率的要求越来越高。但考虑建设成本,目前绝大多数楼宇的LTE室内分布系统方案为在原有的单通道分布系统基础上进行简单的合路,无法发挥LTE MIMO双流传输模式的技术优势,损失LTE室内分布系统约50%的容量。为低成本实现4G室内分布系统中的MIMO双流效果,提高4G用户感知,本文提出错层单支路泄漏实现MIMO双流效果的方法。     

System characteristic and cost analysis of a two unit standby system with spare units

This paper deals with the stochastic analysis of a standby system having two main units and two spare units.A spare unit is only used for operation when both main units fail and if it fails,it is replaced by the new one until the repair of the failed main unit is completed. The system fails when the last spare unit fails while one main unit is under repair and the other has failed. Using renewal theoretical arguments, certain characteristics of the system are derived and using them the cost of the system is calculated. Particular cases of the model are also considered.     

Optimal Age-Replacement Policy Under an Imperfect Renewing Free-Replacement Warranty

This paper investigates the effects of an imperfect renewing free-replacement warranty (RFRW) on the classical age-replacement policy for a product with an increasing failure rate. Under the imperfect RFRW, whenever a product fails during the warranty period, it is replaced by a repaired one from an infinite stock of refurbished items, at no cost to the purchaser, with a new full warranty. We assume that the failure potential of the repaired product is inferior to that of a new product; that is, the repaired product is less reliable than a new one. Long-run expected cost rates for the age-replacement policy are developed for two cases: when the preventive replacement age occurs before, and when it occurs after the warranty expires. The optimal replacement ages that minimize the cost rates are determined, and the impact of an imperfect RFRW on the optimal replacement age is illustrated with a numerical example. We review the literature dealing with warranty and maintenance against this framework, and conclude with some discussions on topics for research in the future. The imperfect RFRW proposed in this paper is practical, and novel; and this study represents a useful extension of Yeh that promises to be of interest to reliability engineers, managers, and theoreticians.     

An M/M/1 system with an unreliable device and a threshold recovery policy

An M/M/1 queueing system with an unreliable device is considered in the study. The device fails in an exponentially distributed time during which it is in the working condition and serves a demand. The device recovers during an exponentially distributed time according to the threshold policy specified by threshold level q ≥ 1. After a successive failure, the device does not recover until the number of demands exceeds level q. In the study, the system operating in the stationary regime is analyzed and the problem of optimal recovery control aimed at the minimization of the mean cost for a given penalty structure is solved.     

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     

Cost analysis of a two-unit warm standby reliability system with two types of repair facilities

This paper deals with a two-unit warm standby system. These units are identical, but have different failure rates and repair time distributions, when failed in operating or standby state. If the unit fails in operating state, we wait for the repairman for some maximum time or until the other unit fails, and if the unit fails in standby state we wait for the repairman until the other unit fails. On the failure of the second unit or on the completion of the maximum time, we call the repairman immediately at the higher cost.The system has been analysed to determine the various reliability measures by using semi-Markov processes and regenerative processes. Numerical results pertaining to some particular cases are also added.     

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     

System Availability and Optimum Spare Units

The steady-state availability of a repairable system with cold standbys and nonzero replacement time is maximized under constraints of total cost and total weight. Likewise the cost can be minimized under constraints of steady-state availability and total weight. A new, more efficient algorithm is used for the constrained optimization. The problem is formulated as a nonlinear integer programming problem. Since the objective functions are monotone, it is easy to obtain optimal solutions. These new algorithms are natural extensions of the Lawler-Bell algorithm. Availability is adjusted by the number of spares allowed. Other measures of system goodness are considered, viz, failure rate, weight, price, mean repair time, mean repair cost, mean replacement time, and mean replacement cost of a unit.