A model for the integrity assessment of ageing repairable systems

The failure rate of mechanical repairable systems that deteriorate with time due to ageing can usually be visualized by a bathtub curve. This study shows that an equation that is valid in other respects for describing creep curves can easily be deduced from functional forms of the failure rate of mechanical repairable systems. Creeping pieces can be considered repairable systems that evolve under an applied load, as combining positive and negative feedback loops. More generally, this can be extended to mechanical repairable systems, the negative feedback loops corresponding to repair and overhaul operations. The equation describing creep curves reflects the ageing of mechanical repairable systems. A critical time at which the system can no longer be restored to full performance, in spite of repair and/or replacement of subparts, can then be predicted. An application example is given using published failure data corresponding to a submarine main-propulsion diesel engine. The proposed model should apply every time that mechanical system ageing is expressed by a bathtub curve     

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.     

An optimal replacement policy for a three-state repairable system with a monotone process model

In this paper, a deteriorating simple repairable system with three states, including two failure states and one working state, is studied. Assume that the system after repair cannot be "as good as new", and the deterioration of the system is stochastic. Under these assumptions, we use a replacement policy N based on the failure number of the system. Then our aim is to determine an optimal replacement policy N/sup */ such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. An explicit expression of the average cost rate is derived. Then, an optimal replacement policy is determined analytically or numerically. Furthermore, we can find that a repair model for the three-state repairable system in this paper forms a general monotone process model. Finally, we put forward a numerical example, and carry through some discussions and sensitivity analysis of the model in this paper.     

A Two-Unit Cold Standby Repairable System with One Replaceable Repair Facility and Delay Repair: Some Reliability Problems

1 Model and Assumption In reliability analysis of repairable systems, it is usually assumed that the repair facility neither fails nor deteriorates as well as the repairman is instantaneously available. So that the repair is started immediately upon the failure of a unit provided that he is not busily repairing another unit. However, in actual practice, the repair facility in a repairable system is subject to failure and can be replaced (or can be repaired) after it fails, and certain delay ac…     

Optimum system availability and spare allocation

This paper presents a method for optimizing the number of spare units in order to maximize the steady-state availability of a repairable system with cold standbys and non-zero replacement time under constraints of “costs”. The problem is formulated as a non-linear integer programming problem and a new algorithm named Multiple Gradient is used for the constrained optimization. The practical calculation is carried out on a computer, the results being presented in a form of a list of necessary spare units. At the same time, information is received concerning the steady-state availability of the system and the “costs” of the maintenance philosophy.     

Optimal replacement of improving and deteriorating repairablesystems

System improvement and deterioration are defined in terms of partial orderings between life distributions. The effects of ageing of `the distribution of time to first failure' on improvement and deterioration of a repairable system subject to minimal repairs, are investigated. Under various types of life distributions we derive explicitly the times at which the system should be condemned (replaced by a new one) to minimize the total cost of maintenance and replacement in terms of parameters of the distribution and of the cost function     

雷达装备可修复备件三级库存优化仿真

针对雷达装备器材供应保障中可修复备件配置问题,在分析三级保障结构下可修复备件运转流程的基础上,构建了可修复备件三级供应保障结构下库存优化模型。模型采用基层级供应可用度作为优化目标,以备件订购费用作为约束条件,运用边际分析法优化可修复备件三级库存配置,实现了在有限购置费用约束条件下的基层级供应可用度最大化。最后,通过实例对三级库存模型进行了仿真分析,并评估了中继级维修时间、基地级补给时间等因素对基层级供应可用度的影响,仿真结果可为雷达装备可修复备件合理配置提供参考。     

Reliability analysis of a two state repairable parallel redundant system under human failure

In this paper, the investigations have been carried out for the MTTF and reliability analysis of a repairable two-unit redundant electronic equipment having two states under human failures. The two-unit repairable parallel redundant system suffers two types of failures; viz; unit failure and human failure. Human failure brings the system to a complete failure stage. There is only one server who is always available. Laplace transforms of the probabilities of the complex system being in up and down states have been derived and have been inverted to obtain time dependent probabilities. Two graphs have also been given in the end.     

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 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     

关于可修复系统的MTBF和MTTR

在可修复系统中，可用性作为一种可靠性测度，其指标可用度是基本的；然而从实际应用角度来说平均无故障工作时间和平均修复时间有时显得更为重要，却又往往难以得知，本文首次提供了计算一般的ＭＴＢＦ和ＭＴＴＲ的有效公式，此系统具有负指数分布失效和修复时间部件。     

可修排队系统中可靠性指标的分解

本文提出了一种分析可修排队系统的新信息处理－分解法，应用该方法我们重新讨论了服务器可修的Ｍ／Ｇ／１排队系统，获得服务器在时刻ｔ失效的概率和在（０，ｔ］中失效的平均次数这两个主要可靠性指标的分解结果，而且进一步分析了服务器可修的ＧＩ／Ｇ１排队系统。值得注意的是本文提出的解解法新颖、简洁。     

Cost analysis of a three-state repairable redundant complex system under various modes of failures

In this paper investigations have been carried out for the availability and mean time to failure analysis of a three unit repairable electronic equipment having three states; viz; good, degraded and failed under critical human errors. The three states three units repairable electronic equipment suffers two types of failures; viz; unit failure and failure due to critical human errors. Entire system can fail due to critical human errors. The failure and repair times for the system follow exponential and general distributions respectively. Laplace transforms of the probabilities of the complex system being in various states are obtained along with steady state behaviour of the equipment. A numerical example has also been appended to highlight the important results. Three graphs have also been given in the end. There is only one repair facility, which is availed only when the system is in either degraded or failed state due to unit failure.     

Cost-benefit analysis of a system with intermittent repair and inspection under abnormal weather

This paper studies a repairable system with intermittent repair. Weather under which the system works changes randomly (in time) from normal to abnormal weather and vice-versa. By intermittent repair, we mean that the repair facility is not available instantaneously but takes random time to be available. The system operating under abnormal weather is sent for inspection randomly with Poisson process. Failure rates of the system and rates of change of weather are constant while repair times, inspection time and inter-inspection time are arbitrarily distributed. The system is analysed by using regenerative point technique to obtain various economic measures such as mean time to system failure, steady state availability, probability that the repairman is busy, expected number of visits by repairman and expected profit earned by the system.     

Distribution of total uptime during a given time interval

The distribution of total uptime during a given time interval for a repairable system is obtained. The total uptime is the total amount of time the system is up (in operation) during the interval. It is assumed that: (1) the system starts to operate at the beginning of the interval and alternately takes only the two states, up and down (under repair); (2) repair restores the system to “like-new”. A simple approximation to the distribution function of total uptime for a shorter interval is presented     

Reliability of a 2-Unit Standby Redundant System with Repair, Maintenance and Standby Failure

A repairable 2-unit warm-standby system with repair and preventive maintenance is discussed. Two models are presented. In each of the models the mean time to system failure and the steady state availability are calculated. Some numerical calculations illustrate the results.     

Parametric Programming Approach for a Two-Unit Repairable System With Imperfect Coverage, Reboot and Fuzzy Parameters

This paper proposes a procedure for constructing the membership functions of the system characteristics of a two-unit repairable system in which the coverage factor for an operating unit failure is possibly considered. Times to failure, and times to repair of the operating units are assumed to follow fuzzified exponential distributions. In addition, the recovery times, and reboot times of the failed units also follow fuzzified exponential distributions. The $alpha$-cut approach is used to extract the fuzzy repairable system from a family of conventional crisp intervals for the desired system characteristics, determined with a set of parametric nonlinear programs using their membership functions. Two numerical examples illustrate the practicality of the proposed approach. Because the system characteristics are governed by the membership functions, more information is provided for use by designers and practitioners. The successful extension of the parameter spaces to fuzzy environments permits the repairable system to have wider practical applications.      

Optimal monitoring strategies for slowly deteriorating repairablesystems

A simple model for determination of an optimal limit on taking corrective action in a slowly deteriorating repairable system is presented. The performance of such a system is assumed to be characterized by a single parameter which is continuously being monitored. The underlying deterioration process is assumed to be governed by a Brownian motion process with a positive drift. When the measured value of the parameter reaches the action limit, the repair/replacement procedure is initiated. The optimal action limit is derived so that the expected long run average total cost is minimized. Some simple numerical examples illustrate the model and the optimization     

Stochastic behaviour of a repairable system operating under fluctuating weather

A repairable system which operates under fluctuating weather conditions is considered. There are 3 types of weathers: normal, abnormal 1 and abnormal 2. Weather changes from normal to abnormal 1 and abnormal 2 at exponential rates. Failure time distribution of the system from normal weather is exponential whereas it is general from abnormal states. Repair time distributions are different and general. The model is analysed by the help of SMP technique and reliability parameters viz MTSF, steady-state availability, absorption probabilities etc. are obtained.     

Stochastic behaviour and profit function of a system with precautionary measures under abnormal weather

A repairable system under normal and abnormal weather conditions is analysed. The system can be in one of the three modes—normal, partial and total failure. Failure rates of system and rates of change of weather conditions are constant while the repair rates are arbitrary functions of time. The repair time distributions depend upon the state from which the repair starts and are invariant with the change of weather. Using regenerative point technique various reliability characteristics such as mean time to system failure, steady state availability, the probability that the repairman is busy, expected number of visits by repairman and expected profit earned by the system are obtained.