A sequential method for preventive maintenance and replacement of a repairable single-unit system

This paper is concerned with when to implement preventive maintenance (PM) and replacement for a repairable ‘single-unit’ system in use. Under the main assumption that a ‘single-unit’ system gradually deteriorates with time, a sequential method is proposed to determine an optimal PM and replacement strategy for the system based on minimising expected loss rate. According to this method, PM epochs are determined one after the other, and consequently we can make use of all previous information on the operation process of the system. Also the replacement epoch depends on the effective age of the system. A numerical example shows that the sequential method can be used to solve the PM and replacement problem of a ‘single-unit’ system efficiently. Some properties of the loss functions W(L? _n ,b? _n ) and W? _r (N) with respect to PM and replacement respectively are discussed in the appendix.     

Preventive maintenance in a 1 out of n system: The uptime,downtime and costs

In repairable systems with redundancy, failed units can be replaced by spare units in order to reduce the system downtime. The failed units are sent to a repair shop or manufacturer for corrective maintenance and subsequently are returned for re-use. In this paper we consider a 1 out of n system with cold standby and we assume that repaired units are “as good as new”.When a unit has an increasing failure rate it can be advantageous to perform preventive maintenance in order to return it to its “as good as new” state, because preventive maintenance will take less time and tends to be cheaper. In the model we present we use age-replacement; a machine is taken out for preventive maintenance and replaced by a standby one if its age has reached a certain value, T_pm. In this paper we derive an approximation scheme to compute the expected uptime, the expected downtime and the expected costs per time unit of the system, given the total number of units and the age-replacement value, T_pm. Consequently the number of units and the value T_pm can be determined for maximum long-term economy.     

Optimization of a fully adaptive quality and maintenance model in the presence of multiple location and scale quality shifts

This paper presents a new model for the economic-statistical optimization of a Variable-Parameter Shewhart control scheme. The proposed model can be utilized to monitor processes where apart from multiple independent assignable causes, affecting both the mean and variance, failures can also occur. Each time an alarm is issued by the control scheme, preventive maintenance actions are initiated, whereas, corrective maintenance actions are required after a failure. The more realistic assumption of imperfect preventive maintenance actions has been considered. The optimal parameter values are selected through a bi-objective optimization problem formulated by the long-run average cost per time unit minimization, and the long-run expected availability maximization, subject to statistical constraints. A real case example is presented to illustrate the application of the model. An extended numerical investigation is utilized to evaluate the superiority of the proposed model.     

Tramcar Maintenance

This article describes the work done to determine age limits for preventive replacements and overhauls in tramcar maintenance, where opportunities are provided by a failed component or an essential overhaul. A brief review of existing literature is also presented and two pair-wise suboptimal preventive replacement policies are considered. These policies are applicable to any "n" component system with subassemblies, where the cost of dismantling and assembling the various sub-units is of the same order as the cost of new parts. The results of a search to find more economical control limits are also presented.     

Optimal scheduling of non-perfect inspections

^** Corresponding author. Email: romulo.zequeira{at}utt.fr^*** Email: christophe.berenguer{at}utt.fr In this paper, we study the determination of optimal inspectionpolicies when three types of inspections are available: partial,perfect and imperfect. Perfect inspections diagnose withouterror the system state. The system can fail because of threecompeting failure types: I, II and III. Partial inspectionsdetect without error type I failures. Failures of type II canbe detected by imperfect inspections which have non-zero probabilityof false positives. Partial and imperfect inspections are madeat the same time. Type III failures are detectable only by perfectinspections. If the system is found failed in an inspection,a repair is made which renders the system in a good-as-new condition.The system is preventively maintained following an age-basedpolicy. Preventive maintenance actions return the system toa good-as-new condition. We consider cost contributions of inspections,repairs, preventive maintenance and periods of unavailability.The model presented permits to determine the optimal (constant)inter-inspection period for partial, imperfect and perfect inspectionsand the optimal times of preventive maintenance actions.     

A hybrid maintenance model with imperfect inspection for a system with deterioration and Poisson failure

A new maintenance model for a system with both deterioration and Poisson failures is proposed. In this model, at any time-instant G _S and when the system is operating, one of the following decisions may be taken: (1) stop the system to perform a scheduled minimal maintenance; (2) stop the system to perform an inspection; and (3) no action and allow the system to go on with its operation. Following an inspection, based on the deterioration condition of the system, one of the following decisions may be taken: (a) if the system is in a ‘good’ condition, no maintenance action is taken and a number of periodic minimal maintenance activities are scheduled, starting T1 later; (b) if the system is in an ‘intermediate’ condition, a minimal maintenance is performed and an inspection is scheduled for T2 later (T2 < T1); and (c) if the system is in a ‘bad’ condition, a major maintenance is performed and a number of periodic minimal maintenances are scheduled, starting T1 later. In addition, a deterioration failure is restored by a major repair and a Poisson failure is restored by a minimal repair. Generalised stochastic Petri nets are used to represent and analyse the model, which represents a ‘composite’ maintenance strategy. Based on maximisation of the throughput of the system the benefit of this model compared to (1) an equivalent periodic inspection model and (2) an equivalent planned scheduled maintenance model, is demonstrated. This study presents a new hybrid model with a general framework for incorporating various types of maintenance policies. Also by incorporation of a number of features, this model will be more applicable to real world technical systems (complex systems), although it can be applied to individual components that are part of a complex system.     

Optimal replacement policy for a multistate repairable system

In this paper, a deteriorating simple repairable system with k + 1 states, including k failure states and one working state, is studied. The system after repair is not ‘as good as new’ and the deterioration of the system is stochastic. Under these assumptions, we study a replacement policy, called policy N, based on the failure number of the system. The objective is to maximize the long-run expected profit per unit time. The explicit expression of the long-run expected profit per unit time is derived and the corresponding optimal solution may be determined analytically or numerically. Furthermore, we prove that the model for the multistate system in this paper forms a general monotone process model which includes the geometric process repair model as a special case. A numerical example is given to illustrate the theoretical results.     

Reliability Analysis of a One-Unit System with Unrepairable Spare Units and its Optimization Applications

It is assumed that a unit is either in operation or is in repair. When the main unit is under repair, spare units which cannot be repaired are used. In this system the following quantities are of interest: (i) The time distribution and the mean time to first-system failure, given that the n spare units are provided at time 0. (ii) The probability that the number of the failed spare units are equal to exactly n during the interval (0, t], and its expected number during the interval (0, t]. These quantities are derived by solving the renewal-type equations.Two optimization problems are discussed using the results obtained, viz.: (i) The expected cost of two systems, one with both a main unit and spare units and the other with only spare units is considered. (ii) A preventive maintenance policy of the main unit is considered in order to minimize the expected cost rate. Some policies of the two problems are discussed under suitable conditions. Numerical examples are also presented.     

自保护相依多部件系统的预防维修建模及策略优化

自保护技术作为自愈技术的一种,能够使系统在环境或工况条件变化的干扰下以较高可靠性运行。本文构建了一个新的具有相依主要部件和辅助部件的系统可靠性模型,其中主要部件的退化速率与工作中的辅助部件的数量有关。此外,基于定期检测和预防维修策略,本文利用半再生过程技术求解了系统的长期运行平均成本,并以长期运行平均成本最小化为目标给出了系统的最优预防维修策略。最后,以镗刀系统为例,利用所提方法给出了预防更换阈值和检测周期的最优值,以期望为实际维修行为决策提供理论参考。     

Prioritization of medical equipment for maintenance decisions

Clinical engineering departments in hospitals are responsible for establishing and regulating a Medical Equipment Management Program to ensure that medical devices are safe and reliable. In order to mitigate functional failures, significant and critical devices should be identified and prioritized. In this paper, we present a multi-criteria decision-making model to prioritize medical devices according to their criticality. Devices with lower criticality scores can be assigned a lower priority in a maintenance management program. However, those with higher scores should be investigated in detail to find the reasons for their higher criticality, and appropriate actions, such as ‘preventive maintenance’, ‘user training’, ‘redesigning the device’, etc, should be taken. In this paper,we also describe how individual score values obtained for each criterion can be used to establish guidelines for appropriate maintenance strategies for different classes of devices. The information of 26 different medical devices is extracted from a hospital's maintenance management system to illustrate an application of the proposed model.     

Evaluation of the expected makespan of a set of non-resumable jobs on parallel machines with stochastic failures

In this paper we consider a production process at operative level on m$m$ identical parallel machines, which are subject to stochastic machine failures. To avoid long downtime of the machines, caused by unexpected failures, preventive maintenance activities are planned and conducted, but if a failure could not be averted a corrective maintenance has to be performed. Both maintenance activities are assumed to restore the machine to be “as good as new”. The maintenance activities, the number of jobs and their allocation to machines as well as their sequence have a large impact on the performance of the production process and the delivery dates.     

A condition-based maintenance model

Condition-based maintenance (CBM) is very appealing becauseit enables one to make maintenance decisions based on the currentinformation about the system. Various monitoring techniqueshave been developed to obtain this information, but there arestill very few mathematical models capable of utilizing it foreffective maintenance decision making. In this paper, we propose a CBM model for situations where onlypartial information is available through monitoring a signalprocess that does not necessarily exhibit monotone behaviour.The evolution of the signal process is determined by randomfactors and minor maintenance actions between inspections. Theobjective is to find the replacement policy that maximizes thetotal expected profit during the lifetime of the system. Wewill show that, under weak monotonicity assumptions, the optimalpolicy is of a control-limit type, and we will develop an algorithmfor finding the limit for an -optimal policy.     

基于预防维修和质量损失函数的VSI EWMA控制图经济设计

为了提高过程监控效率的同时降低过程控制成本,研究可变抽样区间(VSI)指数加权移动平均(EWMA)控制图的经济设计问题。首先建立基于预防维修和质量损失函数的VSI EWMA控制图联合经济模型;使单位时间的损失成本函数最小来确定参数的最优值;其次用遗传算法来寻找联合经济模型的最优解,并给出一个算例。最后对VSI EWMA控制图联合经济模型进行灵敏度分析,得出控制图模型参数对设计参数的影响关系。     

A semi-Markov maintenance model with credit rating application

Email: g.damico{at}unich.it Received on 6 December 2006. Accepted on 2 April 2008. The impact of a preventive rating maintenance policy on therating process is investigated through the definition of a semi-Markovmaintenance model with imperfect repair at random times. Theresults allow us to study the rating migrations process in thetransient and the asymptotic case.     

Analysis of multi-level queueing systems with servers breakdown by using recursive solution technique

In this paper we construct a multi-level queueing model that alternates between three modes of an operation system. The service times have followed an Erlang type K   distribution with parameter μ$\mu$. Customers arrive in batches according to a time-homogeneous compound Poisson process with mean rate λ$\lambda$ for the batches. Our aim is to give a recursive scheme for the solution of the steady state equations. Next we derive some important measures of performance which may affect the efficiency of the system under consideration such as the expected waiting time per customer, the expected number of customers who arrive to a full system. The expected number of customers will also be calculated. Finally, we can also calculate the efficiency measures of the system by using the recursive results through an example.     

带有多重休假及预防维修的冲击模型二维更换策略

研究了修理工带有多重休假且定期检测的累积冲击模型.为了延长系统的运行时间,在检测时考虑了预防维修.将事后维修和预防维修结合起来运用于可修系统,且假定预防维修能够"修复如新",而事后维修为"修复非新".以系统的检测周期和故障次数为二维决策变量,选取系统经长期运行单位时间内期望费用为目标函数.并通过数值分析,求出了最优策略.     

Optimal maintenance strategy under renewable warranty with repair time threshold

In this paper, we consider a periodic preventive maintenance model, from the manufacturer's perspective, which can be implemented to reduce the maintenance cost of a repairable product during a given warranty period. The product is assumed to deteriorate with age and the warranty policy we adopt in this paper takes into account the two factors of failure time and repair time of the product when the product failure occurs. Under the proposed two-factor warranty, a repair time threshold is pre-determined and if the repair takes more time than that of the threshold, the failed product is replaced with a renewed warranty policy. Otherwise, the product is only minimally repaired to return to the operating state. During such a renewable warranty period, preventive maintenance is conducted to reduce the rate of degradation periodically while the product is in operation. By assuming certain cost structures, we formulate the expected warranty cost during the warranty period from the manufacturer's perspective when a periodic preventive maintenance strategy is adapted. Although more frequent preventive maintenance increases the warranty cost, the chance of product failures would be reduced. The main aim of this paper is to accomplish the optimal trade-off between the warranty cost and the preventive maintenance period by determining the optimal preventive maintenance period that minimizes the total expected warranty cost during the warranty period. Assuming the power law process for the product failures, we illustrate our proposed maintenance model numerically and study the impact of relevant parameters on the optimal preventive maintenance policy.