A novel repair model for imperfect maintenance

^** Email: shaomin.wu{at}reading.ac.uk Commonly used repair rate models for repairable systems in thereliability literature are renewal processes, generalised renewalprocesses or non-homogeneous Poisson processes. In additionto these models, geometric processes (GP) are studied occasionally.The GP, however, can only model systems with monotonously changing(increasing, decreasing or constant) failure intensities. Thispaper deals with the reliability modelling of failure processesfor repairable systems where the failure intensity shows a bathtub-typenon-monotonic behaviour. A new stochastic process, i.e. an extendedPoisson process, is introduced in this paper. Reliability indicesare presented, and the parameters of the new process are estimated.Experimental results on a data set demonstrate the validityof the new process.     

Generalized stationary models for scheduling single and multiple preventive maintenance routines

This paper is concerned with the development and applicationof stationary models for scheduling single and multiple preventivemaintenance (PM) situations focusing on issues of model implementation.The first part of the paper deals with the practical implementationof the basic single PM scheduling model based on the renewalprocess. The main practical difficulty is lifetime-distributionselection for small data sets which is typical in PM situations.Thus a sensitivity analysis of optimal PM interval to selectedlife distributions following PM and failures (corrective maintenance)is carried out. It has been found that the selected pair ofdistributions using AIC criteria as well as the Weibull–Weibullfitted pair have the smallest availability loss in estimatingthe optimal PM interval. The second part of this paper is concernedwith modelling multi-PM situations—something which hasreceived very little attention in the literature despite itsfrequent implementation in real life. A multi-PM model basedon the renewal process is discussed. The model assumes a multi-PMinterval which is an integer multiple of the single PM intervalsand different renewal functions following each type of PM. Theprocedure of model implementation is discussed through numericalexample.     

考虑不完全检测的冲击模型最优维修策略

针对制造系统中设备检测不完全的情形,研究基于不完全检测的冲击模型的周期检测、维修联合策略．通过定期检测获知系统的劣化状态以进行必要的预防性维修．在假设系统是退化的且有k个不同故障状态的条件下,以最小化系统运行成本为目标,以检测周期T、系统更换前故障次数Ⅳ为联合决策变量,利用更新过程理论建立了系统平均费用率C（T,N）的数学模型,并且给出最优联合策略的数值算法．最后借助数值例子演示了该模型,分析了检测水平对系统运行成本的影响．     

考虑中间库存缓冲区的多目标设备不完美预防维修策略研究

针对考虑库存缓冲区的多目标设备维修问题,以设备维修能力为约束条件,获得随机故障设备的不完美预防维修策略。首先,利用准更新过程,表示出设备的随机故障次数。其次,结合设备故障次数表达式,以最大设备可用度和最小生产总成本为多目标构建不完美预防维修模型,使用粒子群算法求解,优化设备可用度与生产总成本,获得更新周期内的库存量和预防维修周期两个决策变量的最优值。最后,通过算例分析,验证了多目标不完美预防维修模型的可用性。     

有两种故障状态的两部件串联系统的预防维修策略

本文研究的是由两个部件串联组成且有两种故障状态的系统的预防维修策略, 当系统的工作时间达到T时进行预防维修, 预防维修使部件恢复到上一次故障维修后的状态。每个部件发生故障都有两种状态, 可维修和不可维修。当部件的故障为可维修故障时, 修理工对其进行故障维修, 且每次故障维修后的工作时间形成随机递减的几何过程, 每次故障后的维修时间形成随机递增的几何过程。当部件发生N次可维修故障或一次不可维修故障时进行更换。以部件进行预防维修的间隔和更换前的可维修故障次数N组成的二维策略(T, N) 为策略, 利用更新过程和几何过程理论求出了系统经长期运行单位时间内期望费用的表达式, 并给出了具体例子和数值分析。     

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.     

有延迟修理的两部件串联系统的预防维修策略

研究由两个部件串联组成的系统的预防维修策略, 当系统的工作时间达到T时进行预防维修, 预防维修使部件恢复到上一次故障维修后的状态. 当部件发生故障后进行故障维修, 因为各种原因可能会延迟修理. 部件在每次故障维修后的工作时间形成随机递减的几何过程, 且每次故障后的维修时间形成随机递增的几何过程. 以部件进行预防维修的间隔T和更换前的故障次数N组成的二维策略(T,N)为策略, 利用更新过程和几何过程理论求出了系统经长期运行单位时间内期望费用的表达式, 并给出了具体例子和数值分析.     

基于累积损伤过程的不完全预防维护决策

基于累积损伤过程研究旧系统的不完全预防维护策略,冲击服从非时齐Poisson过程,并产生随机的损伤量,损伤量是加法累加的.系统在累积损伤量达到k或系统运行年龄达到T时进行计划内预防维护.在两次计划内预防维护之间,当累积损伤量达到预定水平K (k K)时,对系统进行计划外维护,其费用高于计划内预防维护,利用再生过程理论得到单位时间维护成本,讨论在时齐Poisson过程下的时间预防维护策略与水平预防维护策略,同时给出算例.     

A new preventive maintenance strategy for items sold under warranty

When products are sold under warranty, the manufacturer incursadditional costs for warranty servicing. Preventive maintenanceactions can be used to reduce this cost and these are worthwhileonly if the extra cost incurred is less than the reduction achieved.In this paper we propose a new preventive maintenance policywhere the parameters are selected optimally to minimize thetotal warranty servicing cost.     

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。     

基于CBM-HTM的复杂系统预防性维修时机优化

针对目前复杂系统因多采用定周期预防性维修而造成维修费用过高、管理效率较低的情况,综合定周期维修(HTM)和基于状态的维修(CBM)两类技术,提出基于CBM-HTM的复杂系统预防性维修时机优化思路.并在此基础上,以费用最小为目标,建立基于CBM-HTM的复杂系统预防性维修时机优化模型.最后以由6个设备组成的复杂系统为例,进行了预防性维修时机优化算例说明.以期借助自主式保障中PHM、CBM技术,优化地面设备预防性维修时机,降低地面设备的预防性维修费用,提高地面设备维修管理的效率和效益.     

带有一个冷贮备部件的两部件串联系统机会维修策略

针对带有一个冷贮备部件的两部件串联系统,本文首先提出一种预防维修与机会维修相结合的维修策略,运用更新报酬定理求得长期运行情况下的单位时间期望维修成本函数的表达式,然后研究最优的机会维修阀值,运用微分学理论求解最优解,最后用实例验证理论的正确性,从实际例子说明本文提出的维修策略可明显节约维修成本,为相应的带有冷贮备的多部件串联系统的维修策略分析提供参考,对企业设备的维修有实际指导意义。     

A Comparison of Two Sequential Metropolis-Hastings Algorithms with Standard Simulation Techniques in Bayesian Inference in Reliability Models Involving a Generalized Gamma Distribution

In this paper we consider the generalized gamma distribution as introduced in Gåsemyr and Natvig (1998). This distribution enters naturally in Bayesian inference in exponential survival models with left censoring. In the paper mentioned above it is shown that the weighted sum of products of generalized gamma distributions is a conjugate prior for the parameters of component lifetimes, having autopsy data in a Marshall-Olkin shock model. A corresponding result is shown in Gåsemyr and Natvig (1999) for independent, exponentially distributed component lifetimes in a model with partial monitoring of components with applications to preventive system maintenance. A discussion in the present paper strongly indicates that expressing the posterior distribution in terms of the generalized gamma distribution is computationally efficient compared to using the ordinary gamma distribution in such models. Furthermore, we present two types of sequential Metropolis-Hastings algorithms that may be used in Bayesian inference in situations where exact methods are intractable. Finally these types of algorithms are compared with standard simulation techniques and analytical results in arriving at the posterior distribution of the parameters of component lifetimes in special cases of the mentioned models. It seems that one of these types of algorithms may be very favorable when prior assessments are updated by several data sets and when there are significant discrepancies between the prior assessments and the data.     

非正态总体控制图和预防维修策略耦合优化的研究

主要探讨非正态有偏总体的过程监控和预防维修耦合优化问题。假定设备故障率随时间递增,设备发生异常前在正常状态的停留时间服从威布尔分布,一旦发生异常将导致过程均值漂移。采用赋权方差法构造X控制图,将过程监控和预防维修策略联系起来,结合生产不合格品损失、抽样成本及维修成本等,构建综合损失模型,提出动态抽样方案、控制图参数和预防维修间隔的确定方法。最后对模型进行了灵敏度分析。     

Bayesian analysis of fixed-interval preventive-maintenance models

This article develops methods for making accurate decisionswhen scheduling preventive maintenance in systems where inter-eventtimes can be modelled by a delayed renewal process or delayedalternating renewal process. A practical application, relatingto the reliability and maintenance of a relatively low-levelcomponent (valve) in a continuous-process industry over a periodof six years is presented to demonstrate and compare the differentapproaches. Our analyses indicate a cost-effective recommendationfor maintenance practice in this context. Our main thrust relates to the use of Bayesian methodology inorder to obtain rational, admissible decisions. Particular advancesover previous research allow for informative prior distributions,better approximations which lead to improved accuracy, non-negligibledowntimes, and general lifetime distributions. General analyticsolutions are sought for the simpler models, in order to achieveaccuracy and insight. The resulting integrals can only be solvedto give an infinite series and one approximation to the requiredsolution is obtained by truncating this series. Two other approximationsare developed, based on expansions of the prior predictive andlog-posterior distributions. A simulation approach is also developed to include prior informationand hence provide alternative approximations to these optimaldecisions. With exponential lifetime distributions, the relevantposterior lifetime distributions are non-central Pareto. Thissimulation is simple to program, compared to the approximations,but requires more computing time. It is accurate and extendseasily to situations involving greater complexity. We considertwo such extensions, the inclusion of downtimes and Weibulllifetime distributions.