基于状态监测数据的产品寿命预测与预测维护规划方法研究
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摘要
基于状态监测的维护是近来逐渐兴起的研究课题，具有重要实用意义与经济价值。以基于状态监测的维护为背景，本文结合理论研究、仿真实验、实验研究，开展目前报道较少，但决定维护策略有效性的预测（prognostics）技术主要方法的研究。
首先，本文开展两类寿命预测方法的研究。
以“基于相似性的寿命预测方法”为主题，开展两项研究：1）提出一个泛化的相似性测度，据此相似性测度，衡量在役设备与参照设备间的相似性时，在役设备当前的状态监测变量较其过往的状态监测变量，权重更高；2）提出一个同时利用失效与非失效历史样本的基于相似性的剩余寿命预测框架，在此框架内提出两种估计未失效历史样本寿命，进而利用其衰退过程信息的方案（记作方案A与方案B）。一项数值仿真实验与一个基于SMT无铅焊点随机振动实验的案例研究表明，采用泛化的相似性测度的基于相似性的寿命预测方法能给出统计意义上更精确的剩余寿命预测。一个系统的数值仿真实验验证了在存在有限失效历史样本与存在大量失效历史样本的情况下，基于方案A的框架始终优于对应的传统方法。此外，仿真实验结果揭示基于方案B的框架在失效历史样本有限情况下并不有效，但随着可获得的失效历史样本增多其表现迅速提升。
以“基于比例风险模型的设备寿命预测”为主题，开展两项研究：1）针对许多设备衰退过程可分为稳态区间和非稳态区间的事实，提出二区间比例风险模型；2）针对经典比例风险模型只适用于不可修系统的事实，提出拓展比例风险模型，用于接受“修复非新”预防维护的可修系统的寿命预测。数值仿真实验的结果表明：1）对于衰退过程可分为稳态区间和非稳态区间的系统，在接近系统失效时，二区间比例风险模型相对于传统比例风险模型，可给出统计意义上更精确、更可靠的剩余寿命预测；2）对于接受“修复非新”预防维护的可修系统，在系统接受预防维护后并接近失效时，拓展比例风险模型相对于传统比例风险模型，可给出统计意义上更精确、更可靠的剩余寿命预测。
其次，本文开展三项设备预测维护规划模型的研究。
相对于传统的“修复非新”预防维护规划模型，提出一个考虑“修复非新”预防维护的单部件系统预测维护(USPdM)规划模型，对接受连续监测的系统在线地计算、更新最优预防维护时序。基于钻头磨损实验的案例研究表明，1）USPdM模型所建议的预防维护时序与系统的状态变化情况相一致；2）USPdM模型能迅速反应系统的快速衰退，并给出预防维护时序。
实际中，将严重衰退的系统修复至一理想状态往往比将轻微衰退的系统修复至同样状态花费更多的时间。基于这样的事实，提出一个考虑“衰退程度相关维修性”的单部件系统预测维护规划模型。该模型中，预防维护的维修性与预防维护前系统所累积的衰退程度相关，并以新近提出的比例维护模型进行建模。数值仿真实验结果表明，对于一批预防维护维修性与系统累积衰退相关的系统，忽视这一效应将导致次优的预防维护时序。此外，仿真实验的结果也表明考虑“衰退程度相关”维护性的预测维护策略对于相应的预防维护策略的优势。
提出一个预测维护规划模型的模块化结构。基于这种模块化得处理方式，将传统的预防/基于状态监测的维护规划模型与基于部件在线衰退指标估计的失效概率相结合便可得到相应的预测维护规划模型，而两者均已有大量研究成果。基于预测维护规划模型的模块化结构，给出了一个多部件串联系统的预测维护规划模型。而后，开展了一仿真实验比较预测维护规划模型中最优预防维护时序与对应的预防维护规划模型中最优预防维护时序的表现，并探究两模型中最优预防维护时序的不同特性。算例的结果表明预测维护规划模型中的最优预防维护时序能更有效地节省维护费用并减少部件失效。算例的结果也突出了预测维护规划模型中最优预防维护时序针对个体、动态更新的特点，这与预防维护规划模型中最优预防维护时序适用全体、静态不变的特点不同。
而后，本文研究寿命预测方法与维护规划模型的结合方案，两者的结合方案文献中未见报道。
提出“统计规划与个体提升（SPII）”维护策略。SPII维护策略同时汲取了1）传统的预防维护策略能进行长期规划的优点，和2)寿命预测方法能提升个体表现的优点。SPII维护策略通过对一部分系统（而非全部系统）合理地使用预测维护技术（如：寿命预测方法），可以期望高于传统预防维护策略的表现。而后者能首先提供一个基准表现以在系统实际运行或生产前实施长期规划。
提出一个结合寿命预测方法与预测维护规划模型的维护框架。在该预测维护框架中，只有在寿命预测方法显示系统已接近失效时才开始进行维护规划。提出一个寿命裕度参数以保证绝大多数系统在维护规划开始前不失效。基于典型随机衰退信号模型的仿真实验演示了该维护框架的执行流程。在仿真实验中，当系统衰退过程噪声水平较低时，与传统的从系统开始运行便开始维护规划的预测维护框架相比，提出的维护框架在预防系统失效方面与前者表现非常相似，同时又能减少预防维护的次数，因而更具经济性。
最后，本文开展两项状态监测数据的应用案例研究。
基于BGA封装在随机振动环境中的实测状态监测数据与事件数据，介绍了从衰退过程分析至确定预防维护时间的全过程，定量地比较了一个引入状态监测技术的预防替换策略、一个传统的基于BGA封装全寿命周期长度分布的预防替换策略，以及一个预测维护策略。在此基础上，分析了状态监测数据带来维护性能提升的原因。分析结果显示，维护策略的表现与确定预防维护时间时对产品寿命预测的精确与可靠程度存在关联。由于基于状态变量的衰退模型给出了最精确、可靠的BGA封装的寿命预测，预测维护策略的维护表现最优。
提出一种基于分布式遥测量的卫星有效载荷在轨可靠性预计方案（包含了电路筛选，遥测量分类，各模块、电路条件可靠性函数集成等步骤），以充分利用当前已有设置但并未充分利用的电路遥测量的信息，同时给出了一个通信侦察主载荷单频段系统的案例以演示该方案的应用过程。
Condition-based maintenance (CBM) is an emerging reaseach topic with vitalapplication and economic significance. With CBM being the background, thisthesis develops and extends several methods for prognostics (i.e. equipmentresidual life (RL) prediction and predictive maintenance (PdM) scheduling)through theoretical investigation, simulation, and experimaetal validation.Equipment RL prediction and PdM have essential impact on the effectivenessof a maintenance policy but have not been fully investiagated in literature.
First of all, the thesis studies two types of methods for equipment RLprediction. Two studies are devoted to the topic of similarity-based residuallife prediction approaches. Within the framework of similarity-based RLprediction methods, a generalized similarity measure is proposed. By theproposed similarity measure, more weight is assigned to a system’s mostrecent performance than to its former performance when measuring itssimilarity with other systems. The experimental results from a numericalexperiment and a case study on RL prediction of ball grid array (BGA)packages show that, compared with the predictions with the classicalsimilarity measure, statistically more accurate predictions can be achievedwith the proposed similarity measure. A framework of similarity-basedresidual life prediction approaches is proposed, where historical samples thatfail and do not fail (do to preventiven maintenance or suspension) are bothutilized. Within the framework, two solutions (namely solution A and solutionB) are proposed to estimate the lifetimes of the preventively maintained orsuspended historical samples, and to utilize their degradation histories. Anextensive numerical investigation verifies the superiority of the proposedframework (using solution A) over the corresponding classical SbRLPapproach from the case of limited failed historical samples to the case ofabundant failed historical samples. In addition, the investigation results revealthat the proposed framework (using solution B) is ineffective when failedhistorical samples are limited, but its performance improves fast with the increment of available failed historical samples. Afterwards, two studies aredevoted to the topic of proportional harards model (PHM) based equipmentresidual life prediction:1) A Two-zone PHM is proposed based on the factthat many systems’ degradation processes can be devided into a stable zoneand an unstable zone;2) An extended PHM (EPHM) is proposed for RLprediction of systems receiving partial recovery preventive maintenance (PM)acts (i.e. imperfect PM acts), while the classical PHM is not applicable tonon-repairable systems. The results from numberical experiments show that:1)For systems whose degradation processes can be devided into a stable zoneand an unstable zone, the proposed two-zone PHM provides statistically moreaccurate and reliable predictions close to system failure, compared with theclassical PHM;2) For systems receiving imperfect PM acts, the proposedEPHM provides statistically more accurate and reliable predictions close tosystem failure, compared with the classical PHM.
Secondly, the thesis contributes three studies on PdM schedulingmodels/policies. Compared with the classical imperfect PM schedulingmodels, an updated sequential PdM (USPdM) policy is proposed consideringthe effect of imperfect PM acts. The USPdM calculates and updates theoptimal PM schedules for continuously monitored single-unit degradingsystems to minimize the long-term maintenance cost rate. A case study onPdM scheduling of wearing drill bits show that:1) The proposed USPdMmodel yields PM schedules that are consistent with the change in systemstates and2) the USPdM is able to quickly react to drastic degradation of thesystem and provide an optimal PM schedule in real time. In practice, itusually takes more time to restore a much degraded system to a desire statethan to restore a slightly degradaed system to the same state. Based on suchfact, a PdM policy is proposed for maximizing the average system availabilityof continuously monitored single-unit systems, considering the effect ofdegradation correlated maintainability. In the PdM policy, the maintainabilityof PM acts is correated with the accumulated degradation level, which ismodeled by the recently proposed proportional repair model (PRM). Theresults from the numerical experiment show that, for a batch of systemswhose PM maintainability is indeed correlated with the accumulateddegradation level, simply neglecting such effect would lead to suboptimal PMschedules. In addition, the results provide evidence of the superiority of thePdM policy over the corresponding PM polices in terms of higher averagesystem availability. The3rdstudy on PdM scheduling models/policies proposes a modularized framework of PdM scheduling. Based on themodularization treatment, a PdM scheduling model can be established byintegrating the classical PM/CBM scheduling models with components’failure probability estimated based on their degradation variables, and both ofthem have been widely studied. An unreported PdM scheduling model forserial systems is further established. Numerial experiments are conducted tocompare the optimal PM schedules from the PdM scheduling model for serialsystems and the counterparts from the corresponding PM scheduling model,and investigate the characteristics of the PM schedules from these two models.The experimental results show that the PdM model is more effective inmaintenance cost reduction. The results also highlight the individual-oriented,dynamically updating characteristics of the PM schedules from a PdMscheduling model, which is different from the population-oriented, static PMschedules from a PM scheduling model.
Thirdly, the thesis studies two integration schemes of two main aspects ofprognostics (i.e., equipment RL prediction methods and PdM schedulingmodels,), which has not been reported in literature. In the1ststudy, astatistically planned and individually improved (SPII) PdM policy is proposedfor continuously monitored single-unit systems. The SPII PdM policysimultaneously takes advantage of1) the capability of the classical statisticallifetime distribution based PM scheduling policy in long-term planning and2)the capability of RL prediction methods in improving individual performance.The value of the SPII PdM policy is that it demonstrates the possibility ofpartially applying the emerging RL prediction techniques in the widely usedstatistical lifetime distribution based PM policy in an (approximately)theoretically effective manner. By reasonably applying the RL predictiontechniques to a part of (but not all) individuals, a better performance of themaintenance policy can be expected, while the performance of the classicalPM policy can first provide baseline indexes for long-term palnning prior tosystem operation or real production. In the2ndstudy, a PdM framework isproposed for continuously monitored single-unit systems, which integratesequipment RL prediction methods and PdM scheduling models. Within theproposed framework, PdM scheduling is trigrred only when the RLpredication methods demonstrate that the system is close to failure. A lifetimemargine is proposed to infer that most systems do not fail before PdMscheduling is triggered. A numerial experiment demonstrates theimplementation procedures of the proposed framework. In the numrial experiment, when the noise level of the degradation process is relatively low,compared with the classical PdM scheduling model which starts maintenancescheduling once a system bengins operating, the proposed PdM framework issimilar effective in failure prevention and more economical in PM costsaving.
Finally, the thesis conducts two application studies on condition monitoringdata. Based on the condition monitoring and event data, the whole processfrom degradation process analysis to determination of PM schedules isdiscussed. A quantitative comparison among a preventive replacementscheduling model using condition monitoring data, a classical preventivereplacement scheduling model using statistical distribution of entire lifetimesof BGA packages, and a PdM scheduling model. Based on theimplementation results, the reason for maintenance performance improvementdue to the application of codition monitoring data is investigated. Theinvestigation results demonstrate the relationship bewtten the performance ofa maintenance policy and the accuracy and reliability of lifetime predictionwhen determing PM schedules. As the degradation model of the degradationindicator provides the most accurate and reliable lifetime prediction of BGApackages, the PdM scheduling model gives the best performance. A on-oribtreliability prediction method for spacebrone effective load is proposed to fullyutilized the remote monitoring variables, which has already been set on manykey circuits of spacebrone main load but has not been fully utilized. A casestudy is provided to illusate the application process of the proposed method.
首先，本文开展两类寿命预测方法的研究。
以“基于相似性的寿命预测方法”为主题，开展两项研究：1）提出一个泛化的相似性测度，据此相似性测度，衡量在役设备与参照设备间的相似性时，在役设备当前的状态监测变量较其过往的状态监测变量，权重更高；2）提出一个同时利用失效与非失效历史样本的基于相似性的剩余寿命预测框架，在此框架内提出两种估计未失效历史样本寿命，进而利用其衰退过程信息的方案（记作方案A与方案B）。一项数值仿真实验与一个基于SMT无铅焊点随机振动实验的案例研究表明，采用泛化的相似性测度的基于相似性的寿命预测方法能给出统计意义上更精确的剩余寿命预测。一个系统的数值仿真实验验证了在存在有限失效历史样本与存在大量失效历史样本的情况下，基于方案A的框架始终优于对应的传统方法。此外，仿真实验结果揭示基于方案B的框架在失效历史样本有限情况下并不有效，但随着可获得的失效历史样本增多其表现迅速提升。
以“基于比例风险模型的设备寿命预测”为主题，开展两项研究：1）针对许多设备衰退过程可分为稳态区间和非稳态区间的事实，提出二区间比例风险模型；2）针对经典比例风险模型只适用于不可修系统的事实，提出拓展比例风险模型，用于接受“修复非新”预防维护的可修系统的寿命预测。数值仿真实验的结果表明：1）对于衰退过程可分为稳态区间和非稳态区间的系统，在接近系统失效时，二区间比例风险模型相对于传统比例风险模型，可给出统计意义上更精确、更可靠的剩余寿命预测；2）对于接受“修复非新”预防维护的可修系统，在系统接受预防维护后并接近失效时，拓展比例风险模型相对于传统比例风险模型，可给出统计意义上更精确、更可靠的剩余寿命预测。
其次，本文开展三项设备预测维护规划模型的研究。
相对于传统的“修复非新”预防维护规划模型，提出一个考虑“修复非新”预防维护的单部件系统预测维护(USPdM)规划模型，对接受连续监测的系统在线地计算、更新最优预防维护时序。基于钻头磨损实验的案例研究表明，1）USPdM模型所建议的预防维护时序与系统的状态变化情况相一致；2）USPdM模型能迅速反应系统的快速衰退，并给出预防维护时序。
实际中，将严重衰退的系统修复至一理想状态往往比将轻微衰退的系统修复至同样状态花费更多的时间。基于这样的事实，提出一个考虑“衰退程度相关维修性”的单部件系统预测维护规划模型。该模型中，预防维护的维修性与预防维护前系统所累积的衰退程度相关，并以新近提出的比例维护模型进行建模。数值仿真实验结果表明，对于一批预防维护维修性与系统累积衰退相关的系统，忽视这一效应将导致次优的预防维护时序。此外，仿真实验的结果也表明考虑“衰退程度相关”维护性的预测维护策略对于相应的预防维护策略的优势。
提出一个预测维护规划模型的模块化结构。基于这种模块化得处理方式，将传统的预防/基于状态监测的维护规划模型与基于部件在线衰退指标估计的失效概率相结合便可得到相应的预测维护规划模型，而两者均已有大量研究成果。基于预测维护规划模型的模块化结构，给出了一个多部件串联系统的预测维护规划模型。而后，开展了一仿真实验比较预测维护规划模型中最优预防维护时序与对应的预防维护规划模型中最优预防维护时序的表现，并探究两模型中最优预防维护时序的不同特性。算例的结果表明预测维护规划模型中的最优预防维护时序能更有效地节省维护费用并减少部件失效。算例的结果也突出了预测维护规划模型中最优预防维护时序针对个体、动态更新的特点，这与预防维护规划模型中最优预防维护时序适用全体、静态不变的特点不同。
而后，本文研究寿命预测方法与维护规划模型的结合方案，两者的结合方案文献中未见报道。
提出“统计规划与个体提升（SPII）”维护策略。SPII维护策略同时汲取了1）传统的预防维护策略能进行长期规划的优点，和2)寿命预测方法能提升个体表现的优点。SPII维护策略通过对一部分系统（而非全部系统）合理地使用预测维护技术（如：寿命预测方法），可以期望高于传统预防维护策略的表现。而后者能首先提供一个基准表现以在系统实际运行或生产前实施长期规划。
提出一个结合寿命预测方法与预测维护规划模型的维护框架。在该预测维护框架中，只有在寿命预测方法显示系统已接近失效时才开始进行维护规划。提出一个寿命裕度参数以保证绝大多数系统在维护规划开始前不失效。基于典型随机衰退信号模型的仿真实验演示了该维护框架的执行流程。在仿真实验中，当系统衰退过程噪声水平较低时，与传统的从系统开始运行便开始维护规划的预测维护框架相比，提出的维护框架在预防系统失效方面与前者表现非常相似，同时又能减少预防维护的次数，因而更具经济性。
最后，本文开展两项状态监测数据的应用案例研究。
基于BGA封装在随机振动环境中的实测状态监测数据与事件数据，介绍了从衰退过程分析至确定预防维护时间的全过程，定量地比较了一个引入状态监测技术的预防替换策略、一个传统的基于BGA封装全寿命周期长度分布的预防替换策略，以及一个预测维护策略。在此基础上，分析了状态监测数据带来维护性能提升的原因。分析结果显示，维护策略的表现与确定预防维护时间时对产品寿命预测的精确与可靠程度存在关联。由于基于状态变量的衰退模型给出了最精确、可靠的BGA封装的寿命预测，预测维护策略的维护表现最优。
提出一种基于分布式遥测量的卫星有效载荷在轨可靠性预计方案（包含了电路筛选，遥测量分类，各模块、电路条件可靠性函数集成等步骤），以充分利用当前已有设置但并未充分利用的电路遥测量的信息，同时给出了一个通信侦察主载荷单频段系统的案例以演示该方案的应用过程。
Condition-based maintenance (CBM) is an emerging reaseach topic with vitalapplication and economic significance. With CBM being the background, thisthesis develops and extends several methods for prognostics (i.e. equipmentresidual life (RL) prediction and predictive maintenance (PdM) scheduling)through theoretical investigation, simulation, and experimaetal validation.Equipment RL prediction and PdM have essential impact on the effectivenessof a maintenance policy but have not been fully investiagated in literature.
First of all, the thesis studies two types of methods for equipment RLprediction. Two studies are devoted to the topic of similarity-based residuallife prediction approaches. Within the framework of similarity-based RLprediction methods, a generalized similarity measure is proposed. By theproposed similarity measure, more weight is assigned to a system’s mostrecent performance than to its former performance when measuring itssimilarity with other systems. The experimental results from a numericalexperiment and a case study on RL prediction of ball grid array (BGA)packages show that, compared with the predictions with the classicalsimilarity measure, statistically more accurate predictions can be achievedwith the proposed similarity measure. A framework of similarity-basedresidual life prediction approaches is proposed, where historical samples thatfail and do not fail (do to preventiven maintenance or suspension) are bothutilized. Within the framework, two solutions (namely solution A and solutionB) are proposed to estimate the lifetimes of the preventively maintained orsuspended historical samples, and to utilize their degradation histories. Anextensive numerical investigation verifies the superiority of the proposedframework (using solution A) over the corresponding classical SbRLPapproach from the case of limited failed historical samples to the case ofabundant failed historical samples. In addition, the investigation results revealthat the proposed framework (using solution B) is ineffective when failedhistorical samples are limited, but its performance improves fast with the increment of available failed historical samples. Afterwards, two studies aredevoted to the topic of proportional harards model (PHM) based equipmentresidual life prediction:1) A Two-zone PHM is proposed based on the factthat many systems’ degradation processes can be devided into a stable zoneand an unstable zone;2) An extended PHM (EPHM) is proposed for RLprediction of systems receiving partial recovery preventive maintenance (PM)acts (i.e. imperfect PM acts), while the classical PHM is not applicable tonon-repairable systems. The results from numberical experiments show that:1)For systems whose degradation processes can be devided into a stable zoneand an unstable zone, the proposed two-zone PHM provides statistically moreaccurate and reliable predictions close to system failure, compared with theclassical PHM;2) For systems receiving imperfect PM acts, the proposedEPHM provides statistically more accurate and reliable predictions close tosystem failure, compared with the classical PHM.
Secondly, the thesis contributes three studies on PdM schedulingmodels/policies. Compared with the classical imperfect PM schedulingmodels, an updated sequential PdM (USPdM) policy is proposed consideringthe effect of imperfect PM acts. The USPdM calculates and updates theoptimal PM schedules for continuously monitored single-unit degradingsystems to minimize the long-term maintenance cost rate. A case study onPdM scheduling of wearing drill bits show that:1) The proposed USPdMmodel yields PM schedules that are consistent with the change in systemstates and2) the USPdM is able to quickly react to drastic degradation of thesystem and provide an optimal PM schedule in real time. In practice, itusually takes more time to restore a much degraded system to a desire statethan to restore a slightly degradaed system to the same state. Based on suchfact, a PdM policy is proposed for maximizing the average system availabilityof continuously monitored single-unit systems, considering the effect ofdegradation correlated maintainability. In the PdM policy, the maintainabilityof PM acts is correated with the accumulated degradation level, which ismodeled by the recently proposed proportional repair model (PRM). Theresults from the numerical experiment show that, for a batch of systemswhose PM maintainability is indeed correlated with the accumulateddegradation level, simply neglecting such effect would lead to suboptimal PMschedules. In addition, the results provide evidence of the superiority of thePdM policy over the corresponding PM polices in terms of higher averagesystem availability. The3rdstudy on PdM scheduling models/policies proposes a modularized framework of PdM scheduling. Based on themodularization treatment, a PdM scheduling model can be established byintegrating the classical PM/CBM scheduling models with components’failure probability estimated based on their degradation variables, and both ofthem have been widely studied. An unreported PdM scheduling model forserial systems is further established. Numerial experiments are conducted tocompare the optimal PM schedules from the PdM scheduling model for serialsystems and the counterparts from the corresponding PM scheduling model,and investigate the characteristics of the PM schedules from these two models.The experimental results show that the PdM model is more effective inmaintenance cost reduction. The results also highlight the individual-oriented,dynamically updating characteristics of the PM schedules from a PdMscheduling model, which is different from the population-oriented, static PMschedules from a PM scheduling model.
Thirdly, the thesis studies two integration schemes of two main aspects ofprognostics (i.e., equipment RL prediction methods and PdM schedulingmodels,), which has not been reported in literature. In the1ststudy, astatistically planned and individually improved (SPII) PdM policy is proposedfor continuously monitored single-unit systems. The SPII PdM policysimultaneously takes advantage of1) the capability of the classical statisticallifetime distribution based PM scheduling policy in long-term planning and2)the capability of RL prediction methods in improving individual performance.The value of the SPII PdM policy is that it demonstrates the possibility ofpartially applying the emerging RL prediction techniques in the widely usedstatistical lifetime distribution based PM policy in an (approximately)theoretically effective manner. By reasonably applying the RL predictiontechniques to a part of (but not all) individuals, a better performance of themaintenance policy can be expected, while the performance of the classicalPM policy can first provide baseline indexes for long-term palnning prior tosystem operation or real production. In the2ndstudy, a PdM framework isproposed for continuously monitored single-unit systems, which integratesequipment RL prediction methods and PdM scheduling models. Within theproposed framework, PdM scheduling is trigrred only when the RLpredication methods demonstrate that the system is close to failure. A lifetimemargine is proposed to infer that most systems do not fail before PdMscheduling is triggered. A numerial experiment demonstrates theimplementation procedures of the proposed framework. In the numrial experiment, when the noise level of the degradation process is relatively low,compared with the classical PdM scheduling model which starts maintenancescheduling once a system bengins operating, the proposed PdM framework issimilar effective in failure prevention and more economical in PM costsaving.
Finally, the thesis conducts two application studies on condition monitoringdata. Based on the condition monitoring and event data, the whole processfrom degradation process analysis to determination of PM schedules isdiscussed. A quantitative comparison among a preventive replacementscheduling model using condition monitoring data, a classical preventivereplacement scheduling model using statistical distribution of entire lifetimesof BGA packages, and a PdM scheduling model. Based on theimplementation results, the reason for maintenance performance improvementdue to the application of codition monitoring data is investigated. Theinvestigation results demonstrate the relationship bewtten the performance ofa maintenance policy and the accuracy and reliability of lifetime predictionwhen determing PM schedules. As the degradation model of the degradationindicator provides the most accurate and reliable lifetime prediction of BGApackages, the PdM scheduling model gives the best performance. A on-oribtreliability prediction method for spacebrone effective load is proposed to fullyutilized the remote monitoring variables, which has already been set on manykey circuits of spacebrone main load but has not been fully utilized. A casestudy is provided to illusate the application process of the proposed method.
引文
[1] Heng A, Zhang S, Tan A C C, et al. Rotating machinery prognostics: state of the art, challengesand opportunities [J]. Mechanical Systems and Signal Processing,2009,23(3):724-739.
[2] Jardine A K S, Lin D, Banjevic D. A review on machinery diagnostics and prognosticsimplementing condition-based maintenance [J]. Mechanical Systems and Signal Processing,2006,20(7):1483-1510.
[3] Saranga H, Knezevic J. Reliability prediction for condition-based maintenance systems [J].Reliability Engineering and System Safety,2001,71(2):219-224.
[4] Camci F. Process monitoring, diagnostics and prognostics using support vector machines andhidden Markov models [D]. Detroit: Wayne State University,2005.
[5] Harbor Research Pervasive Internet Report. Approaching zero downtime: the Center forIntelligent Maintenance Systems,2003.
[6] Ray A, Tangirala S. Stochastic modeling of fatigue crack dynamics for on-line failureprognostics [J]. IEEE Transactions on Control System Technology,1996,4(4):443-451.
[7] Li Y, Billington S, Zhang C, et al. Adaptive prognostics for rolling element bearing condition [J].Mechanical Systems and Signal Processing,1999,13(1):103-113.
[8] Li, Y, Kurfeess T R, Liang S Y. Stochastic prognostics for rolling element bearings [J].Mechanical Systems and Signal Processing,2000,14(5):747-762.
[9] Glodez S, Sraml M, Kramberger J. A computational model for determination of service life ofgears [J]. International Journal of Fatigue,2002,24(10):1013-1020.
[10] Qiu J. Damage mechanics approach for bearing lifetime prognostics [J]. Mechanical Systemsand Signal Processing,2002,16(5):817-829.
[11] Oppenheimer C H, Loparo K A. Physically based diagnosis and prognosis of cracked rotorshafts [J]. Proceedings of SPIE.2002:122-132.
[12] Wang W. Towards dynamic model-based prognostics for transmission gears [J]. Proceedings ofSPIE,2002:157-167.
[13] Orsagh R F, Sheldon J, Klenke C J. Prognostics/Diagnostics for gas turbine engine bearings [J].ASME, International Gas Turbine Institute, Turbo Expo (Publication) ICTI,2003:159-167.
[14] Chelidze D, Cusumano J P, Chatterjee A. A dynamical systems approach to damage evolutiontracking, part1: description and experimental application [J]. Journal of Vibration and Acoustics,Transactions of the ASME,2002,124(2):250-257.
[15] Cusumano J P, Chelidze D, Chatterjee A. A dynamical systems approach to damage evolutiontracking, part2: model-based validation and physical interpretation [J]. Journal of Vibration andAcoustics, Transactions of the ASME,2002,124(2):258-264.
[16] Chelidze D. A dynamic systems approach to failure prognosis [J]. Journal of Vibration andAcoustics, Transactions of the ASME,2004,126(1):2-8.
[17] Luo J, Pattipati K R, Qiao L, et al. Model-based prognostic techniques applied to a suspensionsystem [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans,2008,38(5):1156-1168.
[18] Kacprzynskl G J, Sarlashkar A, Roemer M J, et al. Predicting remaining life by fusing thephysics of failure modeling with diagnostics [J]. JOM,2004,56(3):29-35.
[19] Li C J, Lee H. Gear fatigue crack prognosis using embedded model, gear dynamic model andfacture mechanics [J]. Mechanical Systems and Signal Processing,2005,19(4):836-846.
[20] Marble S, Morton B P. Predicting the remaining life of propulsion system bearings [J].Proceedings of the2006IEEE Aerospace Conference,2006.
[21] Ramakrishnan A, Pecht M G. A life consumption monitoring methodology for electronicsystems [J]. IEEE Transactions on Components and Packaging Technologies,2003,26(3):625-634.
[22] Gu J, Barker D, Pecht M. Prognostics implementation of electronics under vibration loading [J].Microelectronics Reliability,2007,47(12):1849-1856.
[23] Musallam M, Johnson C M, Yu C, et al. In-service life consumption estimation in powermodules [J].200813thInternational Power Electronics and Motion Control Conference,2008:76-83.
[24] Lu H, Kolarik W J, Lu S S. Real-time performance reliability prediction [J]. IEEE Transactionson Reliability,2001,50(4):353-357.
[25] Lu S, Lu H, Kolarik W J. Multivariate performance reliability prediction in real-time [J].Reliability Engineering and System Safety,2000,72(1):39-45.
[26] Swanson D C, Spencer J M, Arzoumanian S H. Prognostic modeling of crack growth in atensioned steel band [J]. Mechanical Systems and Signal Processing,2000,14(5):789-803.
[27] Engel S J, Gilmartin B J, Bongort K, et al. Prognostics, the real issues involved predicting liferemaining [J]. IEEE Aerospace Conference Proceedings,2000,6:457-470.
[28] Cheng S, Pecht M. A fusion method for remaining useful life prediction of electronic products[J].2009IEEE International Conference on Automation Science and Engineering,2009:102-107.
[29] Vachtsevanos G, Wang P. Fault prognosis using dynamic wavelet neural networks [J].AUTOTESTCON (Proceedings),2001,857-870.
[30] Chinnam R B, Baruah P. A neuro-fuzzy approach for estimating mean residual life incondition-based maintenance systems [J]. International Journal of Materials and ProductTechnology,2004,20(1-3):166-179.
[31] Orchard M E, Vachtsevanos G J. A particle filtering approach for on-line failure prognosis in aplanetary carrier plate [J]. International Journal of Fuzzy Logic and Intelligent Systems,2007,7(4):221-227.
[32] Gebraeel N Z, Lawley M A, Li R, et al. Residual-life distributions from component degradationsignals: a Bayesian approach [J]. IIE Transactions,2005,37(6),543-557.
[33] Gebraeel N Z. Sensory-updated residual life distributions for components with exponentialdegradation patterns [J]. IEEE Transactions on Automation Science and Engineering,2006,3(4):382-393.
[34] Gebraeel N Z, Pan J. Prognostic degradation models for computing and updating residual lifedistributions in a time-varying environment [J]. IEEE Transactions on Reliability,2008,57(4):539-550.
[35] Gebraeel N Z, Elwany A, Pan J. Residual life predictions in the absence of prior degradationknowledge [J]. IEEE Transactions on Reliability,2009,58(1):106-116.
[36] Chakraborty S, Gebraeel N Z, Lawley M, et al. Residual-life estimation for components withnon-symmetric priors [J]. IIE Transactions,2009,41(4),372-387.
[37] Goode K B, Moore J, Roylance B J. Plant machinery working life prediction method utilizingreliability and condition-monitoring data [J]. Proceedings of the Institution of MechanicalEngineers,2000,214(2):109-122.
[38] Wang W, Scarf P A, Smith M A J. On the application of a model of condition-basedmaintenance [J]. The Journal of the Operational Research Society,2000,51(11):1218-1227.
[39] Kwan C, Zhang X, Xu R, et al. A novel approach to fault diagnostics and prognostics [J].Proceedings of the2003IEEE International Conference on Robotics&Automation,2003:604-609.
[40] Zhang X, Xu R, Kwan C, et al. An integrated approach to bearing fault diagnostics andprognostics [J]. Proceedings of the American Control Conference,2005,4:2750-2755.
[41] Chinnam R B, Baruah P. Autonomous diagnostics and prognostics through competitive learningdriven HMM-based clustering [J]. Proceedings of the International Joint Conference on NeuralNetworks,2003,4:2466-2471.
[42] Chinnam R B, Baruah P. HMMs for diagnostics and prognostics in machining processes [J].International Journal of Production Research,2005,43(6):1275-1293.
[43] Camci F, Chinnam R B. Hierarchical HMMs for autonomous diagnostics and prognostics [J].2006International Joint Conference on Neural Networks,2006:2445-2452.
[44] Camci F, Chinnam R B. Health-state estimation and prognostics in machining processes [J].IEEE Transactions on Automation Science and Engineering, to be published.
[45] Chinnam R B, Baruah P. Autonomous diagnostics and prognostics in machining processesthrough competitive learning driven HMM-based clustering [J]. International Journal ofProduction Research,2009,47(23):6739-6758.
[46] Dong M, He D. Hidden semi-Markov model based methodology for multi-sensor equipmenthealth diagnosis and prognosis [J]. European Journal of Operational Research,2007,178(3):858-878.
[47] Dong M, He D. A segmental hidden semi-Markov model (HSMM) based diagnostics andprognostics framework and methodology [J] Mechanical Systems and Signal Processing,2007,21(5):2248-2266.
[48] Peng Y, Dong M. A prognosis method using age-dependent hidden semi-Markov model forequipment health prediction [J]. Mechanical System and Signal Processing, to be published.
[49] Yan J, Kog M, Lee J. A prognostic algorithm for machine performance assessment and itsapplication [J]. Production Planning&Control,2004,15(8):796-801.
[50] Volk P J. Dynamic residual life estimation of industrial equipment based on failure intensityproportions [D]. Pretoria: University of Pretoria,2001.
[51] Volk P J, Wnek M, Zygmunt M. Utilising statistical residual life estimates of bearings toquantify the influence of preventive maintenance actions [J]. Mechanical Systems and SignalProcessing,2004,18(4):833-847.
[52] Banjevic D, Jardine A K S. Calculation of reliability function and remaining useful life for aMarkov failure time processes [J]. IMA Journal of Management Mathematics,2006,17(2):115-130.
[53] Liao H, Zhao W, Guo H. Predicting remaining useful life of an individual unit usingproportional hazards model and logistic regression model [J]. Proceedings-Annual Reliabilityand Maintainability Symposium,2006:127-132.
[54] Ghasemi A, Yacout S, Ouali M-S. Evaluating the reliability function and the mean residual lifefor equipment with unobservable states [J]. IEEE Transactions on Reliability,2010,59(1):45-54.
[55] Wang W. A model to predict the residual life of rolling element bearings given monitoredcondition information to date [J]. IMA Journal of Management Mathematics,2002,13(1):3-16.
[56] Carr M J, Wang W. Modeling failure modes for residual life prediction using stochastic filteringtheory [J]. IEEE Transactions on Reliability, to be published.
[57] Tian Z, Wong L, Safaei N. A neural network approach for remaining useful life predictionutilizing both failure and suspension histories [J]. Mechanical Systems and Signal Processing,2010,24:1542-1555.
[58] Zio E, Maio F D. A data-driven fuzzy approach for predicting the remaining useful life indynamic failure scenarios of a nuclear system [J]. Reliability Engineering and System Safety,2010,95(1):49-57.
[59] Wang T, Yu J, Siegel D, et al. A similarity-based prognostics approach for remaining useful lifeestimation of engineered systems [J].2008International Conference on Prognostics and HealthManagement,2008.
[60] Gebraeel N Z, Lawley M, Liu R, et al. Residual life predictions from vibration-baseddegradation signals: a neural network approach [J]. IEEE Transactions on Industrial Electronics,2004,51(3):694-700.
[61] Huang R, Li L, Xi L, et al. Residual life predictions for ball bearings based on self-organizingmap and back propagation neural network methods [J]. Mechanical Systems and SignalProcessing,2007,21(1):193-207.
[62] Gebraeel N Z, Lawley M A. A neural network degradation model for computing and updatingresidual life distributions [J]. IEEE Transactions on Automation Science and Engineering,2008,5(1):154-163.
[63] Makis V, Jardine A K S. Optimal replacement in the proportional hazards model [J]. INFORJournal,1992,30(2):172-183.
[64] Kumar D, Westberg U. Maintenance scheduling under age replacement policy usingproportional hazards model and TTT-plotting [J]. European Journal of Operational Research,1997,99(3):507-515.
[65] Banjevic D, Jardine A K S, Makis V, et al. A control-limit policy and software forcondition-based maintenance optimization [J]. INFOR Journal,2001,39(1):32-50.
[66] Jardine A K S, Banjevic D, Makis V. Optimal replacement policy and the structure of softwarefor condition-based maintenance [J]. Journal of Quality in Maintenance Engineering,1997,3(2):109-119.
[67] Jardine A K S, Banjevic D. Optimizing a mine haul truck wheel motor’s condition monitoringprogram: use of proportional hazards modeling [J]. Journal of Quality in MaintenanceEngineering,2001,7(4):286-301.
[68] Lin D, Wiseman M, Banjevic D, Jardine A K S. An approach to signal processing andcondition-based maintenance for gearboxes subject to tooth failure [J]. Mechanical Systems andSignal Processing,2004,18(5):993-1007.
[69] Lin D, Banjevic D, Jardine A K S. Using principal components in a proportional hazards modewith applications in condition-based maintenance [J]. Journal of Operational Research Society,2006,57(8):910-919.
[70] Ghasemi A, Yacout S, Ouali M S. Optimal condition based maintenance with imperfectinformation and the proportional hazards model [J]. International Journal of ProductionResearch,2007,45(4):989-1012.
[71] Ghasemi A, Yacout S, Ouali M S. Optimal replacement policy and observation interval forCBM with imperfect information [J]. Proceedings of the World Congress on Engineering andComputer Science,2007.
[72] Barbera F, Schneider H, Kelle P. A condition based maintenance model with exponentialfailures and fixed inspection intervals [J]. Journal of Operational Research Society,1996,47(8):1037-1045.
[73] Barbera F, Schneider H, Watson E. A condition based maintenance model for a two-unit seriessystem [J]. European Journal of Operational Research,1999,116(2):281-290.
[74] Shahanaghi K, Babaei H, Bakhsha A, et al. A new condition based maintenance model withrandom improvements on the system after maintenance actions: optimizing by Monte Carlosimulation [J]. World Journal of Modelling and Simulation,2008,4(3):230-236.
[75] Aven T. Condition based replacement policies-a counting process approach [J]. ReliabilityEngineering and System Safety,1996,51(3),275-281.
[76] Hontelez J A M, Burger H H, Wijnmalen D J D. Optimum condition-based maintenance policiesfor deteriorating systems with partial information [J]. Reliability Engineering and System Safety,1996,51(3):267-274.
[77] Maillart L M. Maintenance policies for systems with condition monitoring and obvious failures[J]. IIE Transactions,2006,38(6):463-475.
[78] Wang W. A model to determine the optimal critical level and the monitoring intervals incondition-based maintenance [J]. International Journal of Production Research,2000,38(6):1425-1436.
[79] Grall A, Berenguer C, Dieulle L. A condition-based maintenance policy for stochasticallydeteriorating systems [J]. Reliability Engineering and System Safety,2002,76(2):167-180.
[80] Castanier B, Berenguer C, Grall A. A sequential condition-based repair/replacement policy withnon-periodic inspections for a system subject to continuous wear [J]. Applied Stochastic Modelsin Business and Industry,2003,19(4):327-347.
[81] Castanier B, Berenguer C, Grall A. A condition-based maintenance policy with non-periodicinspections for a two-unit series system [J]. Reliability Engineering and System Safety,2005,87(1):109-120.
[82] Dieulle L, Berenguer C, Grall A, et al. Sequential condition-based maintenance scheduling for adeteriorating system [J]. European Journal of Operational Research,2003,150(2),451-461.
[83] Grall A, Dieulle L, Berenquer C, et al. Continuous-time predictive maintenance scheduling for adeteriorating system [J]. IEEE Transactions on Reliability,2002,51(2):141-150.
[84] Deloux E, Castanier B, Berenguer C. Predictive maintenance policy for a graduallydeteriorating system subject to stress [J]. Reliability Engineering and System Safety,2009,94(2):418-431.
[85] Zhao X, Fouladirad M, Berenguer C, et al. Condition-based inspection/replacement policies fornon-monotone deteriorating systems with environmental covariates [J]. Reliability Engineeringand System Safety,2010,95:921-934.
[86] Nakagawa T, Ito K. Optimal maintenance policies for a system with multiechelon risks [J].IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans,2008,38(2):461-469.
[87] Wang L, Chu J, Mao W. A condition-based order-replacement policy for a single-unit system [J].Applied Mathematical Modelling,2008,32(11):2274-2289.
[88] Wang L, Chu J, Mao W. An optimum condition-based replacement and spare provisioningpolicy based on Markov chains [J]. Journal of Quality in Maintenance Engineering,2008,14(4):387-401.
[89] Wang L, Chu J, Mao W. A condition-based replacement and spare provisioning policy fordeteriorating systems with uncertain deterioration to failure [J]. European Journal ofOperational Research,2009,194(1):184-205.
[90] Liao H, Elsayed E A, Chan L-Y. Maintenance of continuously monitored degradation systems[J]. European Journal of Operational Research,2006,175(2):821-835.
[91] Marsequerra M, Zio E, Podofillini L. Condition-based maintenance optimization by means ofgenetic algorithms and Monte Carlo simulation [J]. Reliability Engineering and System Safety,2002,77(2):151-166.
[92] Barata J, Soares C G, Marseguerra M, et al. Simulation modeling of repairable multi-componentdeteriorating systems for ‘on condition’ maintenance optimization [J]. Reliability Engineeringand System Safety,2002,76(3):255-264.
[93] Makis V, Jiang X. Optimal Replacement under partial observations [J]. Mathematics ofOperations Research,2003,28(2):382-294.
[94] Zhou X, Xi L, Lee J, Reliability-centered predictive maintenance scheduling for a continuouslymonitored system subject to degradation [J]. Reliability Engineering and System Safety,2007,92(4):530-534.
[95] Camci F. System maintenance scheduling with prognostics information using genetic algorithm[J]. IEEE Transactions on Reliability,2009,58(3):539-552.
[96] Yang Z, Djurdjanovic D, Ni J. Maintenance scheduling in manufacturing systems based onpredicted machine degradation [J]. Journal of Intelligent Manufacturing,2008,19(1):87-98.
[97] Christer A H, Wang W, Sharp J M. A state space condition monitoring model for furnace erosionprediction and replacement [J]. European Journal of Operational Research,1997,101(1):1-14.
[98] Pedregal D J and Carnero M C. State space models for condition monitoring: a case study.Reliability Engineering and System Safety,2006,91(2):171-180.
[99] Lu S, Tu Y-C, Lu H. Predictive condition-based maintenance for continuously deterioratingsystems [J]. Quality and Reliability Engineering International,2007,23(1):71-81.
[100] Kaiser K A, Gebraeel N Z. Predictive maintenance management using sensor-based degradationmodels [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans,2009,39(4):840-849.
[101] Wu S-J, Gebraeel N Z, Lawley M A, et al. A neural network integrated decision support systemfor condition-based optimal predictive maintenance policy [J]. IEEE Transactions on Systems,Man, and Cybernetics-Part A: Systems and Humans,2007,37(2):226-236.
[102] Kharoufeh J P, Cox S M. Stochastic models for degradation-based reliability [J]. IIETransactions,2005,37:533-542.
[103] Kharoufeh J P, Solo C J, Ulukus M Y. Semi-Markov models for degradation-based reliability [J].IIE Transactions,2010,42:599-612.
[104] Liu F, Meng G, Zhao M, Zhao J F. Board level drop test analysis based on modal test andsimulation [J]. Journal of Electronic Packaging, the ASME Transactions.2008;130(2):021007(1-6).
[105]王文. SMT无铅焊点在随机振动载荷下的可靠性分析[D].上海：上海交通大学，2010.
[106] Meeker W Q, Escobar L A. Statistical Methods for Reliability Data [M]. New York: Wiley,1998.
[107] Kim Y S, Kolarik W J. Real-time conditional reliability prediction from on-line toolperformance data [J]. International Journal of Production Research,1992,30(8):1831-1844.
[108] Wang P, Coit D W. Reliability and degradation modeling with random or uncertain failurethreshold [C].2007Annual Reliability and Maintainability Symposium, Orlando, FL, USA,2007.
[109] Christer A H, Waller. Delay time models of industrial inspection maintenance problems [J].Journal of the Operational Research Society,1984,35,401-406.
[110] Cox D R. Regression models and life-tables (with discussion)[J]. Journal of Royal StatisticalSociety. Series B (Methodological),1972,34(2),187-220.
[111] Lagarias J C, Reeds J A, Wright M H, and Wright P E. Convergence properties of theNelder-Mead simplex method in low dimensions. SIAM Journal of Optimization,1998,9(1),112-147.
[112] Pandit S M and Wu S–M. Time Series and System Analysis with Applications [M]. New York:Wiley,1983.
[113] Connor J T, Martin R D, and Atlas L E. Recurrent neural networks and robust time seriesprediction [J]. IEEE Transactions on Neural Networks,1994,42(4),240-254.
[114] Liu J, Djurdjanovic D, Ni J, Casoettlo N,et al. Similarity based method for manufacturingprocess performance prediction and diagnosis [J]. Computers in Industry,2007,58(6),558-566.
[115] Volk P J, Coetzee J L, Banjevic D, et al. Optimal component replacement decisions usingvibration monitoring and the proportional-hazards model [J]. Journal of Opeartional ResearchSociety,2002,53(2),193-202.
[116] Wang W. A two-stage prognosis model in condition based maintenance [J]. European Journal ofOperational Research,2007,182,1177-1187.
[117] Kourti T and MacGregor J F. Process analysis, monitoring and diagnosis, using multivariateprojection methods [J]. Chemometrics and Intelligent Laboratory Systems,1995,28,3-21.
[118] Lin D, Zuo M J, Yam R C M. Sequential imperfect preventive maintenance models with twocategories of failure modes [J]. Naval Research Logistics,2001;48(2):172-183.
[119] Nakagawa T. Sequential imperfect preventive maintenance policies [J]. IEEE Transactions onReliability,1988;37(3),295-298.
[120] EI-Ferik S, Ben-Daya M. Age-based hybrid model for imperfect preventive maintenance [J]. IIETransactions,2006;38(4),365-375.
[121] Barlow R E and Prochan F. Mathematical Theory of Reliability [M]. New York: Wiley,1965.
[122] Dekker R. Applications of maintenance optimization models: A review and analysis [J].Reliability Engineering and System Safety,1996,51(3),229-240.
[123] Pham H and Wang H. Imperfect maintenance [J]. European Journal of Operational Research,1996,94(3),425-438.
[124] Wang H. A survey of maintenance policies of deteoriating systems [J]. European Journal ofOperational Research,2002,139(3),469-489.
[125] Montgomery D C. Introduction to Statistical Quality Control (5thedition)[M]. New York: Wiley,2005.
[126] Mobley R K. An Introduction to Predictive Maintenance [M]. New York:Butterworth-Heinemann,1989.
[127] Barlow R E and Hunter L C. Optimum preventive maintenance policies [J]. OperationsResearch,1960,8(1),90-100.
[128] Nowakowski T and Weibińka. On problems of multicomponent maintenance modeling [J].International Journal of Aotomation and Computing,2009,6(4),364-378.
[129] Nicolai R P and Dekker R. Optimal maintenance of multi-component systems: A review [M].Complex System Maintenance Handbook-11, London: Springer,2008.
[130] Yam R C M, Tse P W, L. Li, et al. Intelligent predictive decision support system forcondition-based maintenance [J]. International Journal of Advanced Manufacturing Technology,2001,17,383-391.
[131] Wireman T. World Class Maintenance Management [M]. New York: Industrial Press,1990.
[132] Bevilacqua M and Braglia M. The analytic hierarchy process applied to maintenance stratrgyselection [J]. Reliability Engineering and System Safety,2000,70(1),71-83.
[133] Li L, You M Y, and Ni J. Reliability-based dynamic maintenance threshold for continuouslymonitored degrading systems [J]. Journal of Manufacturing Science and engineering,Transactions of the ASME,2009,131(3),031010(1-9).
[134] You M Y, Li L, Meng G, et al. Cost-effective updated sequential predictive maintenance policyfor continuously monitored degrading systems [J]. IEEE Transactions on Automation Scienceand Engineering,2010,7(2),257-265.
[135] Elwany A H, Gebraeel N Z. Sensor-driven prognostic models for equipment replacement andspare parts inventory [J]. IIE Transactions,2008,40(7),629-639.
[136] Tsai Y–T, Wang K–S, Tsai L–C. A study of availability-centered preventive maintenance formulti-component systems [J]. Reliability Engineering and System Safety,2004,84(3),261-270.
[137] Maciejewski H, Caban D. Estimation of repairable system within fixed time horizon [J].Reliability Engineering and System Safety,2008,93(1),100-106.
[138] Sarkar J, Chaudhuri G. Availability of a system with gamma life and exponential repair timeunder a perfect repair policy [J]. Statistics&Probbaility Letters,1999,43(2),189-196.
[139] Biswas A, Sarkar J, Sarkar S. Availability of a periodically inspected system, maintenanedunder an imperfect-repair policy [J]. IEEE Transactions on Reliability,2003,52(3),311-318.
[140] Klutke G–A, Yang Y. The availability of inspected systems subject to shocks and gracefuldegradation [J]. IEEE Transactions on Reliability,2002,51(3),311-318.
[141] Bao X, Cui L. An analysis of availability for series Markov repairable system with negencted ordelayed failures [J]. IEEE Transactions on Reliability,2010,59(4),734-743.
[142] Wang H, Pham H. Survey of reliability and availability evaluation of complex networks usingMonte Carlo techniques [J]. Microelectronics Reliability,1997,37(2),187-209.
[143] Marquez A C, Heguedas A S, Iung B. Monte Carlo-based assessment of system availability. Acase study for cogeneration plants [J]. Reliability Engineering and System Safety,2005,88(3),273-289.
[144] Cassady C R, Iyoob I M, Schneider K, et al. A generic model of equipment availability underimperfect maintenance [J]. IEEE Transactions of Reliability,2005,54(4),564-571.
[145] You M–Y, Liu F, Wang W, et al. Statistically planned and individually improved redictivemaintenance management for continuously monitored degrading systems [J]. IEEE Transactionson Reliability,2010,59(4),744-753.
[146] Gao X, Barabady J, Markeset T. An approach for prediction of petroleum production facilityperformance considering Arctic influence factors [J]. Reliability Engineering and System Safety,2010,95(8),837-846.
[147] Kalbfleisch J D, Prentice R L. The Statistical Analysis for Failure Time Data [M]. New Jersey:Wiley,2002.
[148] Barabadi A, Barabady J, Markeset T. Maintainability analysis considering time-dependnet andtime-independent covariates [J]. Reliability Engineering and System Safety,2011,96(1),210-217.
[149] Doksum K A, Hóyland A. Models for variable-stress accelerated life testing experiments basedon wiener processes and the inverse Gaussian distribution [J]. Technometrics,1992,34(1),74-82.
[150]周东华，徐正国.工程系统的实时可靠性评估与预测技术[J].空间控制技术与应用.2008(34)：3-10.
[151]曾声奎，Pecht M G，吴际.故障预测与健康管理（PHM）技术的现状与发展[J].航空学报.2005(26)：626-632.
[152] Wang T. Trajectory similarity-based prediction for remaining useful life estimation [D].Cincinnati: University of Cincinnati,2010.
[153] Saxena A, Goebel K, Simon D, Eklund N. Damage propagation modeling for aircraft enginerun-to-failire simulation [C]. Proceedings of the International Conference on Prognostics andHealth Management,2008.
[154]尤明懿.基于相似性的剩余寿命预测：鲁棒性与不确定性研究[J].电子产品可靠性与环境实验，2011，录用.
[155] Swindemana R W, Swindemanb M J. A Comparison of creep models for nickel base alloy foradvanced energy systems [J]. International Journal of Pressure and Piping,2008,85(1-2):72-79.
[2] Jardine A K S, Lin D, Banjevic D. A review on machinery diagnostics and prognosticsimplementing condition-based maintenance [J]. Mechanical Systems and Signal Processing,2006,20(7):1483-1510.
[3] Saranga H, Knezevic J. Reliability prediction for condition-based maintenance systems [J].Reliability Engineering and System Safety,2001,71(2):219-224.
[4] Camci F. Process monitoring, diagnostics and prognostics using support vector machines andhidden Markov models [D]. Detroit: Wayne State University,2005.
[5] Harbor Research Pervasive Internet Report. Approaching zero downtime: the Center forIntelligent Maintenance Systems,2003.
[6] Ray A, Tangirala S. Stochastic modeling of fatigue crack dynamics for on-line failureprognostics [J]. IEEE Transactions on Control System Technology,1996,4(4):443-451.
[7] Li Y, Billington S, Zhang C, et al. Adaptive prognostics for rolling element bearing condition [J].Mechanical Systems and Signal Processing,1999,13(1):103-113.
[8] Li, Y, Kurfeess T R, Liang S Y. Stochastic prognostics for rolling element bearings [J].Mechanical Systems and Signal Processing,2000,14(5):747-762.
[9] Glodez S, Sraml M, Kramberger J. A computational model for determination of service life ofgears [J]. International Journal of Fatigue,2002,24(10):1013-1020.
[10] Qiu J. Damage mechanics approach for bearing lifetime prognostics [J]. Mechanical Systemsand Signal Processing,2002,16(5):817-829.
[11] Oppenheimer C H, Loparo K A. Physically based diagnosis and prognosis of cracked rotorshafts [J]. Proceedings of SPIE.2002:122-132.
[12] Wang W. Towards dynamic model-based prognostics for transmission gears [J]. Proceedings ofSPIE,2002:157-167.
[13] Orsagh R F, Sheldon J, Klenke C J. Prognostics/Diagnostics for gas turbine engine bearings [J].ASME, International Gas Turbine Institute, Turbo Expo (Publication) ICTI,2003:159-167.
[14] Chelidze D, Cusumano J P, Chatterjee A. A dynamical systems approach to damage evolutiontracking, part1: description and experimental application [J]. Journal of Vibration and Acoustics,Transactions of the ASME,2002,124(2):250-257.
[15] Cusumano J P, Chelidze D, Chatterjee A. A dynamical systems approach to damage evolutiontracking, part2: model-based validation and physical interpretation [J]. Journal of Vibration andAcoustics, Transactions of the ASME,2002,124(2):258-264.
[16] Chelidze D. A dynamic systems approach to failure prognosis [J]. Journal of Vibration andAcoustics, Transactions of the ASME,2004,126(1):2-8.
[17] Luo J, Pattipati K R, Qiao L, et al. Model-based prognostic techniques applied to a suspensionsystem [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans,2008,38(5):1156-1168.
[18] Kacprzynskl G J, Sarlashkar A, Roemer M J, et al. Predicting remaining life by fusing thephysics of failure modeling with diagnostics [J]. JOM,2004,56(3):29-35.
[19] Li C J, Lee H. Gear fatigue crack prognosis using embedded model, gear dynamic model andfacture mechanics [J]. Mechanical Systems and Signal Processing,2005,19(4):836-846.
[20] Marble S, Morton B P. Predicting the remaining life of propulsion system bearings [J].Proceedings of the2006IEEE Aerospace Conference,2006.
[21] Ramakrishnan A, Pecht M G. A life consumption monitoring methodology for electronicsystems [J]. IEEE Transactions on Components and Packaging Technologies,2003,26(3):625-634.
[22] Gu J, Barker D, Pecht M. Prognostics implementation of electronics under vibration loading [J].Microelectronics Reliability,2007,47(12):1849-1856.
[23] Musallam M, Johnson C M, Yu C, et al. In-service life consumption estimation in powermodules [J].200813thInternational Power Electronics and Motion Control Conference,2008:76-83.
[24] Lu H, Kolarik W J, Lu S S. Real-time performance reliability prediction [J]. IEEE Transactionson Reliability,2001,50(4):353-357.
[25] Lu S, Lu H, Kolarik W J. Multivariate performance reliability prediction in real-time [J].Reliability Engineering and System Safety,2000,72(1):39-45.
[26] Swanson D C, Spencer J M, Arzoumanian S H. Prognostic modeling of crack growth in atensioned steel band [J]. Mechanical Systems and Signal Processing,2000,14(5):789-803.
[27] Engel S J, Gilmartin B J, Bongort K, et al. Prognostics, the real issues involved predicting liferemaining [J]. IEEE Aerospace Conference Proceedings,2000,6:457-470.
[28] Cheng S, Pecht M. A fusion method for remaining useful life prediction of electronic products[J].2009IEEE International Conference on Automation Science and Engineering,2009:102-107.
[29] Vachtsevanos G, Wang P. Fault prognosis using dynamic wavelet neural networks [J].AUTOTESTCON (Proceedings),2001,857-870.
[30] Chinnam R B, Baruah P. A neuro-fuzzy approach for estimating mean residual life incondition-based maintenance systems [J]. International Journal of Materials and ProductTechnology,2004,20(1-3):166-179.
[31] Orchard M E, Vachtsevanos G J. A particle filtering approach for on-line failure prognosis in aplanetary carrier plate [J]. International Journal of Fuzzy Logic and Intelligent Systems,2007,7(4):221-227.
[32] Gebraeel N Z, Lawley M A, Li R, et al. Residual-life distributions from component degradationsignals: a Bayesian approach [J]. IIE Transactions,2005,37(6),543-557.
[33] Gebraeel N Z. Sensory-updated residual life distributions for components with exponentialdegradation patterns [J]. IEEE Transactions on Automation Science and Engineering,2006,3(4):382-393.
[34] Gebraeel N Z, Pan J. Prognostic degradation models for computing and updating residual lifedistributions in a time-varying environment [J]. IEEE Transactions on Reliability,2008,57(4):539-550.
[35] Gebraeel N Z, Elwany A, Pan J. Residual life predictions in the absence of prior degradationknowledge [J]. IEEE Transactions on Reliability,2009,58(1):106-116.
[36] Chakraborty S, Gebraeel N Z, Lawley M, et al. Residual-life estimation for components withnon-symmetric priors [J]. IIE Transactions,2009,41(4),372-387.
[37] Goode K B, Moore J, Roylance B J. Plant machinery working life prediction method utilizingreliability and condition-monitoring data [J]. Proceedings of the Institution of MechanicalEngineers,2000,214(2):109-122.
[38] Wang W, Scarf P A, Smith M A J. On the application of a model of condition-basedmaintenance [J]. The Journal of the Operational Research Society,2000,51(11):1218-1227.
[39] Kwan C, Zhang X, Xu R, et al. A novel approach to fault diagnostics and prognostics [J].Proceedings of the2003IEEE International Conference on Robotics&Automation,2003:604-609.
[40] Zhang X, Xu R, Kwan C, et al. An integrated approach to bearing fault diagnostics andprognostics [J]. Proceedings of the American Control Conference,2005,4:2750-2755.
[41] Chinnam R B, Baruah P. Autonomous diagnostics and prognostics through competitive learningdriven HMM-based clustering [J]. Proceedings of the International Joint Conference on NeuralNetworks,2003,4:2466-2471.
[42] Chinnam R B, Baruah P. HMMs for diagnostics and prognostics in machining processes [J].International Journal of Production Research,2005,43(6):1275-1293.
[43] Camci F, Chinnam R B. Hierarchical HMMs for autonomous diagnostics and prognostics [J].2006International Joint Conference on Neural Networks,2006:2445-2452.
[44] Camci F, Chinnam R B. Health-state estimation and prognostics in machining processes [J].IEEE Transactions on Automation Science and Engineering, to be published.
[45] Chinnam R B, Baruah P. Autonomous diagnostics and prognostics in machining processesthrough competitive learning driven HMM-based clustering [J]. International Journal ofProduction Research,2009,47(23):6739-6758.
[46] Dong M, He D. Hidden semi-Markov model based methodology for multi-sensor equipmenthealth diagnosis and prognosis [J]. European Journal of Operational Research,2007,178(3):858-878.
[47] Dong M, He D. A segmental hidden semi-Markov model (HSMM) based diagnostics andprognostics framework and methodology [J] Mechanical Systems and Signal Processing,2007,21(5):2248-2266.
[48] Peng Y, Dong M. A prognosis method using age-dependent hidden semi-Markov model forequipment health prediction [J]. Mechanical System and Signal Processing, to be published.
[49] Yan J, Kog M, Lee J. A prognostic algorithm for machine performance assessment and itsapplication [J]. Production Planning&Control,2004,15(8):796-801.
[50] Volk P J. Dynamic residual life estimation of industrial equipment based on failure intensityproportions [D]. Pretoria: University of Pretoria,2001.
[51] Volk P J, Wnek M, Zygmunt M. Utilising statistical residual life estimates of bearings toquantify the influence of preventive maintenance actions [J]. Mechanical Systems and SignalProcessing,2004,18(4):833-847.
[52] Banjevic D, Jardine A K S. Calculation of reliability function and remaining useful life for aMarkov failure time processes [J]. IMA Journal of Management Mathematics,2006,17(2):115-130.
[53] Liao H, Zhao W, Guo H. Predicting remaining useful life of an individual unit usingproportional hazards model and logistic regression model [J]. Proceedings-Annual Reliabilityand Maintainability Symposium,2006:127-132.
[54] Ghasemi A, Yacout S, Ouali M-S. Evaluating the reliability function and the mean residual lifefor equipment with unobservable states [J]. IEEE Transactions on Reliability,2010,59(1):45-54.
[55] Wang W. A model to predict the residual life of rolling element bearings given monitoredcondition information to date [J]. IMA Journal of Management Mathematics,2002,13(1):3-16.
[56] Carr M J, Wang W. Modeling failure modes for residual life prediction using stochastic filteringtheory [J]. IEEE Transactions on Reliability, to be published.
[57] Tian Z, Wong L, Safaei N. A neural network approach for remaining useful life predictionutilizing both failure and suspension histories [J]. Mechanical Systems and Signal Processing,2010,24:1542-1555.
[58] Zio E, Maio F D. A data-driven fuzzy approach for predicting the remaining useful life indynamic failure scenarios of a nuclear system [J]. Reliability Engineering and System Safety,2010,95(1):49-57.
[59] Wang T, Yu J, Siegel D, et al. A similarity-based prognostics approach for remaining useful lifeestimation of engineered systems [J].2008International Conference on Prognostics and HealthManagement,2008.
[60] Gebraeel N Z, Lawley M, Liu R, et al. Residual life predictions from vibration-baseddegradation signals: a neural network approach [J]. IEEE Transactions on Industrial Electronics,2004,51(3):694-700.
[61] Huang R, Li L, Xi L, et al. Residual life predictions for ball bearings based on self-organizingmap and back propagation neural network methods [J]. Mechanical Systems and SignalProcessing,2007,21(1):193-207.
[62] Gebraeel N Z, Lawley M A. A neural network degradation model for computing and updatingresidual life distributions [J]. IEEE Transactions on Automation Science and Engineering,2008,5(1):154-163.
[63] Makis V, Jardine A K S. Optimal replacement in the proportional hazards model [J]. INFORJournal,1992,30(2):172-183.
[64] Kumar D, Westberg U. Maintenance scheduling under age replacement policy usingproportional hazards model and TTT-plotting [J]. European Journal of Operational Research,1997,99(3):507-515.
[65] Banjevic D, Jardine A K S, Makis V, et al. A control-limit policy and software forcondition-based maintenance optimization [J]. INFOR Journal,2001,39(1):32-50.
[66] Jardine A K S, Banjevic D, Makis V. Optimal replacement policy and the structure of softwarefor condition-based maintenance [J]. Journal of Quality in Maintenance Engineering,1997,3(2):109-119.
[67] Jardine A K S, Banjevic D. Optimizing a mine haul truck wheel motor’s condition monitoringprogram: use of proportional hazards modeling [J]. Journal of Quality in MaintenanceEngineering,2001,7(4):286-301.
[68] Lin D, Wiseman M, Banjevic D, Jardine A K S. An approach to signal processing andcondition-based maintenance for gearboxes subject to tooth failure [J]. Mechanical Systems andSignal Processing,2004,18(5):993-1007.
[69] Lin D, Banjevic D, Jardine A K S. Using principal components in a proportional hazards modewith applications in condition-based maintenance [J]. Journal of Operational Research Society,2006,57(8):910-919.
[70] Ghasemi A, Yacout S, Ouali M S. Optimal condition based maintenance with imperfectinformation and the proportional hazards model [J]. International Journal of ProductionResearch,2007,45(4):989-1012.
[71] Ghasemi A, Yacout S, Ouali M S. Optimal replacement policy and observation interval forCBM with imperfect information [J]. Proceedings of the World Congress on Engineering andComputer Science,2007.
[72] Barbera F, Schneider H, Kelle P. A condition based maintenance model with exponentialfailures and fixed inspection intervals [J]. Journal of Operational Research Society,1996,47(8):1037-1045.
[73] Barbera F, Schneider H, Watson E. A condition based maintenance model for a two-unit seriessystem [J]. European Journal of Operational Research,1999,116(2):281-290.
[74] Shahanaghi K, Babaei H, Bakhsha A, et al. A new condition based maintenance model withrandom improvements on the system after maintenance actions: optimizing by Monte Carlosimulation [J]. World Journal of Modelling and Simulation,2008,4(3):230-236.
[75] Aven T. Condition based replacement policies-a counting process approach [J]. ReliabilityEngineering and System Safety,1996,51(3),275-281.
[76] Hontelez J A M, Burger H H, Wijnmalen D J D. Optimum condition-based maintenance policiesfor deteriorating systems with partial information [J]. Reliability Engineering and System Safety,1996,51(3):267-274.
[77] Maillart L M. Maintenance policies for systems with condition monitoring and obvious failures[J]. IIE Transactions,2006,38(6):463-475.
[78] Wang W. A model to determine the optimal critical level and the monitoring intervals incondition-based maintenance [J]. International Journal of Production Research,2000,38(6):1425-1436.
[79] Grall A, Berenguer C, Dieulle L. A condition-based maintenance policy for stochasticallydeteriorating systems [J]. Reliability Engineering and System Safety,2002,76(2):167-180.
[80] Castanier B, Berenguer C, Grall A. A sequential condition-based repair/replacement policy withnon-periodic inspections for a system subject to continuous wear [J]. Applied Stochastic Modelsin Business and Industry,2003,19(4):327-347.
[81] Castanier B, Berenguer C, Grall A. A condition-based maintenance policy with non-periodicinspections for a two-unit series system [J]. Reliability Engineering and System Safety,2005,87(1):109-120.
[82] Dieulle L, Berenguer C, Grall A, et al. Sequential condition-based maintenance scheduling for adeteriorating system [J]. European Journal of Operational Research,2003,150(2),451-461.
[83] Grall A, Dieulle L, Berenquer C, et al. Continuous-time predictive maintenance scheduling for adeteriorating system [J]. IEEE Transactions on Reliability,2002,51(2):141-150.
[84] Deloux E, Castanier B, Berenguer C. Predictive maintenance policy for a graduallydeteriorating system subject to stress [J]. Reliability Engineering and System Safety,2009,94(2):418-431.
[85] Zhao X, Fouladirad M, Berenguer C, et al. Condition-based inspection/replacement policies fornon-monotone deteriorating systems with environmental covariates [J]. Reliability Engineeringand System Safety,2010,95:921-934.
[86] Nakagawa T, Ito K. Optimal maintenance policies for a system with multiechelon risks [J].IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans,2008,38(2):461-469.
[87] Wang L, Chu J, Mao W. A condition-based order-replacement policy for a single-unit system [J].Applied Mathematical Modelling,2008,32(11):2274-2289.
[88] Wang L, Chu J, Mao W. An optimum condition-based replacement and spare provisioningpolicy based on Markov chains [J]. Journal of Quality in Maintenance Engineering,2008,14(4):387-401.
[89] Wang L, Chu J, Mao W. A condition-based replacement and spare provisioning policy fordeteriorating systems with uncertain deterioration to failure [J]. European Journal ofOperational Research,2009,194(1):184-205.
[90] Liao H, Elsayed E A, Chan L-Y. Maintenance of continuously monitored degradation systems[J]. European Journal of Operational Research,2006,175(2):821-835.
[91] Marsequerra M, Zio E, Podofillini L. Condition-based maintenance optimization by means ofgenetic algorithms and Monte Carlo simulation [J]. Reliability Engineering and System Safety,2002,77(2):151-166.
[92] Barata J, Soares C G, Marseguerra M, et al. Simulation modeling of repairable multi-componentdeteriorating systems for ‘on condition’ maintenance optimization [J]. Reliability Engineeringand System Safety,2002,76(3):255-264.
[93] Makis V, Jiang X. Optimal Replacement under partial observations [J]. Mathematics ofOperations Research,2003,28(2):382-294.
[94] Zhou X, Xi L, Lee J, Reliability-centered predictive maintenance scheduling for a continuouslymonitored system subject to degradation [J]. Reliability Engineering and System Safety,2007,92(4):530-534.
[95] Camci F. System maintenance scheduling with prognostics information using genetic algorithm[J]. IEEE Transactions on Reliability,2009,58(3):539-552.
[96] Yang Z, Djurdjanovic D, Ni J. Maintenance scheduling in manufacturing systems based onpredicted machine degradation [J]. Journal of Intelligent Manufacturing,2008,19(1):87-98.
[97] Christer A H, Wang W, Sharp J M. A state space condition monitoring model for furnace erosionprediction and replacement [J]. European Journal of Operational Research,1997,101(1):1-14.
[98] Pedregal D J and Carnero M C. State space models for condition monitoring: a case study.Reliability Engineering and System Safety,2006,91(2):171-180.
[99] Lu S, Tu Y-C, Lu H. Predictive condition-based maintenance for continuously deterioratingsystems [J]. Quality and Reliability Engineering International,2007,23(1):71-81.
[100] Kaiser K A, Gebraeel N Z. Predictive maintenance management using sensor-based degradationmodels [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans,2009,39(4):840-849.
[101] Wu S-J, Gebraeel N Z, Lawley M A, et al. A neural network integrated decision support systemfor condition-based optimal predictive maintenance policy [J]. IEEE Transactions on Systems,Man, and Cybernetics-Part A: Systems and Humans,2007,37(2):226-236.
[102] Kharoufeh J P, Cox S M. Stochastic models for degradation-based reliability [J]. IIETransactions,2005,37:533-542.
[103] Kharoufeh J P, Solo C J, Ulukus M Y. Semi-Markov models for degradation-based reliability [J].IIE Transactions,2010,42:599-612.
[104] Liu F, Meng G, Zhao M, Zhao J F. Board level drop test analysis based on modal test andsimulation [J]. Journal of Electronic Packaging, the ASME Transactions.2008;130(2):021007(1-6).
[105]王文. SMT无铅焊点在随机振动载荷下的可靠性分析[D].上海：上海交通大学，2010.
[106] Meeker W Q, Escobar L A. Statistical Methods for Reliability Data [M]. New York: Wiley,1998.
[107] Kim Y S, Kolarik W J. Real-time conditional reliability prediction from on-line toolperformance data [J]. International Journal of Production Research,1992,30(8):1831-1844.
[108] Wang P, Coit D W. Reliability and degradation modeling with random or uncertain failurethreshold [C].2007Annual Reliability and Maintainability Symposium, Orlando, FL, USA,2007.
[109] Christer A H, Waller. Delay time models of industrial inspection maintenance problems [J].Journal of the Operational Research Society,1984,35,401-406.
[110] Cox D R. Regression models and life-tables (with discussion)[J]. Journal of Royal StatisticalSociety. Series B (Methodological),1972,34(2),187-220.
[111] Lagarias J C, Reeds J A, Wright M H, and Wright P E. Convergence properties of theNelder-Mead simplex method in low dimensions. SIAM Journal of Optimization,1998,9(1),112-147.
[112] Pandit S M and Wu S–M. Time Series and System Analysis with Applications [M]. New York:Wiley,1983.
[113] Connor J T, Martin R D, and Atlas L E. Recurrent neural networks and robust time seriesprediction [J]. IEEE Transactions on Neural Networks,1994,42(4),240-254.
[114] Liu J, Djurdjanovic D, Ni J, Casoettlo N,et al. Similarity based method for manufacturingprocess performance prediction and diagnosis [J]. Computers in Industry,2007,58(6),558-566.
[115] Volk P J, Coetzee J L, Banjevic D, et al. Optimal component replacement decisions usingvibration monitoring and the proportional-hazards model [J]. Journal of Opeartional ResearchSociety,2002,53(2),193-202.
[116] Wang W. A two-stage prognosis model in condition based maintenance [J]. European Journal ofOperational Research,2007,182,1177-1187.
[117] Kourti T and MacGregor J F. Process analysis, monitoring and diagnosis, using multivariateprojection methods [J]. Chemometrics and Intelligent Laboratory Systems,1995,28,3-21.
[118] Lin D, Zuo M J, Yam R C M. Sequential imperfect preventive maintenance models with twocategories of failure modes [J]. Naval Research Logistics,2001;48(2):172-183.
[119] Nakagawa T. Sequential imperfect preventive maintenance policies [J]. IEEE Transactions onReliability,1988;37(3),295-298.
[120] EI-Ferik S, Ben-Daya M. Age-based hybrid model for imperfect preventive maintenance [J]. IIETransactions,2006;38(4),365-375.
[121] Barlow R E and Prochan F. Mathematical Theory of Reliability [M]. New York: Wiley,1965.
[122] Dekker R. Applications of maintenance optimization models: A review and analysis [J].Reliability Engineering and System Safety,1996,51(3),229-240.
[123] Pham H and Wang H. Imperfect maintenance [J]. European Journal of Operational Research,1996,94(3),425-438.
[124] Wang H. A survey of maintenance policies of deteoriating systems [J]. European Journal ofOperational Research,2002,139(3),469-489.
[125] Montgomery D C. Introduction to Statistical Quality Control (5thedition)[M]. New York: Wiley,2005.
[126] Mobley R K. An Introduction to Predictive Maintenance [M]. New York:Butterworth-Heinemann,1989.
[127] Barlow R E and Hunter L C. Optimum preventive maintenance policies [J]. OperationsResearch,1960,8(1),90-100.
[128] Nowakowski T and Weibińka. On problems of multicomponent maintenance modeling [J].International Journal of Aotomation and Computing,2009,6(4),364-378.
[129] Nicolai R P and Dekker R. Optimal maintenance of multi-component systems: A review [M].Complex System Maintenance Handbook-11, London: Springer,2008.
[130] Yam R C M, Tse P W, L. Li, et al. Intelligent predictive decision support system forcondition-based maintenance [J]. International Journal of Advanced Manufacturing Technology,2001,17,383-391.
[131] Wireman T. World Class Maintenance Management [M]. New York: Industrial Press,1990.
[132] Bevilacqua M and Braglia M. The analytic hierarchy process applied to maintenance stratrgyselection [J]. Reliability Engineering and System Safety,2000,70(1),71-83.
[133] Li L, You M Y, and Ni J. Reliability-based dynamic maintenance threshold for continuouslymonitored degrading systems [J]. Journal of Manufacturing Science and engineering,Transactions of the ASME,2009,131(3),031010(1-9).
[134] You M Y, Li L, Meng G, et al. Cost-effective updated sequential predictive maintenance policyfor continuously monitored degrading systems [J]. IEEE Transactions on Automation Scienceand Engineering,2010,7(2),257-265.
[135] Elwany A H, Gebraeel N Z. Sensor-driven prognostic models for equipment replacement andspare parts inventory [J]. IIE Transactions,2008,40(7),629-639.
[136] Tsai Y–T, Wang K–S, Tsai L–C. A study of availability-centered preventive maintenance formulti-component systems [J]. Reliability Engineering and System Safety,2004,84(3),261-270.
[137] Maciejewski H, Caban D. Estimation of repairable system within fixed time horizon [J].Reliability Engineering and System Safety,2008,93(1),100-106.
[138] Sarkar J, Chaudhuri G. Availability of a system with gamma life and exponential repair timeunder a perfect repair policy [J]. Statistics&Probbaility Letters,1999,43(2),189-196.
[139] Biswas A, Sarkar J, Sarkar S. Availability of a periodically inspected system, maintenanedunder an imperfect-repair policy [J]. IEEE Transactions on Reliability,2003,52(3),311-318.
[140] Klutke G–A, Yang Y. The availability of inspected systems subject to shocks and gracefuldegradation [J]. IEEE Transactions on Reliability,2002,51(3),311-318.
[141] Bao X, Cui L. An analysis of availability for series Markov repairable system with negencted ordelayed failures [J]. IEEE Transactions on Reliability,2010,59(4),734-743.
[142] Wang H, Pham H. Survey of reliability and availability evaluation of complex networks usingMonte Carlo techniques [J]. Microelectronics Reliability,1997,37(2),187-209.
[143] Marquez A C, Heguedas A S, Iung B. Monte Carlo-based assessment of system availability. Acase study for cogeneration plants [J]. Reliability Engineering and System Safety,2005,88(3),273-289.
[144] Cassady C R, Iyoob I M, Schneider K, et al. A generic model of equipment availability underimperfect maintenance [J]. IEEE Transactions of Reliability,2005,54(4),564-571.
[145] You M–Y, Liu F, Wang W, et al. Statistically planned and individually improved redictivemaintenance management for continuously monitored degrading systems [J]. IEEE Transactionson Reliability,2010,59(4),744-753.
[146] Gao X, Barabady J, Markeset T. An approach for prediction of petroleum production facilityperformance considering Arctic influence factors [J]. Reliability Engineering and System Safety,2010,95(8),837-846.
[147] Kalbfleisch J D, Prentice R L. The Statistical Analysis for Failure Time Data [M]. New Jersey:Wiley,2002.
[148] Barabadi A, Barabady J, Markeset T. Maintainability analysis considering time-dependnet andtime-independent covariates [J]. Reliability Engineering and System Safety,2011,96(1),210-217.
[149] Doksum K A, Hóyland A. Models for variable-stress accelerated life testing experiments basedon wiener processes and the inverse Gaussian distribution [J]. Technometrics,1992,34(1),74-82.
[150]周东华，徐正国.工程系统的实时可靠性评估与预测技术[J].空间控制技术与应用.2008(34)：3-10.
[151]曾声奎，Pecht M G，吴际.故障预测与健康管理（PHM）技术的现状与发展[J].航空学报.2005(26)：626-632.
[152] Wang T. Trajectory similarity-based prediction for remaining useful life estimation [D].Cincinnati: University of Cincinnati,2010.
[153] Saxena A, Goebel K, Simon D, Eklund N. Damage propagation modeling for aircraft enginerun-to-failire simulation [C]. Proceedings of the International Conference on Prognostics andHealth Management,2008.
[154]尤明懿.基于相似性的剩余寿命预测：鲁棒性与不确定性研究[J].电子产品可靠性与环境实验，2011，录用.
[155] Swindemana R W, Swindemanb M J. A Comparison of creep models for nickel base alloy foradvanced energy systems [J]. International Journal of Pressure and Piping,2008,85(1-2):72-79.