可修系统维修的仿真分析
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摘要
随着科学技术的高速发展,生产设备趋于功用智能化、系统结构复杂化,在提高其可靠性的同时,其购买和维修的费用也随之上升。在这个经济全球化的时代,工厂或企业不可能只注重高可靠性而忽略经费的高投入问题,因此,科学的探讨适于生产设备的维修计划或策略是很有必要的。本文主要从以下三个方面展开研究：不同维修类型的故障率变化规律及其仿真抽样方法分析、一种基于费用率最小原则的复杂系统周期性预防维修策略的优化研究和基于维修作业计划的预防维修策略研究。
首先,本文对最小修、不完全维修及完全维修三种情形的故障强度变化进行了分析,探讨了不同情形的故障强度变化规律,并分别对达到预防维修周期前采取最小修及完全维修这两种情形基于最大利用度和经济损失最小原则得到了最优预防维修策略模型,然后对两种原则下的模型形式进行了比较,分析了模型的适用范围,同时对系统不同故障强度变化下是否需要进行预防维修做了阐述。进而基于连续函数的随机抽样方法,重点针对最小修及不完全维修的情形得到了故障时间抽样的递推公式。
其次,针对目前仅从宏观考虑系统经济利用率的缺陷,提出一种微观考虑的思想,将每个部件每次小修的时刻点加以利用,分析部件在整个预防维修间隔中单位时间的利用率,以整个预防维修周期内所有组成部件总的单位时间平均费用率最小为准则,得到了一个求解最优维修周期的方程。并以部件故障率服从威布尔分布的复杂系统为例进行了仿真计算,得到了其最优维修周期。
最后,基于现代维修控制理论的需要,本文针对企业维修作业计划的预防维修周期定额及预防维修工作定额展开研究,利用假设来对实际情形进行模拟：以不同的可靠度阈值反映系统组成部件的重要度,以变化的役龄回退因子和故障率递增因子刻画各部件在实际运行过程中故障率的变化规律,以修理设备可能出现故障来体现实际修理工作中的修理差错。在这种假设情形下,我们成功的通过可靠度阈值确定了各部件最优预防维修的周期,并通过部件全生命周期损失最小的原则得到了每一个部件的最优预防维修次数,即获得了部件的最优更换策略。进而我们引入了一个预防维修控制因子,建立了系统的动态预防维修策略模型,通过这个模型我们可以得到有限时间内的最优维修计划表。最终本文以工程部件常见的寿命分布——威布尔分布为例,对5部件串联的系统进行了算例仿真分析,成功得到了系统的年度最优预防维修作业计划,这具有一定的现实意义。
With the rapid development of science and technology, the system structure of production equipment is more and more complicated. While their reliability are improved, its purchase and maintenance costs will rise. In this era of economic globalization, factories or business can not only pay attention to high reliability but also the funds of high input. In this situation, it is necessary to have a discussion about the production equipment maintenance plans or strategies. This article is mainly to give explanations from the following three aspects:the introduction of failure regularity and simulation sampling method of different maintenance types; an optimization for cyclical periodic preventive maintenance strategy based on rate minimum principle, a research for complex system preventive maintenance strategy based on maintenance scheduling.
Firstly, it analyzes the chang of the failure rate in three circumstances:minor repairs, incomplete maintenances, complete maintenances. The chang rule of the failure rate is discussed in these different situation.And the optimal preventive maintenance strategy model is established by the principle of maximum exploitation degree and minimum loss of life cycle respectively in minor repairs and complete maintenances situation. We get the scope of application of the model by comparison, and then we have a discussion in whether or not to have preventive maintenance by different failure rate changing. Further more,we get the recursive formula of fault time sampling in minor repairs and complete maintenances situation based on the random sampling method of continuous functions.
Secondly, in view of the defects that economic utilization of the system is considered just by macroscopic ways, we propose a microscopic way, that using every minor repairs time value of each component to analysis the unit time utilization of each component throughout the preventive maintenance interval. Then we establish a model which can compute the best repairing cycle according to principle "the average loss cost per unit time minimum ". Meanwhile, we take the example of a system which components obey weibull distribution and get the optimal preventive maintenance period of this system after the simulation calculation.
Finally, basing on the needs of modern maintenance control theory, we launched research on getting preventive maintenance cycle and workload. We make this assumption to simulate the real situation:the different reliability threshold reflects the importance of system components; the changing age reduction factor and failure rate reduction factor show the fault changing rules of each component in real operation; the failures of repairing equipment reflect the fix mistakes in real maintenance. In this assumption, the preventive maintenance cycle can be got by the reliability threshold. We can also obtain the optimal preventive maintenance frequency(optimal replacement policy) for each part through the principle of minimum loss of life cycle. Then we introduce a preventive maintenance control factor and construct a dynamic preventive maintenance policy model for the system. At last, we take the example of Weibull distribution which is a common life distribution for the engineering components to analyze numerical simulation of 5 unit series systems, and get the annual optimal preventive maintenance plan. This case shows some practical significance for the real operation.
首先,本文对最小修、不完全维修及完全维修三种情形的故障强度变化进行了分析,探讨了不同情形的故障强度变化规律,并分别对达到预防维修周期前采取最小修及完全维修这两种情形基于最大利用度和经济损失最小原则得到了最优预防维修策略模型,然后对两种原则下的模型形式进行了比较,分析了模型的适用范围,同时对系统不同故障强度变化下是否需要进行预防维修做了阐述。进而基于连续函数的随机抽样方法,重点针对最小修及不完全维修的情形得到了故障时间抽样的递推公式。
其次,针对目前仅从宏观考虑系统经济利用率的缺陷,提出一种微观考虑的思想,将每个部件每次小修的时刻点加以利用,分析部件在整个预防维修间隔中单位时间的利用率,以整个预防维修周期内所有组成部件总的单位时间平均费用率最小为准则,得到了一个求解最优维修周期的方程。并以部件故障率服从威布尔分布的复杂系统为例进行了仿真计算,得到了其最优维修周期。
最后,基于现代维修控制理论的需要,本文针对企业维修作业计划的预防维修周期定额及预防维修工作定额展开研究,利用假设来对实际情形进行模拟：以不同的可靠度阈值反映系统组成部件的重要度,以变化的役龄回退因子和故障率递增因子刻画各部件在实际运行过程中故障率的变化规律,以修理设备可能出现故障来体现实际修理工作中的修理差错。在这种假设情形下,我们成功的通过可靠度阈值确定了各部件最优预防维修的周期,并通过部件全生命周期损失最小的原则得到了每一个部件的最优预防维修次数,即获得了部件的最优更换策略。进而我们引入了一个预防维修控制因子,建立了系统的动态预防维修策略模型,通过这个模型我们可以得到有限时间内的最优维修计划表。最终本文以工程部件常见的寿命分布——威布尔分布为例,对5部件串联的系统进行了算例仿真分析,成功得到了系统的年度最优预防维修作业计划,这具有一定的现实意义。
With the rapid development of science and technology, the system structure of production equipment is more and more complicated. While their reliability are improved, its purchase and maintenance costs will rise. In this era of economic globalization, factories or business can not only pay attention to high reliability but also the funds of high input. In this situation, it is necessary to have a discussion about the production equipment maintenance plans or strategies. This article is mainly to give explanations from the following three aspects:the introduction of failure regularity and simulation sampling method of different maintenance types; an optimization for cyclical periodic preventive maintenance strategy based on rate minimum principle, a research for complex system preventive maintenance strategy based on maintenance scheduling.
Firstly, it analyzes the chang of the failure rate in three circumstances:minor repairs, incomplete maintenances, complete maintenances. The chang rule of the failure rate is discussed in these different situation.And the optimal preventive maintenance strategy model is established by the principle of maximum exploitation degree and minimum loss of life cycle respectively in minor repairs and complete maintenances situation. We get the scope of application of the model by comparison, and then we have a discussion in whether or not to have preventive maintenance by different failure rate changing. Further more,we get the recursive formula of fault time sampling in minor repairs and complete maintenances situation based on the random sampling method of continuous functions.
Secondly, in view of the defects that economic utilization of the system is considered just by macroscopic ways, we propose a microscopic way, that using every minor repairs time value of each component to analysis the unit time utilization of each component throughout the preventive maintenance interval. Then we establish a model which can compute the best repairing cycle according to principle "the average loss cost per unit time minimum ". Meanwhile, we take the example of a system which components obey weibull distribution and get the optimal preventive maintenance period of this system after the simulation calculation.
Finally, basing on the needs of modern maintenance control theory, we launched research on getting preventive maintenance cycle and workload. We make this assumption to simulate the real situation:the different reliability threshold reflects the importance of system components; the changing age reduction factor and failure rate reduction factor show the fault changing rules of each component in real operation; the failures of repairing equipment reflect the fix mistakes in real maintenance. In this assumption, the preventive maintenance cycle can be got by the reliability threshold. We can also obtain the optimal preventive maintenance frequency(optimal replacement policy) for each part through the principle of minimum loss of life cycle. Then we introduce a preventive maintenance control factor and construct a dynamic preventive maintenance policy model for the system. At last, we take the example of Weibull distribution which is a common life distribution for the engineering components to analyze numerical simulation of 5 unit series systems, and get the annual optimal preventive maintenance plan. This case shows some practical significance for the real operation.
引文
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3.蔡景,左洪福.复杂系统成组维修策略优化模型研究[J].应用科学学报,2006,24(5)：534-537
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9.侯文瑞,蒋祖华.基于可靠度的多设备混联系统机会维护模型[J].上海交通大学学报,2009,4：659-662
10.黄宝旭,韩帮军.蒙特卡罗仿真在设备预防性维修周期确定中的应用[J].聊城大学学报(自然科学版),2004,17(3)：48-50
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2.蔡景,左洪福.基于机会维修的复杂系统维修费用仿真研究[J].系统仿真学报,2007,19(6)：1397-1399
3.蔡景,左洪福.复杂系统成组维修策略优化模型研究[J].应用科学学报,2006,24(5)：534-537
4.陈学楚.现代维修理论.北京：国防工业出版社,2003
5.曹晋华.带失效小修的多状态单部件可修系统的预防性维修策略[J].应用数学学报,1986,9(1)：113—123
6.杜小平.确定费用最小原则下设备最佳预防维修周期的计算机仿真方法[J].设备管理,1996,2：4-6
7.杜小平.利用计算机仿真技术确定系统的最佳预防维修周期[J].设备管理,1994,10：4-5
8.官洪运,禹素萍,韩帮军.电力设备预防性维修策略的优化[J].江南大学学报(自然科学版),2004,(3)3：253-255
9.侯文瑞,蒋祖华.基于可靠度的多设备混联系统机会维护模型[J].上海交通大学学报,2009,4：659-662
10.黄宝旭,韩帮军.蒙特卡罗仿真在设备预防性维修周期确定中的应用[J].聊城大学学报(自然科学版),2004,17(3)：48-50
11.胡立臣,刘立.复杂可维修设备寿命周期费用仿真[J].车辆与动力技术,2004,3：39-43
12.韩帮军,范秀敏,马登哲.基于可靠度约束的预防性维修策略的优化研究[J].机械工程学报,2003,39(6)：103-105
13.金玉兰.生产系统有限时间区间弹性周期预防性维修策略研究.[博士学位论文].上海：上海交通大学,2009
14.贾积身.冷备可修系统最优更换策略下的数学模型[J].系统工程学报,2003,18(2)：177-182
15.蒋仁言,杜颖.定期预防维修最佳周期的确定[J].长沙交通学院学报,1987,3(2)：27-35
16.李志全.可维修机械产品使用可靠性研究.[硕士学位论文].南京航空航天大学民航学院,2007
17.刘云,赵玮.系统最佳维修策略研究[J].运筹与管理,2004,2：59-61
18.宓乐英,吕柏荣.多设备串行系统预防性维护的动态决策优化研究[J].机械设计与研究,2008,11：8-10
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