数控系统可用性分析
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摘要
可靠性是数控机床用户最关心的技术指标之一,被人们视为数控机床的“大脑”与“核心”的数控系统的可靠性更是用户关注的焦点。数控系统可靠性的评价体系和评价软件已经基本趋于成熟,但是多数是从故障间隔时间的角度切入。
本文主要以国内某厂生产的数控系统为研究对象,对现阶段数控系统的可用性评价进行了研究。主要方法是在比较成熟的可靠性研究上增加了维修性分析、可用性分析和评价及GO法分析。分别从整体和系统的角度分析了该数控系统可用性情况,为提高其可用性提供了理论的指导。
首先建立故障间隔时间模型和故障维修时间模型,确定MTBF和MTTR的观测值和点估计值。再根据可靠性、维修性研究的结果对该数控系统进行可用性分析,求出数控系统的瞬时可用度模型及稳态可用度的值,并对其进行可用性评价。为从系统角度分析数控系统的可靠性,本文将再使用GO法原理对该数控系统进行可靠性分析。GO法是近几年快速发展起来的一个新的方法,已经在天然气管道系统、核电站电源系统和配电网络等领域取得了很好的成绩,然而在数控系统可靠性研究领域尚未得到广泛应用,因此本文将使用GO法对数控系统进行系统的可靠性分析。
1. Introduction
CNC system is the Control core of the CNC machine. The reliability of the CNC system is the quality attribute by the most concerned when most users want to purchase products. And if the reliability is well or not is the key of our homemade NC industries survival. The availability research on the CNC system can increase the level of the homemade NC industry and direct decrease the expense of the suppliers’after service\three guarantees costs\downtime losses and machine maintenance. So this research has an important historical and practical significance.
This thesis is just put forward under this kind of background. It is a part of the JiLin province Scientific and technological development project-The key technology of the computer-assistant NC machine tool’s availability research for the life cycle(Contract No.: 20050535).
At present, the reliability research technique of the CNC system has been basically mature, but most of them are from the point of view of the time between failures. This paper will add maintainability analysis\availability analysis and GO methodology analysis. And it analyses the availability of some factory CNC system which is produced in recent years. This paper’s research provided theoretical guidance for the improvement of CNC system availability.
2. The reliability of CNC system
According to the large quantity of data collected to establish time between failures model, and then analyses CNC system’s reliability.
CNC system belongs to electronic products. Because of what is called“no memory”, its failure data should be exponential model, and we usually call it exponential production. Basing on this point, the paper must check up the data to find out if the data contain some uncommon data. After this work, I found a uncommon big one, so I will eliminate this data in order not to affect the whole data’s authenticity. By dealing with the data, this paper will establish the mathematic model first, and use the optimal distribution pattern as criterion to scale the fit on the graph later. The index of correlation is 0.99064 by calculating,and the model has passed the test. So the eliminating of the data is rational.
The paper gives out the mathematic model of four basic functions, which are the failure probability consistency, f(t), accumulated failure probability, F(t), instantaneous failure probability,λ(t), reliability grade, R(t).
The observation value of MTBF is 1228.7 hour.
The spot estimation value of MTBF is 941.2 hour.
3. The maintainability of CNC system
If the reliability is well or not is measured on maintaining time. The maintenance goes better as maintaining time goes shorter. The paper collected a mass of data to analyze the maintenance of the CNC system, and make sure that the distribution function model of maintaining time is lognormal distribution. The paper will establish maintainability function model. Using the relatively accurate d inspection and taking the significance levelαequal to 0.1, the hypothesis test statistic D_n (=0.080043) less than the critical value D_(n,α) that equals to 0.2799, is obtained. So these maintaining data are matched to the lognormal distribution model.
The paper gives out the mathematic model of three basic functions, which are the maintenance probability consistency, (m|^) (t), maintenance time distribution function, (M|^) (t), maintainability probability function, (μ|^) (t).
The observation value of MTTR is 5.47 hour.
The spot estimation value of MTTR is 5.94 hour.
4. The availability of CNC system
The availability contains reliability、maintainability and maintenance indemnification. Because of the maintenance indemnification data is rarely few in CNC system test data, so the paper will not consider the maintenance indemnification, only analyze on the basis of reliability and maintainability. Using the conclusion of reliability and maintainability analysis, the paper analyzes the CNC system’s availability to establish instantaneous availability model and the inherent availability. And evaluate the CNC system’s availability.
The CNC system’s the inherent availability Ai is 0.993728 and instantaneous availability model is A ( t)= 0.993728+0.006272e-~(0.169413t). Draw the two curve in one coordinate chart (Chart 1), and the curve 1 is the instantaneous availability model and the curve 2 is the inherent availability. We can see that the instantaneous availability is falling gradually from the zero times, and after 30~40 hours the instantaneous availability and the inherent availability will be nearly superposition. Evaluating the CNC system’s availability, the paper found that the estimate is 0.995189 and the unilateral lower confidence limit of the interval estimate is 0.9925. So, it is obvious that the CNC system’s availability is well.
5. GO Methodology analysis on CNC system
For analyzing CNC system’s reliability from inner and system point of view, the paper will use GO methodology to analyze CNC system’s failure. GO methodology is a new reliability method, which has been developing fast in recent years, but has never been used in CNC system’s reliability area in-depth. So the paper will use it in CNC system’s reliability research in-depth.
According to the inner configuration and principle, we divide the CNC system into several parts. Analyze CNC system’s reliability according to the communication transfer among the parts. So the GO methodology can represent its reliability more accurately. In the GO operation, we use the steady availability of every part as normal state probability, and work out the CNC system’s every state value: the average normal working probability is 0.9920779, the average un-normal working probability is 0.0079221, the failure probability is 0.0015319, and the maintainability probability is 0.1918381.
6. Conclusion
The paper analyzed the CNC system’s reliability first, and found out the observation value and spot estimation value of MTBF. It also analyzed the CNC system’s maintainability, and educed the observation value and spot estimation value of MTTR. And then use these results to analyze and evaluate the CNC system’s availability. For analyzing CNC system’s reliability from inner and system point of view, the paper used GO methodology to analyze CNC system’s reliability, and educed reliability value according to the inner parts’logic connection.
本文主要以国内某厂生产的数控系统为研究对象,对现阶段数控系统的可用性评价进行了研究。主要方法是在比较成熟的可靠性研究上增加了维修性分析、可用性分析和评价及GO法分析。分别从整体和系统的角度分析了该数控系统可用性情况,为提高其可用性提供了理论的指导。
首先建立故障间隔时间模型和故障维修时间模型,确定MTBF和MTTR的观测值和点估计值。再根据可靠性、维修性研究的结果对该数控系统进行可用性分析,求出数控系统的瞬时可用度模型及稳态可用度的值,并对其进行可用性评价。为从系统角度分析数控系统的可靠性,本文将再使用GO法原理对该数控系统进行可靠性分析。GO法是近几年快速发展起来的一个新的方法,已经在天然气管道系统、核电站电源系统和配电网络等领域取得了很好的成绩,然而在数控系统可靠性研究领域尚未得到广泛应用,因此本文将使用GO法对数控系统进行系统的可靠性分析。
1. Introduction
CNC system is the Control core of the CNC machine. The reliability of the CNC system is the quality attribute by the most concerned when most users want to purchase products. And if the reliability is well or not is the key of our homemade NC industries survival. The availability research on the CNC system can increase the level of the homemade NC industry and direct decrease the expense of the suppliers’after service\three guarantees costs\downtime losses and machine maintenance. So this research has an important historical and practical significance.
This thesis is just put forward under this kind of background. It is a part of the JiLin province Scientific and technological development project-The key technology of the computer-assistant NC machine tool’s availability research for the life cycle(Contract No.: 20050535).
At present, the reliability research technique of the CNC system has been basically mature, but most of them are from the point of view of the time between failures. This paper will add maintainability analysis\availability analysis and GO methodology analysis. And it analyses the availability of some factory CNC system which is produced in recent years. This paper’s research provided theoretical guidance for the improvement of CNC system availability.
2. The reliability of CNC system
According to the large quantity of data collected to establish time between failures model, and then analyses CNC system’s reliability.
CNC system belongs to electronic products. Because of what is called“no memory”, its failure data should be exponential model, and we usually call it exponential production. Basing on this point, the paper must check up the data to find out if the data contain some uncommon data. After this work, I found a uncommon big one, so I will eliminate this data in order not to affect the whole data’s authenticity. By dealing with the data, this paper will establish the mathematic model first, and use the optimal distribution pattern as criterion to scale the fit on the graph later. The index of correlation is 0.99064 by calculating,and the model has passed the test. So the eliminating of the data is rational.
The paper gives out the mathematic model of four basic functions, which are the failure probability consistency, f(t), accumulated failure probability, F(t), instantaneous failure probability,λ(t), reliability grade, R(t).
The observation value of MTBF is 1228.7 hour.
The spot estimation value of MTBF is 941.2 hour.
3. The maintainability of CNC system
If the reliability is well or not is measured on maintaining time. The maintenance goes better as maintaining time goes shorter. The paper collected a mass of data to analyze the maintenance of the CNC system, and make sure that the distribution function model of maintaining time is lognormal distribution. The paper will establish maintainability function model. Using the relatively accurate d inspection and taking the significance levelαequal to 0.1, the hypothesis test statistic D_n (=0.080043) less than the critical value D_(n,α) that equals to 0.2799, is obtained. So these maintaining data are matched to the lognormal distribution model.
The paper gives out the mathematic model of three basic functions, which are the maintenance probability consistency, (m|^) (t), maintenance time distribution function, (M|^) (t), maintainability probability function, (μ|^) (t).
The observation value of MTTR is 5.47 hour.
The spot estimation value of MTTR is 5.94 hour.
4. The availability of CNC system
The availability contains reliability、maintainability and maintenance indemnification. Because of the maintenance indemnification data is rarely few in CNC system test data, so the paper will not consider the maintenance indemnification, only analyze on the basis of reliability and maintainability. Using the conclusion of reliability and maintainability analysis, the paper analyzes the CNC system’s availability to establish instantaneous availability model and the inherent availability. And evaluate the CNC system’s availability.
The CNC system’s the inherent availability Ai is 0.993728 and instantaneous availability model is A ( t)= 0.993728+0.006272e-~(0.169413t). Draw the two curve in one coordinate chart (Chart 1), and the curve 1 is the instantaneous availability model and the curve 2 is the inherent availability. We can see that the instantaneous availability is falling gradually from the zero times, and after 30~40 hours the instantaneous availability and the inherent availability will be nearly superposition. Evaluating the CNC system’s availability, the paper found that the estimate is 0.995189 and the unilateral lower confidence limit of the interval estimate is 0.9925. So, it is obvious that the CNC system’s availability is well.
5. GO Methodology analysis on CNC system
For analyzing CNC system’s reliability from inner and system point of view, the paper will use GO methodology to analyze CNC system’s failure. GO methodology is a new reliability method, which has been developing fast in recent years, but has never been used in CNC system’s reliability area in-depth. So the paper will use it in CNC system’s reliability research in-depth.
According to the inner configuration and principle, we divide the CNC system into several parts. Analyze CNC system’s reliability according to the communication transfer among the parts. So the GO methodology can represent its reliability more accurately. In the GO operation, we use the steady availability of every part as normal state probability, and work out the CNC system’s every state value: the average normal working probability is 0.9920779, the average un-normal working probability is 0.0079221, the failure probability is 0.0015319, and the maintainability probability is 0.1918381.
6. Conclusion
The paper analyzed the CNC system’s reliability first, and found out the observation value and spot estimation value of MTBF. It also analyzed the CNC system’s maintainability, and educed the observation value and spot estimation value of MTTR. And then use these results to analyze and evaluate the CNC system’s availability. For analyzing CNC system’s reliability from inner and system point of view, the paper used GO methodology to analyze CNC system’s reliability, and educed reliability value according to the inner parts’logic connection.
引文
[1] 盛伯浩.数控机床的现状与发展[J]. 数控机床市场 ,2006,(1):40-43
[2] 冯建平.数控机床发展新趋势[J].现代制造,2007,(11):12-13
[3] 杨皖苏,严鸿和.加入 WTO 后我国数控产业发展的战略思路与对策[J].组合机床与自动化加工技术,2002,(10)
[4] 中国机床工具工业协会数控系统分会. CIMT2001 巡礼[J]. 世界制造技术与装备市场,2001(5):13-17
[5] 盛伯浩.我国数控机床现状与技术发展策略[J].现代金属加工,2005.06:41-44
[6] 古文生.数控机床及应用[M].电子工业出版社,2002.04
[7] 章富元,方江龙,汤季安. 对我国数控技术发展的思考[J]. 中国机械工程, 2001,(5):15-17
[8] 边述华.提高数控系统可靠性的探讨[J].中国科技信息,2006,( 20):91-92
[9] 贾亚洲.数控系统可靠性国内外现状及对策[J]. 中国制造业信息化,2006,(12)
[10]孙斌,杨汝清.基于PC的数控系统的研究现状和发展趋势[J].机床与液压,2001,(4):3-5
[11]周延佑.国产数控系统的特点和机床数控化改造的迫切性[J]. 制造技术与机床, 1999, (6):6-9
[12]张俊,魏红根. 数控技术发展趋势[J]. 制造技术与机床,2000,(4):23-25
[13]侯长合. 数控系统的发展方向[J]. 航空制造技术,2004,(4):50-52
[14]李佳特. 现代 CNC 发展趋势[J]. 制造技术与机床,2003,(4):5-7
[15]舒志兵; 严彩忠; 黄益群; 张海荣. 数控机床和数控系统和发展综述[J].伺服控制,2006,(1)
[16]江仁洁,何建新. 我国数控机床的现状及发展趋势[J].湖南农机,2007,(30):140-141
[17]范存德.液压技术手册[M].辽宁科学技术出版社,2004.05:130-131
[18]孙大涌.先进制造技术[M].机械工业出版社,2000.03 :152-154
[19]郭永基 可靠性工程原理[M],北京:清华大学出版社,2002.1,第 1 版
[20]董玉革.机械模糊可靠性设计[M].北京:机械工业出版社,2000.10:4-9
[21]王超,王金等.机械可靠性工程[M].北京:冶金工业出版社,1992
[22]刘惟信.机械可靠性设计[M].第一版,北京:清华大学出版社,1995
[23]Martin, P. Consequential failures in mechanical systems[M]. Reliability Engineering, 1982,22(3):23-45
[24]拓耀飞,李少宏.论结构可靠性的发展[J].榆林学院学报.2006,16(4): 32-35
[25]石荣德,康锐.FMECA 技术及其应用[M]。国防工业出版社,2006.10
[26]陈黎敏.数控机床的故障树分析[J].常州信息职业技术学院学报, 2007,(03)
[27]彭道勇,刘春和,刘海敏,刘雪峰. 以可靠性为中心的维修 RCM 综述[J]. 第二届电子信息系统质量与可靠性学术研讨会. 2005.05:55-60
[28]周源泉 翁朝曦.AMSAA—BISE 模型及其统计推断[J].系统工程与电子技术,1991,13(11):72-78
[29]梅文华.可靠性增长试验[M].国防工业出版社,2003.5
[30]闻邦椿.产品设计的重要性与面向产品总体质量的综合设计法[J].质量与工程,2003(9):11-13
[31]范存德.液压技术手册[M].辽宁科学技术出版社 2004.05:130
[32]江妙富 龚庆祥. 美军装备可靠性维修性保障性验证管理的特点与启示[J]. 航空标准化与质量, 2004
[33]高春翔.树立科学的武器装备优劣观[J]. 解放军报,2000.12.05,第 6版
[34]李良巧 冯欣 可靠性工程概述 [J] 四川兵工学报.2003.4
[35](苏)普罗尼科夫. 数控机床的精度与可靠性[M]. 北京:机械工业出版社,1987.08
[36]A.Z.Keller, A.R.R.Kamth & U.D.Perea,RELIABILITY ANALYSIS OF CNC MACHINE TOOLS.Reliability Engineering 1982.3:449-473
[37]P.W. Prickett.An integrated approach to autonomous maintenance management. Integrated Manufacturing Systems,1999.10(4)
[38]王润孝 秦现生. 机床数控原理与系统[M].西北工业大学出版社,1997.06,第 2 版
[39]迟向磊,我国数控机床可靠性研究概况[J],机械工艺师,2001(3)
[40]胡亚波,吴玉文,我国数控机床的状况与发展[J],机床与液压,2004(07)床与液压,2005(3)
[41]B.V.Vershinin.Automatic system for troubleshooting systems with positional numerical control. Metallurgist, Volume 31, Number 6, 1987.06
[42]周祖德 陈幼平.先进制造技术系列 现代机械制造系统的监控与故障诊断[M].华中理工大学出版社,1999.06
[43]何沛霖 李斌. CNC 系统可靠性的模糊评价[J].中国机械工程,1999.11
[44]王立杰 缑斌丽,袁成荣.数控系统开发中的广义可靠性增长[J]. 机械设计与制造, 2001.02
[45]张强.数控系统的可靠性设计与评估技术[J].中国机械工程, 1999.10
[46]邬义杰 CNC 数控系统的故障自诊断和抗干扰方法[J].机电工程, 1997,(03)
[47]姜巍巍,贾亚洲,数控机床顾客满意度提升措施的研究[J],制造技术与机床,2005(11)
[48]张英芝,贾亚洲,数控冲床的故障概率模型[J],吉林大学学报(工学版),2004(2)
[49]王秉刚.汽车可靠性工程方法[M].北京:机械工工业出版社,1991,11:47~49
[50]Blalkrishann N, Cohen A C, Order Statistics and Inference [M]. Estimation Methods. Academic Press , 1991
[51]彭求实.指数型寿命数据中异常值的检验[J].数理统计与管理,2006.7
[52]G.C.哥德温 R.L.潘恩.动态系统辨识试验设计与数据分析[M].北京:科学出版社,1983 :28
[53]Tand N S, et al, Unmasking test for multiple outliers in an exponential sample [J] . Chinese Journal of Applied Probability and Statistics , 1997 , 13(4):384～386.
[54]Tand N S, et al, Testing for k upper and s lower outliers in an exponential sample [J]. Mathematical Statistics and Applied Probability , 1998 , 13 (3):228～229.
[55]电子科技大学应用数学系.概率论与数理统计[M].成都:电子科技大学出版社,1999.08:389
[56]郑天丕,方珍.使用威布尔函数的一点体会[J].机电元件,2001(6):38-46
[57]巫少龙.机床主轴模糊可靠性设计方法[J].机械设计与研究,2004(12):34-37
[58]潘吉安. 可靠性维修性可用性评估手册[M].北京:国防工业出版社,1995.12:253
[59]MIL STD 781D 工程研制、鉴定和生产的可靠性试验.1986
[60]MIL HDBK 189 可靠性增长管理手册.1981
[61]徐文征.GO 法理论及应用研究.北京轻工业学院硕士学位论文.1999
[62]Chu B B.Overview Manual GO Methodology.EPRI NP-3123 Vol 1.Washington: Electric Power Research Institute,1983
[63]沈祖培 黄祥瑞 GO 法原理及应用[M].北京:清华大学出版社 2004.8
[64]Chu B B.Modeling Manual GO Methodology.EPRI NP-3123 Vol 3.Washington: Electric Power Research Institute,1983
[65]赵再军.数控机床编程与加工技术[M].浙江大学出版社,2004:212
[2] 冯建平.数控机床发展新趋势[J].现代制造,2007,(11):12-13
[3] 杨皖苏,严鸿和.加入 WTO 后我国数控产业发展的战略思路与对策[J].组合机床与自动化加工技术,2002,(10)
[4] 中国机床工具工业协会数控系统分会. CIMT2001 巡礼[J]. 世界制造技术与装备市场,2001(5):13-17
[5] 盛伯浩.我国数控机床现状与技术发展策略[J].现代金属加工,2005.06:41-44
[6] 古文生.数控机床及应用[M].电子工业出版社,2002.04
[7] 章富元,方江龙,汤季安. 对我国数控技术发展的思考[J]. 中国机械工程, 2001,(5):15-17
[8] 边述华.提高数控系统可靠性的探讨[J].中国科技信息,2006,( 20):91-92
[9] 贾亚洲.数控系统可靠性国内外现状及对策[J]. 中国制造业信息化,2006,(12)
[10]孙斌,杨汝清.基于PC的数控系统的研究现状和发展趋势[J].机床与液压,2001,(4):3-5
[11]周延佑.国产数控系统的特点和机床数控化改造的迫切性[J]. 制造技术与机床, 1999, (6):6-9
[12]张俊,魏红根. 数控技术发展趋势[J]. 制造技术与机床,2000,(4):23-25
[13]侯长合. 数控系统的发展方向[J]. 航空制造技术,2004,(4):50-52
[14]李佳特. 现代 CNC 发展趋势[J]. 制造技术与机床,2003,(4):5-7
[15]舒志兵; 严彩忠; 黄益群; 张海荣. 数控机床和数控系统和发展综述[J].伺服控制,2006,(1)
[16]江仁洁,何建新. 我国数控机床的现状及发展趋势[J].湖南农机,2007,(30):140-141
[17]范存德.液压技术手册[M].辽宁科学技术出版社,2004.05:130-131
[18]孙大涌.先进制造技术[M].机械工业出版社,2000.03 :152-154
[19]郭永基 可靠性工程原理[M],北京:清华大学出版社,2002.1,第 1 版
[20]董玉革.机械模糊可靠性设计[M].北京:机械工业出版社,2000.10:4-9
[21]王超,王金等.机械可靠性工程[M].北京:冶金工业出版社,1992
[22]刘惟信.机械可靠性设计[M].第一版,北京:清华大学出版社,1995
[23]Martin, P. Consequential failures in mechanical systems[M]. Reliability Engineering, 1982,22(3):23-45
[24]拓耀飞,李少宏.论结构可靠性的发展[J].榆林学院学报.2006,16(4): 32-35
[25]石荣德,康锐.FMECA 技术及其应用[M]。国防工业出版社,2006.10
[26]陈黎敏.数控机床的故障树分析[J].常州信息职业技术学院学报, 2007,(03)
[27]彭道勇,刘春和,刘海敏,刘雪峰. 以可靠性为中心的维修 RCM 综述[J]. 第二届电子信息系统质量与可靠性学术研讨会. 2005.05:55-60
[28]周源泉 翁朝曦.AMSAA—BISE 模型及其统计推断[J].系统工程与电子技术,1991,13(11):72-78
[29]梅文华.可靠性增长试验[M].国防工业出版社,2003.5
[30]闻邦椿.产品设计的重要性与面向产品总体质量的综合设计法[J].质量与工程,2003(9):11-13
[31]范存德.液压技术手册[M].辽宁科学技术出版社 2004.05:130
[32]江妙富 龚庆祥. 美军装备可靠性维修性保障性验证管理的特点与启示[J]. 航空标准化与质量, 2004
[33]高春翔.树立科学的武器装备优劣观[J]. 解放军报,2000.12.05,第 6版
[34]李良巧 冯欣 可靠性工程概述 [J] 四川兵工学报.2003.4
[35](苏)普罗尼科夫. 数控机床的精度与可靠性[M]. 北京:机械工业出版社,1987.08
[36]A.Z.Keller, A.R.R.Kamth & U.D.Perea,RELIABILITY ANALYSIS OF CNC MACHINE TOOLS.Reliability Engineering 1982.3:449-473
[37]P.W. Prickett.An integrated approach to autonomous maintenance management. Integrated Manufacturing Systems,1999.10(4)
[38]王润孝 秦现生. 机床数控原理与系统[M].西北工业大学出版社,1997.06,第 2 版
[39]迟向磊,我国数控机床可靠性研究概况[J],机械工艺师,2001(3)
[40]胡亚波,吴玉文,我国数控机床的状况与发展[J],机床与液压,2004(07)床与液压,2005(3)
[41]B.V.Vershinin.Automatic system for troubleshooting systems with positional numerical control. Metallurgist, Volume 31, Number 6, 1987.06
[42]周祖德 陈幼平.先进制造技术系列 现代机械制造系统的监控与故障诊断[M].华中理工大学出版社,1999.06
[43]何沛霖 李斌. CNC 系统可靠性的模糊评价[J].中国机械工程,1999.11
[44]王立杰 缑斌丽,袁成荣.数控系统开发中的广义可靠性增长[J]. 机械设计与制造, 2001.02
[45]张强.数控系统的可靠性设计与评估技术[J].中国机械工程, 1999.10
[46]邬义杰 CNC 数控系统的故障自诊断和抗干扰方法[J].机电工程, 1997,(03)
[47]姜巍巍,贾亚洲,数控机床顾客满意度提升措施的研究[J],制造技术与机床,2005(11)
[48]张英芝,贾亚洲,数控冲床的故障概率模型[J],吉林大学学报(工学版),2004(2)
[49]王秉刚.汽车可靠性工程方法[M].北京:机械工工业出版社,1991,11:47~49
[50]Blalkrishann N, Cohen A C, Order Statistics and Inference [M]. Estimation Methods. Academic Press , 1991
[51]彭求实.指数型寿命数据中异常值的检验[J].数理统计与管理,2006.7
[52]G.C.哥德温 R.L.潘恩.动态系统辨识试验设计与数据分析[M].北京:科学出版社,1983 :28
[53]Tand N S, et al, Unmasking test for multiple outliers in an exponential sample [J] . Chinese Journal of Applied Probability and Statistics , 1997 , 13(4):384～386.
[54]Tand N S, et al, Testing for k upper and s lower outliers in an exponential sample [J]. Mathematical Statistics and Applied Probability , 1998 , 13 (3):228～229.
[55]电子科技大学应用数学系.概率论与数理统计[M].成都:电子科技大学出版社,1999.08:389
[56]郑天丕,方珍.使用威布尔函数的一点体会[J].机电元件,2001(6):38-46
[57]巫少龙.机床主轴模糊可靠性设计方法[J].机械设计与研究,2004(12):34-37
[58]潘吉安. 可靠性维修性可用性评估手册[M].北京:国防工业出版社,1995.12:253
[59]MIL STD 781D 工程研制、鉴定和生产的可靠性试验.1986
[60]MIL HDBK 189 可靠性增长管理手册.1981
[61]徐文征.GO 法理论及应用研究.北京轻工业学院硕士学位论文.1999
[62]Chu B B.Overview Manual GO Methodology.EPRI NP-3123 Vol 1.Washington: Electric Power Research Institute,1983
[63]沈祖培 黄祥瑞 GO 法原理及应用[M].北京:清华大学出版社 2004.8
[64]Chu B B.Modeling Manual GO Methodology.EPRI NP-3123 Vol 3.Washington: Electric Power Research Institute,1983
[65]赵再军.数控机床编程与加工技术[M].浙江大学出版社,2004:212