贝叶斯理论的可靠性评估方法及在数控系统评估中的运用

中国机械工程 ›› 2011, Vol. 22 ›› Issue (3): 314-317.

贝叶斯理论的可靠性评估方法及在数控系统评估中的运用

游达章1,2;唐小琦1;戴怡3;郑小年1;金健1

1.华中科技大学国家数控系统工程技术研究中心，武汉，430074

2.湖北工业大学，武汉,430068;;3.天津工程师范学院，天津，300222

出版日期:2011-02-10 发布日期:2011-03-02
基金资助:
国家自然科学基金资助项目(50875186)；国家科技重大专项(2009ZX04009-011，2009ZX04014-013-02)；武汉市科技局资助项目(200951830559)
National Natural Science Foundation of China（No. 50875186）;
National Science and Technology Major Project ( No. 2009ZX04009-011，2009ZX04014-013-02)

Reliability Estimation of CNC System Based on Bayes Method

You Dazhang1,2;Tang Xiaoqi1;Dai Yi3;Zhen Xiaonian1;Jin Jian1

1.National Numerical Control System Engineering Research Center, Huazhong of University Science and Technology, Wuhan, 430074

2.Hubei University of technology,Wuhan, 430068
3.Tianjin University of Technology and Education, Tianjin, 300222

Online:2011-02-10 Published:2011-03-02
Supported by:

National Natural Science Foundation of China（No. 50875186）;
National Science and Technology Major Project ( No. 2009ZX04009-011，2009ZX04014-013-02)

摘要/Abstract

摘要：

数控系统故障概率符合威布尔分布，如果以威布尔分布来构造似然函数，运用Bayes方法进行可靠性估计，将涉及大量的积分运算，并且不便于选择合适的先验分布。为了减小计算工作量和提高评估效率，将威布尔分布转化为指数分布，并取倒伽玛分布为先验分布;采用先验矩的方法估计先验分布的超参数;利用伽玛函数性质进行指数分布参数的估计，并转化为威布尔分布特征寿命参数的点估计和区间估计，进一步推导计算其他可靠性指标。给出数字实例，证明该方法可行。

关键词:

威布尔分布, 指数分布, 可靠性评估, 贝叶斯

Abstract:

Weibull distribution was used to describe the times-to-failure of a CNC system. Lots of integral operation would be involved in Bayes estimation with using Weibull distribution to construct likelihood function. To reduce the amount of calculation, the Weibull distribution was transformed to exponential distribution, and the obverse-Gamma distribution was chosen as the prior distribution. Then the hyper-parameters of the prior distribution were estimated by moment method, lastly the parameter of the exponential distribution was be estimated, which was transformed into the size parameter and the other reliability parameters of the Weibull distribution. An example was given to show that the result is proper and the method is feasible.

Key words:

Weibull distribution, exponential distribution, reliability estimation, Bayes

中图分类号:

TH17

游达章, 唐小琦, 戴怡, 郑小年, 金健.

贝叶斯理论的可靠性评估方法及在数控系统评估中的运用

[J]. 中国机械工程, 2011, 22(3): 314-317.

LIU Da-Zhang, TANG Xiao-Qi, DAI Yi, ZHENG Xiao-Nian, JIN Jian.

Reliability Estimation of CNC System Based on Bayes Method

[J]. China Mechanical Engineering, 2011, 22(3): 314-317.

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