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  • ISSN：0577-6686
机械工程学报

机械工程学报 ›› 2017, Vol. 53 ›› Issue (7): 129-137.doi: 10.3901/JME.2017.07.129

• 数字化设计与制造 • 上一篇    下一篇

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考虑定时截尾数据的数控机床可靠性Bootstrap
区间估计方法*

杨兆军1, 李洪洲1,2, 陈传海1, 李国发1, 王彦鹍1   

  1. 1. 吉林大学机械科学与工程学院 长春 130025;
    2. 北华大学机械工程学院 吉林 132011
  • 出版日期:2017-04-05 发布日期:2017-04-05
  • 作者简介:

    杨兆军，男，1956年出生，教授，博士研究生导师。主要研究方向为数控装备可靠性理论与技术的研究。

    E-mail：yzj@jlu.edu.cn

    陈传海(通信作者)，男，1983年出生，讲师。主要研究方向为数控机床载荷谱与关键功能部件可靠性加速试验技术。

    E-mail：cchchina@foxmail.com

  • 基金资助:
    * 国家科技重大专项资助项目(2014ZX04014-011); 20160309收到初稿，20161019收到修改稿;

Bootstrap Interval Estimation of Reliability for Numerical Controlled Machine Tools Considering the Time-censored Data

YANG Zhaojun1, LI Hongzhou1,2, CHEN Chuanhai1, LI Guofa1, WANG Yankun1   

  1. 1. College of Mechanical Science and Engineering， Jilin University， Changchun 130025;
    2. College of Mechanical Engineering， Beihua University， Jilin 132011
  • Online:2017-04-05 Published:2017-04-05

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摘要：

针对采用参数Bootstrap方法进行数控机床可靠性区间估计时，在重抽样过程中因缺失定时截尾数据而产生较大估计误差的问题，提出一种能够充分利用数控机床定时截尾数据的可靠性Bootstrap区间估计方法。分析数控机床定时截尾试验中完整数据与定时截尾数据的时间关系，在重抽样时依据该时间关系重新生成Bootstrap重抽样样本，解决了采用参数Bootstrap方法重抽样时无法利用定时截尾数据，进而导致数控机床可靠性评估误差较大的问题。采用极大似然估计和Newton-Raphson方法得到了试验样本的点估计，采用纠偏加速系数对极大似然估计带来偏性误差进行纠偏，进而得到区间估计。结合具体实例，对抽样试验时间长度及初步生成完整数据的个数的设定原则进行了论述。试验结果表明：与其他区间估计方法相比，在同一置信水平下，考虑定时截尾数据的Bootstrap方法得到的可靠性区间长度短，可用于数控机床的可靠性评估。

关键词: Bootstrap, MTBF, 区间估计, 数控机床

Abstract:

A larger error will be induced due to the lack of time-censored data in the re-sampling process when parametric Bootstrap method is applied to estimate the confidence interval of a reliability index of NC (Numerical controlled) machine tools, and aiming at this problem, a Bootstrap method fully utilizing the time-censored data of the NC machine tools is proposed. Firstly, the relation between the complete and time-censored data in the time-censored test of NC machine tools is analyzed, and the Bootstrap samples are generated based on this relation, solving the problem that the time-censored data can’t be utilized in the Bootstrap’s re-sampling process. The reliability parameters’ point estimators are obtained by the maximum likelihood estimation and the Newton-Raphson. The bias-correction and accelerated method is used to decrease Biased error caused by the maximum likelihood, and then the confidence intervals are estimated. In combination with a real case, the principle of specifying the length of test timeT and the number of the initially generated complete datum k are discussed and proved. The results indicates that, under the same confidence level, the length of the confidence interval estimated by the proposed method considering the time-censored data is shorter than those estimated by other interval estimation method, and can be used in the reliability evaluation of NC machine tools.

Key words: Bootstrap, interval estimation, MTBF, NC machine tools

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