无失效数据下液体火箭发动机的E-Bayes可靠性分析

doi:CNKI:11-1929/V.20110616.1730.003

流体力学与飞行力学

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无失效数据下液体火箭发动机的E-Bayes可靠性分析

韩明

福建工程学院数理系, 福建福州 350108

收稿日期:2011-03-30 修回日期:2011-05-12 出版日期:2011-12-25 发布日期:2011-12-08
通讯作者: 韩明 E-mail:hanming618@21cn.com
作者简介:韩明(1961-) 男,博士,教授,硕士生导师。主要研究方向:数理统计与可靠性理论。 Tel: 0591-22863118 E-mail: hanming618@21cn.com
基金资助:
福建省自然科学基金 (2009J01001)

E-Bayes Reliability Analysis for Liquid Rocket Engine with Zero-failure Data

HAN Ming

Department of Mathematics and Physics, Fujian University of Technology, Fuzhou 350108, China

Received:2011-03-30 Revised:2011-05-12 Online:2011-12-25 Published:2011-12-08

摘要/Abstract

摘要： 为了解决航空航天产品、造价昂贵的产品及高可靠性产品的可靠性评估,本文在无失效数据情况下,对液体火箭发动机进行了可靠性分析。应用E-Bayes(Expected-Bayesian)估计法,在有关研究的基础上,针对液体火箭发动机热试车过程中可能出现的无失效数据情况,确定了失效概率的先验分布,并给出了E-Bayes估计和多层Bayes(Bayesian)估计。然后用最小二乘法和加权最小二乘法给出寿命分布的参数估计,进而得到了可靠度的点估计和区间估计。最后结合实际问题进行了计算,说明了方法的可行性,且便于工程应用。

关键词: 液体火箭发动机, E-Bayes估计, 多层Bayes估计, 可靠性, 无失效数据, 最小二乘法, 区间估计

Abstract: A reliability analysis of a liquid rocket engine for the case of zero-failure data is given in this paper to provide reference for the reliability evaluation of expensive and high-quality products such as those used in aviation and space travel. By means of Expected-Bayesian (E-Bayes) estimation, a prior distribution of failure probability is determined for the case where there is zero-failure data available in the trial run of the liquid rocket engine, and the E-Bayes estimation and hierarchical Bayesian (Bayes) estimation of failure probabilities are presented based on the related literature. After that the least square method and weighted least square method are used to obtain the parameters of life distribution and its reliability as well as the point and interval estimates. Finally, the calculated results of a practical problem show that the proposed method is feasible and convenient in engineering application.

Key words: liquid rocket engine, E-Bayes estimation, hierarchical Bayes estimation, reliability, zero-failure data, least square method, interval estimation

中图分类号:

韩明. 无失效数据下液体火箭发动机的E-Bayes可靠性分析[J]. 航空学报, 2011, 32(12): 2213-2219.

HAN Ming. E-Bayes Reliability Analysis for Liquid Rocket Engine with Zero-failure Data[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2011, 32(12): 2213-2219.

参考文献

[1] Martz H F, Waller R A. A Bayes zero-failure (BAZE) reliability demonstration testing procedure[J]. Journal of Quality Technology, 1979, 11(3): 128-137.

[2] 韩明. 无失效数据可靠性进展[J]. 数学进展, 2002, 31(1): 7-19. Han Ming. The advances of reliability for zero-failure data[J]. Chinese Advances in Mathematics, 2002, 31(1): 7-19. (in Chinese)

[3] 韩明. 基于无失效数据的可靠性参数估计[M]. 北京: 中国统计出版社, 2005. Han Ming. Estimation of reliability parameters based on zero-failure data[M]. Beijing: China Statistics Press, 2005. (in Chinese)

[4] Lindley D V, Smith A F. Bayes estimaters for the linear model[J]. Journal of the Royal Statistical Society: Series B, 1972, 34(1): 1-41.

[5] 韩明. 多层先验分布的构造及其应用[J]. 运筹与管理, 1997, 6(3): 31-40. Han Ming. The structure of hierarchical prior distribution and its applications[J]. Chinese Operations Research and Management Science, 1997, 6(3): 31-40. (in Chinese)

[6] 姜祥周,师义民,沈政. 无失效数据下液体火箭发动机可靠性多层Bayes估计[J]. 航天控制, 2008, 26(3): 88-91. Jiang Xiangzhou, Shi Yimin, Shen Zheng. The hierarchical Bayes reliability estimation for liquid rocket engine with zero-failure data[J]. Aerospace Control, 2008, 26(3): 88-91. (in Chinese)

[7] 韩明. 失效概率的E-Bayes估计及其性质[J]. 数学物理学报,2007, 27A(3): 488-495. Han Ming. E-Bayesian estimation of failure probability and its properties[J]. Acta Mathematica Scientia, 2007, 27A(3): 488-495. (in Chinese)

[8] 茆诗松,罗朝斌. 无失效数据的可靠性分析[J]. 数理统计与应用概率,1989,4(4): 489-506. Mao Shisong, Luo Chaobin. Reliability analysis of zero-failure data [J]. Chinese Mathematical Statistics and Applied Probability, 1989, 4(4): 489-506. (in Chinese)

[9] Berger J O. Statistical decision theory and Bayesian analysis[M]. 2nd ed. New York: Springer-Verlag, 1985.

[10] 韩明. Weibull分布可靠性参数的置信限[J]. 机械强度,2009,31(1): 59-62. Han Ming. Confidence limits of reliability parameters for weibull distribution[J]. Journal of Mechanical Strength, 2009, 31(1): 59-62. (in Chinese)

[11] 宁江凡, 鄢小清, 张士峰. 液体火箭发动机无失效条件下的可靠性分析方法[J]. 国防科技大学学报, 2006, 28(5): 22-25. Ning Jiangfan, Yan Xiaoqing, Zhang Shifeng. Study on reliability analysis method for liquid rocket engine in the case zero-failure data[J]. Journal of National University of Defense Technology, 2006, 28(5): 22-25. (in Chinese)

[12] Han Ming. Two-sided M-Bayesian credible limits method of reliability parameters and its applications[J]. Communications in Statistics-Theory and Methods, 2008, 37(10): 1659-1670.

[13] 韩明. 可靠性参数的M-Bayes可信限[J]. 系统工程与电子技术, 2008, 30(8): 1592-1594. Han Ming. M-Bayesian credible limit of reliability parameters[J]. Systems Engineering and Electronics, 2008, 30(8): 1592-1594. (in Chinese)

[14] Han Ming. E-Bayesian estimation and hierarchical Bayesian estimation of failure rate [J]. Applied Mathematical Modelling, 2009, 33(4): 1915-1922.

[15] Han Ming. E-Bayesian estimation of the reliability derived from Binomial distribution [J]. Applied Mathematical Modelling, 2011, 35(5): 2419-2424.

[16] Han Ming. E-Bayesian estimation of failure probability and its application[J]. Mathematical and Computer Modelling, 2007, 45(9-10): 1272-1279.

E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

无失效数据下液体火箭发动机的E-Bayes可靠性分析

E-Bayes Reliability Analysis for Liquid Rocket Engine with Zero-failure Data

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