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论文:2013,Vol:31,Issue(1):29-33 |
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引用本文： |
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师义民, 顾昕, 孙天宇, 孙玉东. 相依屏蔽数据下双参数指数部件的可靠性分析[J]. 西北工业大学 |
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Shi Yimin, Gu Xin, Sun Tianyu, Sun Yudong. Two-Parameter Exponential Component's Reliability Analysis Using Dependent Masked Data[J]. Northwestern polytechnical university |
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| 相依屏蔽数据下双参数指数部件的可靠性分析 |
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| 师义民, 顾昕, 孙天宇, 孙玉东 |
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| 西北工业大学 应用数学系, 陕西 西安 710072 |
| 摘要: |
| 当串联系统含有屏蔽数据且屏蔽概率与失效部件相关时,讨论系统中双参数指数部件的可靠性估计问题。在定数截尾场合下,通过给定的屏蔽概率比,推导出双参数指数部件参数和可靠性指标的极大似然估计。鉴于极大似然估计法在完全屏蔽情形下的局限性,利用贝叶斯方法,在平方损失函数下推导出部件参数和可靠性指标的贝叶斯估计。最后利用随机模拟方法对估计结果进行验证,分析不同屏蔽概率比对极大似然估计精度的影响,并在无信息先验和共轭先验分布情形下,比较了贝叶斯估计的效果。 |
| 关键词:
相依屏蔽数据
屏蔽概率比
可靠性分析
贝叶斯估计
双参数指数部件
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| Two-Parameter Exponential Component's Reliability Analysis Using Dependent Masked Data |
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| Shi Yimin, Gu Xin, Sun Tianyu, Sun Yudong |
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| Department of Applied Mathematics,Northwestern Polytechnical University,Xi'an 710072,China |
| Abstract: |
| To our knowledge, there is no paper in the open literature dealing with the subject mentioned in the ti-tle.Therefore, we analyze the reliability of two-parameter exponential components in a series system where themasked data and masking probability are dependent on failure components.With the given masking probabilityratio, we derive the maximum likelihood estimation (MLE) of the parameters of two-parameter exponential compo-nents and that of the reliability index.Since the MLE has its limitations when the data are completely masked, weemploy the squared error loss function to perform the Bayes estimation of the unknown parameters of two-parameterexponential components and their reliability indexes.Finally we carry out the numerical calculation of the measquare error of various estimated values to analyze the influence of different masking probability ratios on the accura-cy of the MLE and to compare the effects of the Bayes estimation under no-information prior distribution and con-junctional prior distribution respectively.The calculation results, given in Tables 2 and 3 and Fig.1, and their a-nalysis show preliminarily that the mean square error of Bayes estimation under conjunctional prior distribution isless than that under non-informative prior distribution. |
| Key words:
maximum likelihood
parameter estimation
probability
reliability analysis;Bayes estimation
de-pendent masked data
two-parameter exponential component
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| 收稿日期: 2012-05-10
修回日期:
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| DOI: |
| 基金项目: 国家自然科学基金(71171164、70471057);西北工业大学创业种子基金(Z2013153)资助 |
| 通讯作者:
Email： |
| 作者简介: 师义民(1952-)，西北工业大学教授、博士生导师，主要从事应用概率统计、系统可靠性理论及应用研究。
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参考文献: |
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[2] Sarhan A M.Reliability Estimation of Components from Masked System Life Data.Reliability Engineering ＆ System Safety,2001,74(1): 107-113
[3] Sarhan A M,El-Gohary A I.Estimations of Parameters in Pareto Reliability Model in the Presence of Masked Data.ReliabilityEngineering and System Safety,2003,82(1): 75-83
[4] 刘 英,师义民,王婷婷.含有屏蔽数据的串联系统中 Burr Ⅻ部件可靠性指标的 Bayes 估计.系统工程理论与实践,2010,30(4):689-694Liu Ying,Shi Yimin,Wang Tingting.Bayes Estimations of the Reliability Performances for the Burr Ⅻ Components in a SeriesSystem Using Masked System Life Data.Systems Engineering-Theory ＆ Practice,2010,30(4): 689-694 (in Chinese)
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[6] 张 帆,师义民.基于屏蔽数据的航空电源系统可靠性分析.航天控制,2009,27(4): 96-100Zhang Fan,Shi Yimin.Parameter Estimation of the Aerospace Power Supply System Using Masked Lifetime Data.AerospaceControl,2009,27(4): 96-100 (in Chinese)
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