多元混合数据回归分析方法

傅惠民; 岳晓蕊

多元混合数据回归分析方法

北京航空航天大学小样本技术研究中心,北京 100191

基金项目: 国家自然科学基金(10472006); 北京市教育委员会共建项目(XK100060418)

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- 被引次数: 0
出版历程
- 收稿日期: 2010-07-26
- 修回日期: 2010-12-06
- 刊出日期: 2011-01-28

Multiple regression analysis method for mixed data

Research Center of Small Sample Technology, Beijing University of Aeronautics and Astronautics,Beijing 100191,China

摘要

摘要: 针对加速寿命试验中经常遇到完全数据、定数截尾数据和定时截尾数据混合的情况,提出一种多元混合数据回归分析方法,建立了多元混合回归模型,给出回归系数和标准差的最佳无偏估计,以及百分位值的点估计和置信限估计.该方法不但适用于正态分布,而且还适用于Weibull分布、极值分布等其他各种位置-尺度分布,从而将传统只适用于完全数据的多元回归分析推广到完全数据和截尾数据混合的情况.与传统方法相比,该方法具有信息量大、精度高的优点.
- 加速寿命试验 /
- 截尾数据 /
- 多元回归分析 /
- 性能测试 /
- 寿命预测 /
- 可靠性分析
Abstract: Aiming at the mixed data composed of complete data, type-Ⅰ censored data and type-Ⅱ censored data which are very common in accelerated life test, a multiple regression analysis method were developed. The multiple regression model was established, and the best unbiased estimations of regression coefficients and the standard deviation were given. Furthermore, the point estimation and confidence limits of percentiles were obtained. The presented method is applicable to not only the normal distribution but also the Weibull distribution, the extreme value distribution and some other location-scale distributions. The traditional multiple regression analysis method which is strictly suitable to the complete data is extended to the mixed data composed of complete data and censored data. Compared with the traditional method, the presented method can reach a high precision and a great number of specimens can be saved.
- accelerated life test /
- censored data /
- multiple regression analysis /
- performance test /
- life prediction /
- reliability analysis

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参考文献(9)

[1]	傅惠民,岳晓蕊.定时截尾数据回归分析方法[J].航空动力学报,2010,25(1):142-147. FU Huimin,YUE Xiaorui.Regression analysis method for type-Ⅰcensored data[J].Journal of Aerospace Power,2010,25(1):142-147.(in Chinese)
[2]	傅惠民,岳晓蕊.混合数据回归分析方法[J].机械强度,2010,32(6):922-927. FU Huimin,YUE Xiaorui.Regression analysis method for mixed data[J].Journal of Mechanical Strength,2010,32 (6):922-927.(in Chinese)
[3]	Nelson W.Accelerated testing:statistical models,test,plans and data analyses[M].New York:John Wiley & Sons, Inc.,2004.
[4]	茆诗松,王玲玲.加速寿命试验[M].北京:科学出版社, 1997.
[5]	李晓阳,姜同敏.加速寿命试验中多应力加速模型综述[J].系统工程与电子技术,2007,29(5):828-831. LI Xiaoyang,JIANG Tongmin.Review of multiple-stress models in accelerated life testing[J].Systems Engineering and Electronics,2007,29(5):828-831.(in Chinese)
[6]	钱萍.航天电连接器综合应力加速寿命试验与统计分析的研究 .杭州:浙江大学,2010. QIAN Ping.Research on multiple stress accelerated life test and statistical analysis of aerospace electrical connector .Hangzhou:Zhejiang University,2010.(in Chinese)
[7]	傅惠民.区间统计量及其分布[J].机械强度,2005,27(6):752-757. FU Huimin.Interval statistic and its distribution[J].Journal of Mechanical Strength,2005,27(6):752-757.(in Chinese)
[8]	Parrish R S.Computing expected values of normal order statistics[J].Communications in Statistics-Simulation and Computation,1992,21(1):57-70.
[9]	Parrish R S.Computing variances and covariances of normal orderstatistics[J].Communications in Statistics-Simulation and Computation,1992,21(1):71-101. 10] 傅惠民,林逢春.大样本顺序统计量均值、方差和协方差计算与验证[J].机械强度,2007,29(1):048-052. FU Huimin, LIN Fengchun.Computation and verification of means, variances and covariances for large sample order statistics.[J].Journal of Mechanical Strength,2007,29(1):048-052.(in Chinese) 11] Balakrishnan N,Chan P S.Order statistics from extreme value distribution:Ⅰ-Table of means,variances and covariances[J].Communications in Statistics-Simulation and Computation,1992,21(4):1199-1217. 12] 傅惠民.连续母体百分位值和百分率的区间估计和假设检验[J].航空学报,1993,14(11):569-577. FU Huimin.Interval estimation and hypothesis test for percen tiles and percentages of continuous distributions[J].Acta Aeronautica et Astronautic Sinica,1993,14(11):569-577.(in Chinese)