多元线性过程回归分析  

MULTIVARIATE REGRESSION ANALYSIS METHOD FOR LINEAR PROCESS

作　　者：傅惠民[1] 吴琼[1] 

机构地区：[1]北京航空航天大学小样本技术研究中心,北京100191

出　　处：《机械强度》2011年第3期343-347,共5页Journal of Mechanical Strength

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

摘　　要：提出多元线性过程的定义及其回归模型,建立多元线性过程回归分析方法,给出其回归方程和高置信水平、高可靠度的置信上、下限曲线。多元线性过程是具有线性函数均值和二次函数方差的独立增量随机过程,也是性能曲线测试和可靠性评估中常见的一类随机过程。传统方法在测定不同条件下产品的性能曲线时,要求在每一种条件下都测得一组样本函数,并对每个测试时刻的数据单独进行统计分析,然后再通过曲线拟合得到该条件下的性能曲线。这需要进行大量的重复试验,导致总的试验时间长、费用高,工程上往往难以承受,而且这种两步估计法还会造成信息丢失和误差累积,影响估计精度。文中方法能对随机过程数据进行回归分析,将多元线性过程作为一个整体进行统计推断,具有信息量大、精度高的特点,能有效解决多种条件下产品性能曲线的小样本测试问题。The definition and regression model for multivariate linear process are put forward,based on which the regression analysis method,regression equation and confidence limit curves with high confidence level and high reliability are established.Multivariate linear process is a kind of independent increment processes with linear mean function and quadratic variance function,which is very common in performance test and reliability assessment.By traditional analysis method for different test conditions,sufficient test curves for each condition are required to obtain the point estimates of the linear process,and then the reliable curves can be obtained by curve fitting technique.Thus it is a two-step method and needs a large amount of specimens,which is always time-consuming and costly.Additionally,the two-step analysis might lose some information and lead to accumulation of computational errors,which result in insufficient estimates.By the presented method the multivariate linear processes can be analyzed as an integration,therefore it can solve the problem of performance test with small sample and higher precision.

关 键 词：随机过程 独立增量过程 多元线性过程 多元回归分析 性能退化 可靠性 置信限曲线 

分 类 号：TB114[理学—概率论与数理统计] O211[理学—数学]