基于改进两阶段法和自助法的寿命数据分析  

Lifetime data analysis based on improved two-stage approach and bootstrap approach

作　　者：王国东[1,2] 牛占文[1] 曲亮[1] 何桢[1] Wang Guodong Niu Zhanwen Qu Liang He Zhen(College of Management and Economics, Tianjin University, Tianjin 300072, China Cooperative Innovation Center for Avation Economy Development, Zhengzhou 450015, China)

机构地区：[1]天津大学管理与经济学部,天津300072 [2]航空经济发展河南省协同创新中心,河南郑州450015

出　　处：《系统工程学报》2016年第5期710-718,共9页Journal of Systems Engineering

基　　金：国家自然科学基金资助项目(71402118;71071107);国家自然科学基金重点资助项目(70931004;71532008);国家自然科学基金杰出青年科学基金资助项目(71225006);航空科学基金资助项目(2013ZG55024;2014ZG55021);河南省高等学校重点科研资助项目(17A630072)

摘　　要：加速寿命试验的样本量通常很小而且截尾会很严重,这样会使得求得的极大似然统计量产生很大的偏差,进而影响到估计的准确度和精度.本文对两阶段法做了较大改进:证明了当各组数据服从Weibull分布且数据类型为无截尾或typeⅡ截尾时,存在两个关于形状参数和尺度参数的枢轴量,并采用无偏因子法修正极大似然统计量;考虑到异方差性,用加权最小二乘法替代最小二乘法估计加速模型的系数.根据两阶段方法不能采用Fisher信息矩阵计算分位数置信区间的缺点,用自助法获得置信区间.本文通过一个实例阐述改进的两阶段法的分析过程.另外,本文用相对偏差和均方误差根作为评判分析方法的准则,将改进的两阶段法和极大似然法在不同的分位点处的寿命估计作了对比.仿真结果表明,改进的两阶段法在低分位点处的寿命估计更优.When the sample sizes of accelerated life test are small and the data are heavily censored, the bias may be very serious and may affect the accuracy and precision of maximum likelihood estimates. In this paper, the two-stage approach is improved in two aspects： after proving that there are two pivotal quantities with shape parameter and scale parameters of Weibull distributions for complete data or type II censored data, Monte Carlo method is used to obtain the unbiased factors and reduce the bias of estimators; and least square method is replaced with the weighted least square method because of the heteroscedasticity. The two-stage approach cannot obtain confidence intervals of percentiles via Fisher information matrix. Therefore, the confidence intervals are predicted using bootstrap approach. After that, an example is provided to illustrate the procedures of proposed approach.Furthermore, the improved two-stage method is compared with maximum likelihood method based on relative bias and root mean square error criteria. The simulated results show that the improved two-stage method is better in the case of low percentiles.

关 键 词：加速寿命试验 自助法 无偏因子 加权最小二乘法 WEIBULL分布 

分 类 号：TB114.3[理学—概率论与数理统计]