摘要
传统的稳健设计一般假定试验数据为正态分布且无污染,然而在实践中,由于缺乏足够的试验数据以及数据中存在污染等因素,导致用传统的点估计方法无法准确获得某设计点下真实过程的输出值。因此,提出了基于bootstrap重抽样技术估计数据污染下最优参数置信区间的稳健设计方法。首先,采用Hodges-Lehman估计量和Shamos估计量分别估计位置参数和尺度参数;其次,构建过程均值和方差双响应曲面模型,实现稳健设计;然后,利用分位数bootstrapping (Percentile Bootstrapping,PB)、偏差校正分位数bootstrapping (Bias-Corrected Percentile Bootstrapping,BCPB)和偏差校正及加速分位数bootstrapping (Bias-Corrected and accelerated Percentile Bootstrapping,BCaPB)方法分别估计最优参数的bootstrap置信区间;最后,引入欧式距离和广义方差分别度量不同置信区间抵抗污染值的稳健性。通过仿真表明,在解决数据污染的稳健设计中BCPB和BCaPB方法估计的精确度明显高于PB方法,同时BCaPB方法在抵抗污染值干扰方面优于BCPB方法。
Due to the fact that the traditional point estimates of optimal settings may not be properly estimated resulting from lack of sufficient experiment data under data contamination,a robust design method is proposed based on bootstrap technique for obtaining confidence interval of the optimum operating conditions.Firstly,Hodges-Lehman and Shamos methods were used to estimate the location parameters and the scale parameters respectively.Secondly,dual response surface model was built for process mean and variance,and the optimal settings were attained by robust optimization.Next,the bootstrap confidence intervals of the optimal settings were estimated according to percentile bootstrapping(PB),bias-corrected percentile bootstrapping(BCPB) and bias-corrected and accelerated percentile bootstrapping(BCaPB) methods respectively.Finally,by introducing Euclidean distance and generalized variance,the robustness of different confidence intervals for outlier-resistant were measured.Through Monte Carlo simulation,the results show that BCaPB method is superior to BCPB method when the data are contaminated,yet also more robust and accurate than the counterpart of PB method in outlier-resistant.
作者
韩云霞
马义中
欧阳林寒
刘丽君
HAN Yun-xia;MA Yi-zhong;OU YANG Lin-han;LIU Li-jun(School of Economics and Management,Nanjing University of Science and Technology,Nanjing 210094,China;College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)
出处
《工业工程与管理》
CSSCI
北大核心
2019年第1期64-71,86,共9页
Industrial Engineering and Management
基金
国家自然科学基金资助项目(71471088
71871119
71702072
71771121
71371099)
中央高校基本科研业务专项资金资助项目(3091511102)
江苏省自然科学基金资助项目(BK20170810)
关键词
稳健设计
双响应曲面
数据污染
置信区间
robust design
dual response surface
data contamination
confidence interval
