残差控制图应用中的自相关过程模型研究  

Research on Selection of Autocorrelation Process Model in Statistical Process Control

作　　者：肖艳 李亚平[1] 俞少君[1] XIAO Yan;LI Yaping;YU Shaojun(School of Economics and Management,Nanjing Forestry University,Nanjing 210037,China)

机构地区：[1]南京林业大学经济管理学院,江苏南京210037

出　　处：《工业工程与管理》2020年第4期69-76,共8页Industrial Engineering and Management

基　　金：国家自然科学基金项目(71701098);江苏省自然科学基金项目(BK20160940);教育部人文社会科学青年基金项目(17YJC630070)。

摘　　要：随着自动化技术的发展,数据自相关现象在现代制造业中普遍存在。基于自相关模型的残差控制图是解决自相关数据统计监控问题的一类较好方法。现有研究均假设数据呈一阶自相关,仅研究一阶自回归模型与残差控制图结合的过程监控问题。但是,实际生产中观测数据可能服从多阶自相关。基于此,针对数据多阶自相关的过程监控问题,运用蒙特卡洛仿真法,研究不同自回归阶数的自回归模型对残差控制图性能的影响。研究表明:在残差控制图应用中,过程受控时,一阶自回归模型的表现与同阶自回归模型的性能表现相当,即二者发生第一类错误的概率相差不大;而在质量偏移诊断中,一阶自回归AR(1)模型的性能表现整体优于同阶的自回归模型,大大降低了漏警的成本。With the rapid development of automation technology in the past decades,the autocorrelation process is ubiquitous in modern manufacturing.The residual control chart based on the autocorrelation models is a reliable solution to the data statics.At present,most studies were assuming the sample data following first-order autocorrelation,thus only considering the residual chart based on the first-order autoregressive model.However,the sample data in actual production might also be subject to multi-order autocorrelation.Therefore,based on the understanding of multi-order autocorrelation and using Monte Carlo simulation method,different autoregressive models with different autoregressive orders were studied to evaluate the effects on the performance of control chart.The results indicate that the first-order autoregressive model has similar performance with the multiorder autoregressive model,while the former is much better than the later for detecting shift regardless of autocorrelation orders,which will significantly reduce the cost of false dismissal.

关 键 词：自相关 自回归模型 残差控制图 

分 类 号：O213.1[理学—概率论与数理统计]