基于自相关观测和隐马尔科夫模型的统计过程监控
|
摘要
自相关现象在实际统计过程中广泛存在,传统控制图无法进行有效的监控。针对该问题,提出一种考虑自相关观测的隐马尔科夫模型。通过建立观测序列概率分布在时域上的一阶自相关关系,优化建模,并将其应用于过程监控,建立基于此模型的残差控制图。实例与仿真分析显示,与基于自回归移动平均模型相比,该方法具有预测准确、灵敏度高、可操作性强的特点,且对自相关过程的监控效果良好。
The observations are usually auto-correlated in actual processes.To solve the problem that the traditional control charts could not monitor effectively caused by auto-correlation in actual processes,by considering the auto-correlated data,a modification of Hidden Markov Model(HMM)was proposed.Through building the first order auto-correlation relation of observation sequence probability on time domain,the residual chart was built.Results of case study and simulation showed that the proposed method made significant improvements in monitoring auto-correlation process.Specifically it performed higher sensitivity and was easier to be implemented by comparing with residual charts based on Auto-Regressive and Moving Average(ARMA)models.
The observations are usually auto-correlated in actual processes.To solve the problem that the traditional control charts could not monitor effectively caused by auto-correlation in actual processes,by considering the auto-correlated data,a modification of Hidden Markov Model(HMM)was proposed.Through building the first order auto-correlation relation of observation sequence probability on time domain,the residual chart was built.Results of case study and simulation showed that the proposed method made significant improvements in monitoring auto-correlation process.Specifically it performed higher sensitivity and was easier to be implemented by comparing with residual charts based on Auto-Regressive and Moving Average(ARMA)models.
引文
[1] LAYTH C,ALWAN.Effects of autocorrelation on control chart performance[J].Communication in Statistics—Theory and Methods,1992,21(4):1025-1049.
[2] LU CW,REYNOLDS MR.CUSUM charts for monitoring an auto-correlated process[J].Journal of Quality Technology,2001,33(3):316-334.
[3] ALWAN L C,ROBERTS H V.Time-Series modeling for statistical process control[J].Journal of Business&Economic Statistics,1988,6(1):87-95.
[4] LU C W,REYNOLDS M R.Control charts for monitoring the mean and variance of auto-correlated processes[J].Journal of Quality Technology,1999,31(3):259-274.
[5] DAWOD A B A,RIAZ M,ABBASI S A.On model selection for auto-correlated processes in statistical process control[J].Quality&Reliability Engineering International,2016,33(4).DOI:10.1002/qre.2063.
[6] NEMBHARD HB,MASTRANGELO CM.Integrated process control for startup operations[J].Journal of Quality Technology,1998,30(3):201-211.
[7] CHIU C C,CHEN M K,LEE K M.Shifts recognition in correlated process data using a neural network[J].International Journal of Systems Science,2001,32(2):137-143.
[8] ZHU Huiming,ZHAO Rui.Bayesian quality control model based on autocorrelation stochastic process[J].Computer Integrated Manufacturing Systems,2008,14(3):615-618(in Chinese).[朱慧明,赵锐.基于自相关过程的贝叶斯质量控制模型研究[J].计算机集成制造系统,2008,14(3):615-618.]
[9] HE Zhen,LIU Dongsheng.Using neural networks to control auto-correlated process[J].Industrial Engineering Journal,2006,9(6):85-90(in Chinese).[何桢,刘冬生.神经网络方法在自相关过程控制中的应用[J].工业工程,2006,9(6):85-90.]
[10] PAN X,JARRETT J.Using vector autoregressive residuals to monitor multivariate processes in the presence of serial correlation[J].International Journal of Production Economics,2007,106(1):204-216.
[11] CUI Jingwei,XIE Liyang.Auto-correlated charts based on dynamic Bayesian mode[J].Journal of Beijing University of Aeronautics and Astronautics,2007,33(3):375-378(in Chinese).[崔敬巍,谢里阳.基于贝叶斯动态模型的自相关控制图[J].北京航空航天大学学报,2007,33(3):375-378.]
[12] SHEN H,LI Q,GUO J,et al.HMM parameter adaptation using the truncated first-order VTS and EM algorithm for robust speech recognition[C]//Proceedings of the International Conference on Computational Intelligence and Security.Berlin,Germany:Springer-Verlag,2005:979-984.
[13] WANG M,WANG J.CHMM for tool condition monitoring and remaining useful life prediction[J].The International Journal of Advanced Manufacturing Technology,2012,59(5/6/7/8):463-471.
[14] YU J.Multiway discrete hidden Markov model-based approach for dynamic batch process monitoring and fault classification[J].AICHE Journal,2012,58(9):2714-2725.
[15] YU J.Hidden Markov models combining local and global information for nonlinear and multimodal process monitoring[J].Journal of Process Control,2010,20(3):344-359.
[16] LI Z,FANG H,XIA L.Increasing mapping based hidden Markov model for dynamic process monitoring and diagnosis[J].Expert Systems with Applications,2014,41(2):744-751.
[17] ALSHRAIDEH H,RUNGER G.Process monitoring using hidden Markov models[J].Quality&Reliability Engineering International,2014,30(8):1379-1387.
[18] LIU Yanrong.Study on quality control chart application in auto-correlated process[D].Beijing:Beijing Institute of Technology,2015(in Chinese).[刘艳荣.自相关过程中控制图的应用研究[D].北京:北京理工大学,2015.]
[19] WU Chuanyin. SPC-based evaluation of auto-correlated process[D].Xi'an:Xidian University,2009(in Chinese).[吴传印.自相关过程的SPC评价[D].西安:西安电子科技大学,2009]
[2] LU CW,REYNOLDS MR.CUSUM charts for monitoring an auto-correlated process[J].Journal of Quality Technology,2001,33(3):316-334.
[3] ALWAN L C,ROBERTS H V.Time-Series modeling for statistical process control[J].Journal of Business&Economic Statistics,1988,6(1):87-95.
[4] LU C W,REYNOLDS M R.Control charts for monitoring the mean and variance of auto-correlated processes[J].Journal of Quality Technology,1999,31(3):259-274.
[5] DAWOD A B A,RIAZ M,ABBASI S A.On model selection for auto-correlated processes in statistical process control[J].Quality&Reliability Engineering International,2016,33(4).DOI:10.1002/qre.2063.
[6] NEMBHARD HB,MASTRANGELO CM.Integrated process control for startup operations[J].Journal of Quality Technology,1998,30(3):201-211.
[7] CHIU C C,CHEN M K,LEE K M.Shifts recognition in correlated process data using a neural network[J].International Journal of Systems Science,2001,32(2):137-143.
[8] ZHU Huiming,ZHAO Rui.Bayesian quality control model based on autocorrelation stochastic process[J].Computer Integrated Manufacturing Systems,2008,14(3):615-618(in Chinese).[朱慧明,赵锐.基于自相关过程的贝叶斯质量控制模型研究[J].计算机集成制造系统,2008,14(3):615-618.]
[9] HE Zhen,LIU Dongsheng.Using neural networks to control auto-correlated process[J].Industrial Engineering Journal,2006,9(6):85-90(in Chinese).[何桢,刘冬生.神经网络方法在自相关过程控制中的应用[J].工业工程,2006,9(6):85-90.]
[10] PAN X,JARRETT J.Using vector autoregressive residuals to monitor multivariate processes in the presence of serial correlation[J].International Journal of Production Economics,2007,106(1):204-216.
[11] CUI Jingwei,XIE Liyang.Auto-correlated charts based on dynamic Bayesian mode[J].Journal of Beijing University of Aeronautics and Astronautics,2007,33(3):375-378(in Chinese).[崔敬巍,谢里阳.基于贝叶斯动态模型的自相关控制图[J].北京航空航天大学学报,2007,33(3):375-378.]
[12] SHEN H,LI Q,GUO J,et al.HMM parameter adaptation using the truncated first-order VTS and EM algorithm for robust speech recognition[C]//Proceedings of the International Conference on Computational Intelligence and Security.Berlin,Germany:Springer-Verlag,2005:979-984.
[13] WANG M,WANG J.CHMM for tool condition monitoring and remaining useful life prediction[J].The International Journal of Advanced Manufacturing Technology,2012,59(5/6/7/8):463-471.
[14] YU J.Multiway discrete hidden Markov model-based approach for dynamic batch process monitoring and fault classification[J].AICHE Journal,2012,58(9):2714-2725.
[15] YU J.Hidden Markov models combining local and global information for nonlinear and multimodal process monitoring[J].Journal of Process Control,2010,20(3):344-359.
[16] LI Z,FANG H,XIA L.Increasing mapping based hidden Markov model for dynamic process monitoring and diagnosis[J].Expert Systems with Applications,2014,41(2):744-751.
[17] ALSHRAIDEH H,RUNGER G.Process monitoring using hidden Markov models[J].Quality&Reliability Engineering International,2014,30(8):1379-1387.
[18] LIU Yanrong.Study on quality control chart application in auto-correlated process[D].Beijing:Beijing Institute of Technology,2015(in Chinese).[刘艳荣.自相关过程中控制图的应用研究[D].北京:北京理工大学,2015.]
[19] WU Chuanyin. SPC-based evaluation of auto-correlated process[D].Xi'an:Xidian University,2009(in Chinese).[吴传印.自相关过程的SPC评价[D].西安:西安电子科技大学,2009]