Journal of Shanghai Jiao Tong University (Science) ›› 2018, Vol. 23 ›› Issue (Sup. 1): 103-108.doi: 10.1007/s12204-018-2029-3

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Residual Chart with Hidden Markov Model to Monitoring the Auto-Correlated Processes

LI Yaping (李亚平), HUANG Mengdie (黄梦蝶), PAN Ershun (潘尔顺)   

  1. (1. College of Economics and Management, Nanjing Forestry University, Nanjing 210037, China; 2. Department of Industrial Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China)
  • 发布日期:2018-12-26
  • 通讯作者: LI Yaping (李亚平) E-mail: yapingli@njfu.edu.cn

Residual Chart with Hidden Markov Model to Monitoring the Auto-Correlated Processes

LI Yaping (李亚平), HUANG Mengdie (黄梦蝶), PAN Ershun (潘尔顺)   

  1. (1. College of Economics and Management, Nanjing Forestry University, Nanjing 210037, China; 2. Department of Industrial Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China)
  • Published:2018-12-26
  • Contact: LI Yaping (李亚平) E-mail: yapingli@njfu.edu.cn

摘要: Autocorrelations exist in real production extensively, and special statistical tools are needed for process monitoring. Residual charts based on autoregressive integrated moving average (ARIMA) models are typically used. However, ARIMA models need a quite amount of experience, which sometimes causes inconveniences in the implementation. With a good performance under less experience or even none, hidden Markov models (HMMs) were proposed. Since ARIMA models have many different performances in positive and negative autocorrelations, it is interesting and essential to study how HMMs affect the performances of residual charts in opposite autocorrelations, which has not been studied yet. Therefore, we extend HMMs to negatively auto-correlated observations. The cross-validation method is used to select the relatively optimal state number. The experiment results show that HMMs are more stable than Auto-Regressive of order one (AR(1) models) in both cases of positive and negative autocorrelations. For detecting abnormalities, the performance of HMMs approach is much better than AR(1) models under positive autocorrelations while under negative autocorrelations both methods have similar performances.

关键词: auto-correlations , hidden Markov models, statistical process control

Abstract: Autocorrelations exist in real production extensively, and special statistical tools are needed for process monitoring. Residual charts based on autoregressive integrated moving average (ARIMA) models are typically used. However, ARIMA models need a quite amount of experience, which sometimes causes inconveniences in the implementation. With a good performance under less experience or even none, hidden Markov models (HMMs) were proposed. Since ARIMA models have many different performances in positive and negative autocorrelations, it is interesting and essential to study how HMMs affect the performances of residual charts in opposite autocorrelations, which has not been studied yet. Therefore, we extend HMMs to negatively auto-correlated observations. The cross-validation method is used to select the relatively optimal state number. The experiment results show that HMMs are more stable than Auto-Regressive of order one (AR(1) models) in both cases of positive and negative autocorrelations. For detecting abnormalities, the performance of HMMs approach is much better than AR(1) models under positive autocorrelations while under negative autocorrelations both methods have similar performances.

Key words: auto-correlations , hidden Markov models, statistical process control

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