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

  • Yaping Li (李亚平)Email author
  • Mengdie Huang (黄梦蝶)
  • Ershun Pan (潘尔顺)


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 

CLC number

F 273 

Document code


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Copyright information

© Shanghai Jiaotong University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Yaping Li (李亚平)
    • 1
    • 2
    Email author
  • Mengdie Huang (黄梦蝶)
    • 2
  • Ershun Pan (潘尔顺)
    • 2
  1. 1.College of Economics and ManagementNanjing Forestry UniversityNanjingChina
  2. 2.Department of Industrial Engineering, School of Mechanical EngineeringShanghai Jiao Tong UniversityShanghaiChina

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