Abstract: 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.

Key words: statistical process control, auto-correlated observations, hidden Markov model, control charts

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。

关键词: 统计过程控制, 自相关观测, 隐马尔科夫模型, 控制图