用残差CUSUM控制图检测自相关过程中的故障

由于累积和控制图(cumulative sum,简称CUSUM)算法应用的基本假设是从过程得到的观测值彼此独立,而工业过程通常是自相关过程,数据自相关性会影响CUSUM控制图的性能.针对这一问题,利用数学推理的方法分析了数据自相关性对CUSUM控制图性能的不利影响,正自相关会使CUSUM控制图的平均运行长度变短,可能引起假警报；负自相关会使CUSUM控制图的平均运行长度变长,可能造成故障漏报.在此基础上,提出用残差CUSUM控制图来检测自相关过程中的故障,运用时间序列模型的残差检测自相关过程中的故障,消除数据自相关性对控制图性能的不利影响.结果表明,该方法具有较好的鲁棒性和较高的准确率.

Application of Residual-Based Cumulative Sum Control Charts for Detecting Faults in Autocorrelated Processes

Cumulative sum(CUSUM) control charts are constructed under the assumption that the observations taken from the process of interest are independent over time.However,the observations in many industrial cases are actually correlated.Serial correlation of observations will result in poor performance of control charts.The effect of serial correlation on the performance of control charts is analyzed through mathematical analysis method.Positive serial correlation decreases the average run length(ARL) of CUSUM control chart,resulting in too many false alarms.Negative serial correlation increases the ARL of CUSUM control chart,which possibly results in missing faults.In addition,a fault detection method for autocorrelated processes is presented by using residual-based CUSUM control chart.The residuals between the process error and its predication are generated using autoregressive time-series models.Then,CUSUM control charts are used to monitor the residuals which are statistically independent.The residual-based CUSUM control chart can improve the accuracy of fault detection through eliminating the effects of serial correlation on the performance of control charts.Some case studies show that the residual-based CUSUM control chart is an effective tool in detecting faults of autocorrelated processes,and the fault detection method has good robustness and high accuracy rate.