小波在自相关过程监控中的应用

Applying Wavelets to Autocorrelated Process Monitoring

常规控制图的应用以观测值之间相互独立且同分布为基本前提.然而由于系统内在因素的影响,实际工业过程的观测值往往呈现自相关的特征.此时,常规控制图将不能有效实现对自相关过程的监控.现将多尺度小波变换引入到自相关过程分析中,并与Shewhart控制图相结合,实现对过程的监控.最后以ARMA(1,1)过程为例,分别对过程发生阶跃、趋势、周期和交替模式干扰时进行大量的Monte-Carlo模拟实验,并对该监控方法各扰动下的失控平均运行链长(ARL)做初步分析,验证了该方法的有效性.

Traditional control charts are based on the statistical assumption that measurements are independent and identically distributed.In industry applications,however,observations are autocorrelated due to the inherent cause of the process.Thus traditional methods will be inappropriate for autocorrelated process monitoring.In this paper,multi-scale wavelets analysis is introduced to autocorrelated processes.Process monitoring is reached by integrating Shewhart control charts with multi-scale wavelets analysis.Finally,take ARMA(1,1) process as an example.Monte-Carlo simulations about step-type,trend-type,cycles-type,and alternating-type disturbances in autocorrelated processes are performed to explain the average run length(ARL) property of the control charts.The simulation results show that the method is effective.