监控多变量自相关过程的可变抽样区间残差T^(2)控制图

Residual Based T^(2) Control Chart for Monitoring Multivariate Autocorrelation Process with Variable Sampling Intervals

残差T^(2)控制图消除统计量的自相关性,满足统计过程控制理论关于统计量彼此独立的基本假设,可以用于监控多变量自相关过程.为了提高多变量自相关过程监控效率,研究可变抽样区间的残差T^(2)控制图.首先,对多变量自相关过程的残差T^(2)控制图进行可变抽样区间(VSI)设计;然后,用蒙特卡洛模拟方法计算其平均报警时间;最后,以平均报警时间为评价准则,对所设计的VSI残差T^(2)控制图与固定抽样区间(FSI)的残差T^(2)图的监控性能进行对比分析,发现过程失控时,VSI残差T^(2)控制图的平均报警时间较小,能更快地检测出异常波动.

Residual based T^(2) control chart eliminates the autocorrelation of statistics and satisfies the basic hypothesis of statistical process control theory that statistics are independent of each other,so it can be used to monitor multivariate autocorrelation process.To improve the monitoring efficiency for multivariate autocorrelation process,residual based T^(2) control chart with variable sampling intervals(VSI)is studied.Firstly,residual based T^(2) control chart with variable sampling intervals for monitoring multivariate autocorrelation process is designed;Secondly,the average time to signal of this control chart is calculated using Monte Carlo simulation method;Finally,taking the average time to signal as the evaluation criterion,residual based T^(2) control chart with variable sampling intervals and fixed sampling intervals are compared.The computing results show that the VSI residual based T^(2)control chart is the more efficient in detecting shifts than the fixed sampling interval(FSI)residual based T^(2)control chart when the process is out of control.