Abstract: Aiming at the inaccuracy estimation of process variance,statistic t was used to substitute statistic ,and a Side-sensitive Conforming Run Length t (SCRL&t) chart was proposed to monitor the process mean.The transition probability matrix of SCRL&t chart was constructed with Markov chain method,and the corresponding Average Run Length (ARL) was given.The optimal parameters of SCRL&t chart were obtained through optimizing the out-of-control ARL while keeping the in-control ARL constant.The simulation results showed that the performance of SCRL&t chart was better than the traditional Conforming RunLength (CRL) t chart,especially for smaller mean shifts.

Key words: statistical process control, t control chart, average run length

摘要： 针对过程方差估计不精确的问题,采用t统计量代替传统X统计量,提出一种单边合格品链长t控制图来监控过程均值偏移。采用马尔科夫链方法构建了该控制图的状态转移矩阵,并推导出其平均运行链长指标。在保证过程处于受控状态的统计性能基础上优化失控状态下的平均运行链长指标,从而获得控制图的最优决策变量和最优性能指标。仿真结果表明,SCRL&t控制图的性能明显优于传统合格品链长t控制图,当过程均值偏移较小时优势更加明显。

关键词: 统计过程控制, t控制图, 平均运行链长