Abstract: Considering the outliers in the process samples, the median(X)is used instead of the mean(X)and a side-sensitive conforming run length X(SCRL & X)chart is proposed to monitor the process mean. A Markov chain method is used to study the properties of the chart. The transition probability matrix of SCRL & X chart is first derived and the corresponding average run length(ARL)is obtained according to the properties of the Markov chain method. In order to obtain the optimal parameters and properties of the SCRL & X chart, the out-of-control ARL is minimized under the constraint of the in-control ARL. The simulation results showed that the SCRL & X chart performs better than the conforming run length(CRL)X chart, especially for smaller mean shifts.

Key words: X chart, sided sensitive conforming run length Xchart, average run length

摘要： 针对过程数据存在异常值的问题,为了监控过程均值的偏移,采用中位数统计量(X)代替传统均值(X)统计量,提出了一种单边合格品链长X(Sided Sensitive Conforming Run Length X, SCRL & X)控制图。采用马尔科夫链方法研究了SCRL & X控制图的性能,首先推导出其一步状态转移矩阵,进一步根据马尔科夫链的性质得到其平均链长(Average Run Length, ARL)。为了获得控制图的最优设计参数和性能指标值,保证其处于过程受控状态下的性能,并使其处于过程失控状态下的平均链长最小。研究结果表明,提出的SCRL & X控制图的统计性能优于传统的双边合格品链长X(Conforming Run Length, CRL & X)控制图,尤其针对过程均值产生较小偏移的情形,其优势较为明显。

关键词: X控制图, 单边合格品链长X控制图, 平均链长