Abstract: To improve the efficiency of the Shewhart control chart for monitoring the ratio of bivariate normal variables(denoted as Shewhart-RZ chart),a new control chart was proposed by combining the Shewhart-RZ chart with a variable sample size strategy(denoted as VSS Shewhart-RZ* chart).Based on the normalized transformation method,a new statistic Z* was designed to eliminate the adverse effects of varying sample size on the design and use of the control chart.The Markov chain method was used to calculate the average run length and average sample size of the VSS Shewhart-RZ* chart,and the corresponding parameter optimization algorithm was given.The statistical performance of VSS Shewhart-RZ* chart was studied through simulation analysis and compared with the Shewhart-RZ chart.The results showed that the performance of VSS Shewhart-RZ* chart was significantly better than Shewhart-RZ chart.

Key words: variable sample size, ratio distribution, average run length, normalized transformation

摘要： 为了提高Shewhart型比例控制图的监控效率,将其与变样本容量策略结合,提出一种新的比例控制图(VSS Shewhart-RZ*控制图)来监控二元正态变量之比。基于正态变换方法设计了新的比例统计量Z*,以消除样本容量变化对比例控制图设计及使用的不利影响。采用马尔科夫链方法计算了该控制图的平均运行长度和平均样本容量,给出该控制图的参数优化算法。通过仿真分析研究了该控制图的统计性能,并与Shewhart比例控制图进行比较,结果表明VSS Shewhart-RZ*控制图的性能明显优于传统固定样本容量Shewhart比例控制图。

关键词: 变样本容量, 比例分布, 平均运行链长, 正态变换