This paper proposes two optimal control charts by using the generalized multiple dependent state (GMDS) plan to monitor the process mean. These charts make advantageous use of the ranked set sampling schemes and integrate them with the GMDS plan to improve the shift detection ability of the Shewhart‐type control charts. The proposed control charts have two pairs of control limits, inner and outer, which enables them to consider the current and previous sample information while making a decision about the process state. The run‐length profiles of the proposed charts are obtained through extensive Monte Carlo simulations. The individual and overall mean shift detection abilities of the proposed charts are compared with various competing control charts by using out‐of‐control average run length ( $AR{L}_1$) and the average extra quadratic loss ( $AEQL$) as performance metrics. The comparison establishes the complete dominance of the proposed charting strategy. In the end, the practical implementation of the proposed charts is demonstrated by using a real data set related to the cement manufacturing industry.

中文翻译：

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排序集抽样下的广义多重依赖状态最优控制图，用于监控过程均值

本文提出了两个最优控制图，通过使用广义多依赖状态（GMDS）计划来监视过程平均值。这些图表利用了排序集采样方案的优势，并将它们与GMDS计划集成在一起，以提高Shewhart型控制图的移位检测能力。建议的控制图具有两对内部和外部控制极限，这使他们能够在确定过程状态时考虑当前和先前的样本信息。拟议图表的行程分布图是通过广泛的蒙特卡洛模拟获得的。通过使用失控的平均游程长度，将建议图表的个体和整体平均移位检测能力与各种竞争控制图表进行比较（$\mathrm{一种}\mathrm{[R}{\mathrm{大号}}_{\mathrm{1个}}$）和平均额外二次损失（ $\mathrm{一种}Ë问\mathrm{大号}$）作为效果指标。比较确定了拟议制图策略的完全优势。最后，通过使用与水泥制造行业相关的真实数据集来演示所建议图表的实际实施。