This article studies the economic and economic-statistical designs of the auxiliary information (AI) based side sensitive group runs (SSGR-AI) chart. The regression estimator that consists of information not only from the primary variable but also from the auxiliary variable is integrated into the control charting statistic. Optimal designs of the SSGR-AI chart, for the minimization of the expected cost function with and without statistical constraints, are developed based on (i) average run length (ARL) and (ii) expected average run length (EARL). Furthermore, sensitivity analyses are conducted, that is, the impact of various input parameters on the optimal parameters and costs for different values of correlation coefficients (ρ) between the primary and auxiliary variables are investigated. In addition, the effects of incorrect specification of the size of the shift on the optimal cost of the SSGR-AI chart are studied. The comparative study reveals that the SSGR-AI chart is superior to the exponentially weighted moving average-AI (EWMA-AI) and synthetic-AI (Syn-AI) charts, for both designs, by giving the smallest costs.

中文翻译：

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带辅助信息的侧敏感组运行图的经济和经济统计设计

本文研究了基于辅助信息 (AI) 的侧敏感组运行 (SSGR-AI) 图的经济和经济统计设计。回归估计量不仅包含来自主要变量的信息，还包含来自辅助变量的信息，它被整合到控制图统计中。SSGR-AI 图表的优化设计，用于在有和没有统计约束的情况下最小化预期成本函数，是基于 (i) 平均运行长度 ( ARL ) 和 (ii) 预期平均运行长度 ( EARL ) 开发的。此外，还进行了敏感性分析，即各种输入参数对不同相关系数值（ρ) 之间的主要和辅助变量进行了调查。此外，还研究了不正确指定偏移大小对 SSGR-AI 图表最优成本的影响。比较研究表明，SSGR-AI 图优于指数加权移动平均 AI (EWMA-AI) 和合成 AI (Syn-AI) 图，对于这两种设计，成本最低。