Memory-type auxiliary-information-based (AIB) control charts are very effective in detecting small-to-moderate shifts in the process mean. In this study, we first develop a unique uniformly minimum variance unbiased estimator of the process mean that requires information on the study variable as well as on several correlated auxiliary variables. Then, based on this estimator, adaptive and nonadaptive CUSUM and EWMA charts are developed with either fixed or variable sampling interval for monitoring the process mean, namely, the multiple AIB (MAIB) charts. The proposed charts encompass existing charts with or without the auxiliary information. The run length characteristics of the proposed charts are computed with the Monte Carlo simulations when sampling from a multivariate normal distribution. Based on the run length comparisons, it is found that the MAIB charts are uniformly and substantially more sensitive than the AIB charts when monitoring the process mean. Real datasets are also considered to explain the implementation of the MAIB charts.

中文翻译：

---

具有多个过程均值辅助信息的记忆型控制图

记忆型基于辅助信息 (AIB) 的控制图在检测过程均值的小到中等变化方面非常有效。在这项研究中，我们首先开发了一个独特的过程均值的统一最小方差无偏估计量，它需要有关研究变量以及几个相关辅助变量的信息。然后，基于该估计量，开发了具有固定或可变采样间隔的自适应和非自适应 CUSUM 和 EWMA 图，用于监控过程均值，即多重 AIB (MAIB) 图。提议的海图包括有或没有辅助信息的现有海图。当从多元正态分布中采样时，建议图表的运行长度特征是用蒙特卡罗模拟计算的。根据游程长度比较，发现在监测过程均值时，MAIB 图比 AIB 图一致且明显更敏感。还考虑使用真实数据集来解释 MAIB 图表的实施。