The control chart and the maintenance management need to control process quality and reduce out-of-control cost. They are two key tools in the production process; however, they have usually been analyzed separately in the literature. Moreover, the existing studies integrating these two concepts suffer from three significant drawbacks as follows: (1) using control charts with fixed parameters to monitor the process, so that the small and middle shifts are detected slowly; (2) monitoring the mean and standard deviation separately, whereas, in real condition, the mean and standard deviation should be monitored simultaneously; (3) quality loss function is not usually used to design economic model, which leads to a large social quality loss in the monitoring process of control chart. To eliminate these weaknesses, the economic design of the exponential weighted moving average (EWMA) control chart with variable sampling intervals (VSI) for monitoring the mean and standard deviation under preventive maintenance and Taguchi’s loss functions is proposed. The optimal values of the parameters are determined to minimize the loss-per-item in an average cycle process. In addition, a genetic algorithm is used in a numerical example to search for the optimal values of the parameters. According to the sensitivity analysis, the effect of the model parameters on the solution of the economic model is obtained. Finally, the comparison study shows that the VSI EWMA control charts designed by the joint economic model are expected to reduce loss.

中文翻译：

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具有可变采样间隔的 EWMA 控制图的经济设计，用于监测预防性维护和田口损失函数下的均值和标准差

控制图和维护管理需要控制过程质量并降低失控成本。它们是生产过程中的两个关键工具；然而，它们通常在文献中被单独分析。此外，现有的整合这两个概念的研究存在以下三个显着缺陷：（1）使用具有固定参数的控制图来监控过程，从而缓慢地检测到中小偏移；(2)分别监测均值和标准差，而在实际情况下，应同时监测均值和标准差；(3)质量损失函数通常不用于设计经济模型，导致在控制图监测过程中产生较大的社会质量损失。为了消除这些弱点，提出了具有可变采样间隔（VSI）的指数加权移动平均（EWMA）控制图的经济设计，用于监测预防性维护和田口损失函数下的均值和标准差。确定参数的最佳值以最小化平均循环过程中的每项损失。此外，在数值例子中使用遗传算法来搜索参数的最佳值。根据敏感性分析，得到模型参数对经济模型求解的影响。最后，对比研究表明，联合经济模型设计的VSI EWMA控制图有望减少损失。