Abstract: As an important tool of statistical process control, control chart has been widely used in the monitoring process of production and service. In the actual production process, for systematic reasons, the scale parameters often change but the position remains unchanged, which will lead to the overall decline in process quality, so it is necessary to monitor the scale parameters. In many production processes, some simple and rapid detection methods are often used to judge the process quality, such as measuring the diameter of cigarettes with a cigarette measuring board and measuring the concentration of alumina with a test paper. These methods are simple and rapid. In this paper, this kind of method is called rapid detection, and it is applied to the control chart.
In the continuous production process of monitoring, if the sampling detection cost is high or the detection time is long, the counting control chart can be considered for monitoring. EWMA chart uses both the data information of the current sample and the data information of the historical sample, which has high monitoring efficiency for small and medium-sized deviations, but the cost of sampling detection is high; NPS diagram can effectively reduce the detection cost, but it is not sensitive to process fluctuation. Dynamic control chart can improve monitoring efficiency and save costs by adjusting sampling strategy, but the degree of improvement and saving is limited. Therefore, through the application of rapid detection method, this paper constructs a VSI-EWMA-NPS scale parameter control chart which can effectively monitor the scale parameters of continuous production process. In order to consider the monitoring efficiency and quality cost of VSI-EWMA-NPS control chart, the economic statistical optimization model of VSI-EWMA-NPS scale parameter control chart is constructed with the Average Product Length (APL) as the statistical evaluation index and the average quality cost per unit product as the economic evaluation index. The optimization model of this paper is illustrated by a case of graphite gasket production. Through the combination and analysis of non-inferior solutions, the relationship among sample size, sampling interval, quality cost per unit time (C) and average product length (APL₁) in out-of-control state is studied. Through sensitivity analysis, the influence of model parameters on economic indicators and statistical indicators is studied. Finally, the optimization method of economic statistics proposed in this paper is compared with the existing models, and the results show that the model in this paper is advanced in economy and statistics.
In this study, it is assumed that the product quality characteristic values obey the normal distribution, but with the development of intelligent manufacturing, the product production mode becomes more flexible and refined. In the process of product production, the process quality characteristic value will follow some non-normal distribution, and even sometimes it is difficult to judge the specific distribution type it obeys. In view of this kind of production process, if the quality monitoring method based on the assumption of normal distribution is still used to monitor the product production in real time, it will lead to large errors and misjudge the production process. Therefore, it is necessary to consider the monitoring of non-normal data by VSI-EWMA-NPS control chart in the subsequent research.

Key words: VSI-EWMA-NPS control chart, scale parameter, average product length, economic and statistical design, multi-objective optimization

摘要： 为了降低质量监控成本并提高对过程尺度参数波动的监控效率,将动态控制图、记忆型控制图、计数型控制图的设计思想结合起来,构造了一种能够实现对连续型变量的尺度参数进行有效监控的VSI-EWMA-NPS控制图,并分别以平均产品长度和单位产品质量成本作为统计性和经济性评价指标,建立了VSI-EWMA-NPS控制图的多目标优化设计模型。通过具体的算例和灵敏度分析说明了该模型的应用方法,并与已有的几种用于监控过程尺度参数的控制图进行比较分析,结果表明本文提出的优化设计方法均优于其他几种控制图方法。

关键词: VSI-EWMA-NPS控制图, 尺度参数, 平均产品长度, 经济统计设计, 多目标优化