基于PSO算法的改进MEWMA控制图经济性—统计性研究

发布时间：2018-05-24 23:40

本文选题：MEWMA + 多元控制图　；参考：《湖南大学》2014年硕士论文

【摘要】：控制图在统计过程控制的建立和维持中有着广泛的应用，常规多元指数加权移动平均（MEWMA）控制图用来监测多元质量过程中存在的小偏移,它要求质量特性间是相互独立的。一种改进的多元指数加权移动平均控制图——GEWMA控制图，可用于监控质量特性之间具有相关性的多元质量过程。本文针对GEWMA控制图，设计出了其经济性以及经济性-统计性模型，并基于粒子群优化算法，运用实例，对模型进行了求解和对比研究，最后，进行了灵敏度的分析。本文的主要研究内容有：（1）介绍了控制图经济性模型以及四类主要求解方法，并运用粒子群的改进研究成果，提出了适用于本文模型的求解方法，结果显示，该方法对本文模型可进行有效的求解。（2）基于LorenzenVance模型，设计了适用于GEWMA控制图的经济性模型，并运用实例对GEWMA控制图和MEWMA控制图的经济性模型进行了求解，最后分析了GEWMA控制图的成本函数中重要参数的灵敏度。结果显示，小偏移时，GEWMA控制图的经济性能比MEWMA控制图更优，反之则相反。此外，偏移量对成本的影响最大，成本函数对调查和研究虚发报警的费用、寻找和消除导致过程失控的因素的花费以及时间间隔的敏感度均较低，可以进行粗略估计。（3）在经济性模型的基础上，构建了GEWMA控制图的经济性-统计性模型，分别对GEWMA控制图和MEWMA控制图的经济性-统计性模型进行了实例研究，并对重要参数的灵敏度进行了分析。最后，还对GEWMA控制图的经济性和经济性-统计性进行对比分析。结果显示，GEWMA控制图在小偏移时经济性-统计性能更好，，反之则相反。成本函数对偏移量敏感度最高，对调查、研究虚发报警的费用、寻找和消除导致过程失控的因素的花费和时间间隔的敏感度较低，可以进行粗略估计。此外，GEWMA控制图的经济性-统计性成本在不同偏移量条件下均高于其经济性成本。
[Abstract]:The control chart is widely used in the establishment and maintenance of statistical process control. The conventional multivariate exponential weighted moving average (MEWMA) control chart is used to monitor the small deviation in the process of multivariate quality, which requires that the quality characteristics are independent of each other. An improved multivariate exponential weighted moving average control chart, GEWMA control chart, can be used to monitor multivariate quality processes with correlation between quality characteristics. In this paper, the economic and economic-statistical model of GEWMA control chart is designed. Based on particle swarm optimization algorithm, the model is solved and compared with an example. Finally, sensitivity analysis is carried out. The main contents of this paper are as follows: In this paper, the economic model of control chart and four kinds of main solving methods are introduced. Using the improved research results of particle swarm optimization, a solution method suitable for this model is proposed. The results show that the method can be used to solve the model effectively. Based on the LorenzenVance model, the economic model suitable for GEWMA control chart is designed, and the economic model of GEWMA control chart and MEWMA control chart is solved by an example. Finally, the sensitivity of important parameters in the cost function of GEWMA control chart is analyzed. The results show that the economic performance of the control chart is better than that of the MEWMA control chart, whereas the opposite is true. In addition, the deviation has the greatest influence on the cost. The cost function is less sensitive to the cost of investigating and researching the false alarm, the cost of finding and eliminating the factors leading to the process losing control and the sensitivity of the time interval, which can be roughly estimated. 3) based on the economic model, the economy-statistic model of GEWMA control chart is constructed, and the economy-statistical model of GEWMA control chart and MEWMA control chart are studied respectively, and the sensitivity of important parameters is analyzed. Finally, the economy and economy-statistics of GEWMA control chart are compared and analyzed. The results show that the economical and statistical performance of the control chart is better when the shift is small, whereas the opposite is true. The cost function is the most sensitive to offset. The cost of investigation, research on false alarm, and the sensitivity of finding and eliminating the factors that lead to the process runaway are low, and the sensitivity of the cost and time interval can be estimated roughly. In addition, the economy-statistical cost of GEWMA control chart is higher than that of economic cost under different offsets.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB114.2

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