可变抽样区间ARMA控制图经济统计设计

发布时间：2018-01-03 02:09

本文关键词：可变抽样区间ARMA控制图经济统计设计　出处：《郑州航空工业管理学院》2017年硕士论文　论文类型：学位论文

【摘要】：控制图是监控质量的重要工具,然而在自相关环境下,传统控制图会出现误警报过于频繁、系统不稳定的缺陷,此时需要使用自相关控制图如ARMA(Autoregressive Moving Average)等控制图来监控。为了尽可能的降低成本,减少企业使用控制图的阻力,很多学者对控制图进行经济设计。但是控制图的经济设计仅考虑了控制图的经济性能,控制图的统计性能大大减弱。因此,如何在保证质量的前提下尽可能降低成本是一个值得研究的课题。控制图的经济统计设计就是在保证控制图监控质量的情况下尽可能的降低成本的一个方法。首先介绍了ARMA控制图,建立了经济设计模型,以降低控制图的使用成本,并在该模型的基础上进行改进,建立了考虑质量损失函数的ARMA控制图经济设计。其次,对可变抽样区间ARMA控制图进行经济设计,并与固定抽样区间ARMA控制图进行比较得出,可变抽样区间控制图具有更低的成本,能够更快的检测出特殊原因的发生。最后对可变抽样区间ARMA控制图进行经济统计设计。与相同条件的经济设计模型相比,经济统计设计模型的成本会小幅增加,但是控制图的统计性能大大提高。本文层层递进的建立可变抽样区间ARMA控制图经济统计设计模型,并加入案例分析和求解,为企业提升产品质量,降低生产成本提供了有效的途径和理论支持。ARMA控制图平均运行长度(Average Run Length,ARL)的马尔可夫链法计算是一个难题。本文构建满足马尔可夫链性质的三维向量,计算状态概率矩阵,进而计算控制图的ARL和平均报警时间(Average Time to Signal,ATS)。建立了可变抽样区间ARMA控制图经济统计设计模型,与ARMA控制图经济设计相比,改模型的成本更低,统计性能更好。
[Abstract]:The control chart is an important tool for monitoring the quality, but in the autocorrelation environment, the traditional control chart will appear false alarm is too frequent, the instability of the system defects, the need to use autocorrelationcontrolcharts such as ARMA (Autoregressive Moving Average) control chart to monitor. In order to reduce the cost as far as possible, reduce the enterprise use control chart the resistance of many scholars to conduct economic design of control charts. But the economic design of control charts only consider the economic performance of control charts, statistical performance control chart is greatly reduced. Therefore, how to ensure the quality of the premise as far as possible to reduce costs is a topic worthy of study. The economic statistical design of control chart is in to ensure the quality control charts to monitor situations as much as possible to reduce a cost. First introduced the ARMA control chart, established the model of economic design, in order to reduce the use of control charts into This, and improved on the basis of the model, establish a control chart of economic design quality loss function of ARMA. Secondly, the variable sampling interval ARMA control chart and economic design, compared with the fixed sampling interval ARMA control chart with variable sampling interval control chart has lower cost, faster detection a special cause. Finally, the economic statistical design of variable sampling interval ARMA control chart. Compared with the economic design model and the same condition, the statistical design model of economic costs will increase slightly, but the statistical performance of control chart is greatly improved. A variable sampling interval control chart ARMA economic statistical model in this thesis and progressive layers. With case analysis and solution for enterprises to improve product quality, to provide the effective way and theoretical support for.ARMA control chart for average length to reduce the production cost ( Average Run Length, ARL) of the Markov chain method is a difficult problem. This paper constructed a three-dimensional vector Markov chain properties, calculation of state probability matrix, then calculate the average control chart and ARL (Average Time to Signal the alarm time, ATS). A variable sampling interval control chart ARMA economic statistical design model. Compared with the economic design of ARMA control model, lower cost, better statistical performance.

【学位授予单位】：郑州航空工业管理学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F222

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