本文選題：MEWMA + 多元控制圖�。� 參考：《湖南大學(xué)》2014年碩士論文

【摘要】：控制圖在統(tǒng)計(jì)過程控制的建立和維持中有著廣泛的應(yīng)用，常規(guī)多元指數(shù)加權(quán)移動(dòng)平均（MEWMA）控制圖用來監(jiān)測(cè)多元質(zhì)量過程中存在的小偏移,它要求質(zhì)量特性間是相互獨(dú)立的。一種改進(jìn)的多元指數(shù)加權(quán)移動(dòng)平均控制圖——GEWMA控制圖，可用于監(jiān)控質(zhì)量特性之間具有相關(guān)性的多元質(zhì)量過程。本文針對(duì)GEWMA控制圖，設(shè)計(jì)出了其經(jīng)濟(jì)性以及經(jīng)濟(jì)性-統(tǒng)計(jì)性模型，并基于粒子群優(yōu)化算法，運(yùn)用實(shí)例，對(duì)模型進(jìn)行了求解和對(duì)比研究，最后，進(jìn)行了靈敏度的分析。 本文的主要研究?jī)?nèi)容有： （1）介紹了控制圖經(jīng)濟(jì)性模型以及四類主要求解方法，并運(yùn)用粒子群的改進(jìn)研究成果，提出了適用于本文模型的求解方法，結(jié)果顯示，該方法對(duì)本文模型可進(jìn)行有效的求解。 （2）基于LorenzenVance模型，設(shè)計(jì)了適用于GEWMA控制圖的經(jīng)濟(jì)性模型，并運(yùn)用實(shí)例對(duì)GEWMA控制圖和MEWMA控制圖的經(jīng)濟(jì)性模型進(jìn)行了求解，最后分析了GEWMA控制圖的成本函數(shù)中重要參數(shù)的靈敏度。結(jié)果顯示，小偏移時(shí)，GEWMA控制圖的經(jīng)濟(jì)性能比MEWMA控制圖更優(yōu)，反之則相反。此外，偏移量對(duì)成本的影響最大，成本函數(shù)對(duì)調(diào)查和研究虛發(fā)報(bào)警的費(fèi)用、尋找和消除導(dǎo)致過程失控的因素的花費(fèi)以及時(shí)間間隔的敏感度均較低，可以進(jìn)行粗略估計(jì)。 （3）在經(jīng)濟(jì)性模型的基礎(chǔ)上，構(gòu)建了GEWMA控制圖的經(jīng)濟(jì)性-統(tǒng)計(jì)性模型，分別對(duì)GEWMA控制圖和MEWMA控制圖的經(jīng)濟(jì)性-統(tǒng)計(jì)性模型進(jìn)行了實(shí)例研究，并對(duì)重要參數(shù)的靈敏度進(jìn)行了分析。最后，還對(duì)GEWMA控制圖的經(jīng)濟(jì)性和經(jīng)濟(jì)性-統(tǒng)計(jì)性進(jìn)行對(duì)比分析。結(jié)果顯示，GEWMA控制圖在小偏移時(shí)經(jīng)濟(jì)性-統(tǒng)計(jì)性能更好，，反之則相反。成本函數(shù)對(duì)偏移量敏感度最高，對(duì)調(diào)查、研究虛發(fā)報(bào)警的費(fèi)用、尋找和消除導(dǎo)致過程失控的因素的花費(fèi)和時(shí)間間隔的敏感度較低，可以進(jìn)行粗略估計(jì)。此外，GEWMA控制圖的經(jīng)濟(jì)性-統(tǒng)計(jì)性成本在不同偏移量條件下均高于其經(jīng)濟(jì)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.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TB114.2

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