本文選題：Profile監(jiān)控　切入點(diǎn)：Metrics統(tǒng)計(jì)量　出處：《華東師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：傳統(tǒng)控制圖在統(tǒng)計(jì)過程控制方面發(fā)揮著重要的作用,而現(xiàn)代工業(yè)領(lǐng)域由于技術(shù)的革新,傳統(tǒng)控制圖已經(jīng)滿足不了實(shí)際監(jiān)控的需要。相比于過去單一地監(jiān)控某個(gè)或某幾個(gè)質(zhì)量特性,現(xiàn)在的生產(chǎn)過程通常需要準(zhǔn)確地刻畫響應(yīng)變量與解釋變量之間的函數(shù)關(guān)系才能更好地把握過程穩(wěn)定性。對(duì)這類回歸曲線的研究就被稱為Profile監(jiān)控問題。本文在Metrics統(tǒng)計(jì)量的基礎(chǔ)上引入CUSUM設(shè)計(jì)思想,提出了一類非線性Profile的控制圖方法,對(duì)Phase II階段進(jìn)行監(jiān)控并及時(shí)對(duì)異常報(bào)警。為了滿足傳統(tǒng)CUSUM控制圖的正態(tài)性假設(shè),我們首先對(duì)Metrics統(tǒng)計(jì)量作一步正態(tài)性變換并利用Shapiro-Wilk檢驗(yàn)證明變換后的統(tǒng)計(jì)量近似服從正態(tài)分布。基于正態(tài)變換的Metrics-CUSUM控制圖(NM-CUSUM)是在固定參考值下計(jì)算對(duì)應(yīng)的控制限,較小參考值在監(jiān)控小漂移時(shí)表現(xiàn)較好,較大參考值在監(jiān)控中大漂移時(shí)表現(xiàn)較好。為了進(jìn)一步提高控制圖監(jiān)控效果,我們接著設(shè)計(jì)了自適應(yīng)的Metrics-CUSUM控制圖(AM-CUSUM),預(yù)先估計(jì)Profile的漂移量后自適應(yīng)地選取最優(yōu)參考值,根據(jù)控制限擬合函數(shù)計(jì)算對(duì)應(yīng)的控制限。最后我們利用bootstrap技術(shù),設(shè)計(jì)了 一個(gè)不依賴于分布的動(dòng)態(tài)控制限的Metrics-CUSUM控制圖(BM-CUSUM),計(jì)算出一系列控制限替代原來的單值控制限。這三個(gè)控制圖都有效改進(jìn)了傳統(tǒng)Metrics控制圖的監(jiān)控效果。結(jié)合數(shù)值模擬可知,監(jiān)控小漂移時(shí)我們推薦較小參考值的NM-CUSUM和AM-CUSUM控制圖,監(jiān)控中大漂移時(shí)我們推薦較大參考值的BM-CUSUM控制圖。另外,若監(jiān)控系數(shù)漂移則優(yōu)先考慮積分形式的Metrics統(tǒng)計(jì)量設(shè)計(jì)控制圖,若監(jiān)控方差漂移則優(yōu)先考慮其它三個(gè)形式的Metrics統(tǒng)計(jì)量設(shè)計(jì)控制圖。
[Abstract]:Traditional control charts play an important role in statistical process control. Traditional control charts can no longer meet the needs of actual monitoring. The present production process usually needs to describe the functional relationship between the response variable and the explanatory variable accurately in order to better understand the stability of the process. The study of this kind of regression curve is called Profile monitoring problem. On the basis of metrology, the design idea of CUSUM is introduced. In this paper, a class of control chart method for nonlinear Profile is proposed, which monitors the stage of Phase II and alerts the abnormal in time. In order to satisfy the normal assumption of traditional CUSUM control chart, We first make a one-step normality transformation of Metrics statistics and prove by Shapiro-Wilk test that the transformed statistics are approximately obedient to normal distribution. The Metrics-CUSUM control graph based on normal transformation is to calculate the corresponding control limit under the fixed reference value. The smaller reference value is better when monitoring small drift, and the larger reference value is better when monitoring medium and large drift. In order to further improve the monitoring effect of control chart, Then, we design an adaptive Metrics-CUSUM control chart (AM-CUSUMN). After estimating the drift of Profile in advance, we adaptively select the optimal reference value and calculate the corresponding control limit according to the fitting function of the control limit. Finally, we use the bootstrap technique. In this paper, a Metrics-CUSUM control chart independent of distributed dynamic control limit is designed, and a series of control limits are calculated to replace the original single-value control limit. These three control charts effectively improve the monitoring effect of the traditional Metrics control chart. We recommend the NM-CUSUM and AM-CUSUM control charts of smaller reference values when monitoring small drift, and the BM-CUSUM control charts with larger reference values when monitoring medium and large drift. In addition, if the monitoring coefficients drift, we give priority to the integral form of Metrics statistics design control charts. If the variance drift is monitored, the other three forms of Metrics statistics are preferred to design the control chart.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O213.1

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本文編號(hào)：1597299