發(fā)布時(shí)間：2018-05-08 15:08

  本文選題：多元統(tǒng)計(jì)過程控制 + Bootstrap　； 參考：《華東師范大學(xué)》2016年博士論文

【摘要】：在多元統(tǒng)計(jì)過程控制中,當(dāng)質(zhì)量特性是連續(xù)性隨機(jī)變量時(shí),已有的控制圖大多是基于正態(tài)分布建立的。而在實(shí)際中,正態(tài)性假定經(jīng)常不成立,在這種情況下,基于正態(tài)分布建立的這些控制圖的表現(xiàn)將會(huì)受到嚴(yán)重影響,因此需要發(fā)展一些非參或者穩(wěn)健的多元控制圖。當(dāng)質(zhì)量特性是屬性變量時(shí),其概率分布經(jīng)常由列聯(lián)表來刻畫。傳統(tǒng)的監(jiān)控列聯(lián)表數(shù)據(jù)的方法都是基于“格子數(shù)小樣本量大”的情形。隨著屬性變量個(gè)數(shù)的增加,列聯(lián)表中的格子數(shù)迅速增加,導(dǎo)致格子中的數(shù)目非常小或者為零,也就是所謂的稀疏列聯(lián)表。在這種情況下,傳統(tǒng)的方法已不再能使用,有必要發(fā)展一些新方法來監(jiān)控稀疏列聯(lián)表數(shù)據(jù)。當(dāng)多元過程分布未知而僅有一些可利用的受控?cái)?shù)據(jù)時(shí),第二章把傳統(tǒng)的多元累積和(MCUSUM)控制圖的常數(shù)控制限擴(kuò)展成一系列動(dòng)態(tài)控制限,這些控制限可以由sprint長度給定下統(tǒng)計(jì)量的條件bootstrap分布確定。同傳統(tǒng)的MCUSUM控制圖相比,這種具有動(dòng)態(tài)控制限的新控制圖表現(xiàn)得更好。然而,它的計(jì)算比較繁瑣,于是進(jìn)一步我們使用sprint長度的連續(xù)函數(shù)來作為它的控制限,發(fā)展了一個(gè)更為便利的控制圖。當(dāng)過程均值漂移僅僅發(fā)生在很少的幾個(gè)分量上時(shí),第三章把傳統(tǒng)的多元LASSO控制圖擴(kuò)展到一個(gè)穩(wěn)健的版本中。新控制圖在橢球方向分布族內(nèi)是不依賴于分布的,這種不依賴于分布性指的是對(duì)橢圓方向分布族內(nèi)的任何連續(xù)分布,其控制限是相同的,因此控制限可以由多元標(biāo)準(zhǔn)正態(tài)分布確定。模擬結(jié)果顯示新提出的控制圖對(duì)監(jiān)控厚尾分布和偏斜分布中的稀疏漂移是非常有效的。當(dāng)過程協(xié)方差漂移僅僅發(fā)生在一些元素上時(shí),第四章把空間符號(hào)協(xié)方差陣和最大范數(shù)應(yīng)用到指數(shù)加權(quán)移動(dòng)平均(EWMA)方案中,構(gòu)造了一個(gè)監(jiān)控協(xié)方差陣的穩(wěn)健控制圖。性質(zhì)研究表明新圖在橢球方向分布族內(nèi)是不依賴于分布的。對(duì)比研究表明新方法對(duì)監(jiān)控厚尾分布下的稀疏漂移更有效,對(duì)監(jiān)控偏斜分布下的稀疏漂移更穩(wěn)健。在稀疏列聯(lián)表下,第五章首先提出一個(gè)兩階段的group lasso方法對(duì)高維log-linear模型進(jìn)行模型選擇和參數(shù)估計(jì),進(jìn)而獲得受控狀態(tài)下的概率分布。然后基于一個(gè)修正的Pearson χ2統(tǒng)計(jì)量,提出一個(gè)新的EWMA控制圖。與傳統(tǒng)的基于Pearson χ2檢驗(yàn)和似然比檢驗(yàn)統(tǒng)計(jì)量的控制圖相比,新控制圖對(duì)模型系數(shù)的各種漂移是有效的,尤其在中小漂移下。
[Abstract]:In multivariate statistical process control, when the quality characteristic is a continuous random variable, most of the existing control charts are based on normal distribution. In practice, the assumption of normality is often not true, in which case, the performance of these control charts based on normal distribution will be seriously affected, so it is necessary to develop some non-parametric or robust multivariate control charts. When the quality property is an attribute variable, its probability distribution is often described by the column table. The traditional method of monitoring column data is based on the case of large sample size. With the increase of the number of attribute variables, the number of lattice in the column table increases rapidly, resulting in the number of the lattice is very small or zero, that is, the so-called sparse column table. In this case, the traditional method can no longer be used, it is necessary to develop some new methods to monitor the sparse column table data. When the distribution of multivariate processes is unknown and only some available controlled data are available, the constant control limits of the traditional multivariate cumulant and MCUSUM control charts are extended to a series of dynamic control limits in Chapter 2. These control limits can be determined by the conditional bootstrap distribution of the statistics given by the sprint length. Compared with the traditional MCUSUM control chart, the new control chart with dynamic control limit performs better. However, its calculation is rather cumbersome, so we further use the continuous function of sprint length as its control limit, and develop a more convenient control graph. When the mean shift of the process occurs on only a few components, the traditional multivariate LASSO control graph is extended to a robust version in Chapter 3. The new control graph does not depend on the distribution in the ellipsoidal distribution family, which means any continuous distribution in the ellipsoidal distribution family, and the control limit is the same. Therefore, the control limit can be determined by multivariate standard normal distribution. The simulation results show that the proposed control chart is very effective for monitoring the sparse drift in the thick tail distribution and skew distribution. When the process covariance drift occurs only on some elements, the fourth chapter applies the spatial symbol covariance matrix and the maximum norm to the exponential weighted moving average (EWMA) scheme, and constructs a robust control chart of the monitoring covariance matrix. It is shown that the new graph is not dependent on distribution in the ellipsoidal distribution family. The comparative study shows that the new method is more effective to monitor the sparse drift under the thick tail distribution and more robust to the sparse drift under the monitoring skew distribution. In the fifth chapter, a two-stage group lasso method is proposed to select the model and estimate the parameters of the high-dimensional log-linear model in the sparse list, and then the probability distribution in the controlled state is obtained. Then, based on a modified Pearson 蠂 2 statistic, a new EWMA control graph is proposed. Compared with the traditional control chart based on Pearson 蠂 2 test and likelihood ratio test, the new control chart is effective for all kinds of drift of model coefficients, especially for small drift.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：C8;TB114.2

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