本文選題：統(tǒng)計過程控制 + 自適應EWMA　； 參考：《南京理工大學》2016年博士論文

【摘要】：質量是產品的核心競爭力,產品之間的競爭最終歸結為產品質量的競爭。21世紀將是質量的世紀,如何提高產品質量是學術界與工業(yè)界研究的焦點。控制圖作為統(tǒng)計質量控制的重要工具之一,通過在線監(jiān)測可以有效地保證產品質量符合要求。Shewhart 型控制圖對小偏移不敏感與 EWMA(Exponentially Weighted Moving Average,EWMA)控制圖慣性較大的問題,一直以來是控制圖研究的重點之一。針對該問題,早期的研究直接將Shewhart控制限加入EWMA控制圖中,這種做法逐漸被更有效方法所取代。其中,通過自適應EWMA濾波方法將Shewhart控制圖與EWMA控制圖相結合而形成的AEWMA(Adaptive EWMA,AEWMA)控制圖具有更加優(yōu)越的性能與更大的研究價值。此外,為了更好地適應市場競爭的需求,越來越多的生產廠商趨向于小批量生產。傳統(tǒng)的控制圖要求有足夠大的樣本空間以精確地估計過程均值與方差,小批量生產模式下的樣本空間往往是受限的,這使得傳統(tǒng)控制圖在小批量生產過程中的應用受到了限制。為了解決該問題學者們提出了新的統(tǒng)計量,其中基于T統(tǒng)計量的t控制圖以其良好的性能而受到廣泛的關注。然而,Shewhart控制圖與EWMA控制圖本身的缺點限制了其與t控制圖相結合后整體性能的發(fā)揮。鑒于AEWMA控制圖與t控制圖優(yōu)越的性能,將二者相結合而構成的AEWMA t控制圖是值得研究的。綜合以上分析,本文考慮不同的生產環(huán)境,對AEWMA t控制圖的性能做了相應研究。本文的主要研究成果如下:1、研究了方差未知情況下AEWMA t控制圖的統(tǒng)計設計問題。推導了利用Markov 鏈求取 AEWMA t 控制圖性能指標 ARL(Average Run Length,ARL)與 SDRL(Standard Deviation of Run Length,SDRL)的算法。考慮到實際生產過程中方差未知這一普遍情況,研究了方差未知時AEWMA t控制圖的統(tǒng)計性能,分析了方差不確定對AEWMAt控制圖統(tǒng)計性能的影響。通過仿真比較了 AEWMA t控制圖與EWMA t控制圖的統(tǒng)計性能,以及兩種控制圖的慣性大小。2、研究了 AEWMA t控制圖的經濟統(tǒng)計設計問題。傳統(tǒng)的經濟設計會降低控制圖的統(tǒng)計性能,經濟統(tǒng)計設計是較為全面的考慮控制圖性能的設計方法。在深入研究AEWMA t控制圖經濟統(tǒng)計設計方法的基礎上,給出了兩種經濟統(tǒng)計設計模型。分析了兩種模型下優(yōu)化設計的AEWMA t控制圖的經濟性能與統(tǒng)計性能,并對關鍵參數做了靈敏度分析。3、研究了短周期生產環(huán)境下AEWMAt控制圖的統(tǒng)計設計Q嬏�。皖l劑死肕arkov鏈求取短周期AEWMA t控制圖性能指標TARL(Truncated ARL,TARL)與報警概率q的算法�；赥ARL指標對短周期下AEWMA t控制圖進行了統(tǒng)計設計,研究了短周期下AEWMAt控制圖的統(tǒng)計性能。通過仿真比較了短周期AEWMA t控制圖與EWAM t控制圖的統(tǒng)計性能。4、研究了短周期AEWMAt控制圖的經濟設計問題。在已有的經濟設計模型基礎上引入Taguchi損失函數,使得經濟設計模型更加符合實際情況。推導了利用二維Markov鏈計算AEWMA t控制圖損失大小的算法。通過仿真分析了短周期AEWMA t控制圖的經濟性能,結果表明AEWMA t控制圖損失小于EWMA t控制圖,對方差不確定的魯棒性明顯強于AEWMA X控制圖。并對關鍵參數做了靈敏度分析,分析了參數的改變對短周期AEWMA t控制圖決策變量與損失大小的影響。
[Abstract]:Quality is the core competitiveness of products. Competition among products is ultimately attributed to product quality competition.21 century will be the century of quality. How to improve product quality is the focus of academic and industrial research. As one of the important tools of statistical quality control, control charts can effectively guarantee the quality of products by on-line monitoring. It is always one of the key points in the study of control chart to require the.Shewhart type control chart to be insensitive to small offset and EWMA (Exponentially Weighted Moving Average, EWMA) control chart, which has been one of the key points in the study of the control chart. In addition, the AEWMA (Adaptive EWMA, AEWMA) control chart formed by combining the Shewhart control diagram with the EWMA control chart by the adaptive EWMA filtering method has a better performance and greater research value. In addition, in order to better adapt to the demand of the market competition, the more and more manufacturers tend to be small mass production. The control chart requires a large enough sample space to accurately estimate the mean and variance of the process. The sample space under the small batch production pattern is often limited. This makes the application of the traditional control graph limited in the small batch production process. In order to solve the problem, a new statistic based on T statistics is proposed. The t control chart is widely concerned for its good performance. However, the shortcomings of the Shewhart control diagram and the EWMA control chart itself limit the overall performance of the combination of the t control diagram and the AEWMA control diagram. In view of the superior performance of the AEWMA control diagram and the t control chart, the AEWMA t control chart consisting of the combination of the two is worth studying. In this paper, the performance of AEWMA t control chart is studied in this paper. The main research results of this paper are as follows: 1, the statistical design problem of AEWMA t control chart under the unknown variance is studied. The performance index ARL (Average Run Length, ARL) and AEWMA t control diagram ARL are derived from the Markov chain. The algorithm of iation of Run Length, SDRL). Considering the general situation of variance unknown in the actual production process, the statistical performance of AEWMA t control graph is studied when the variance is unknown, and the influence of variance uncertainty on the statistical performance of AEWMAt control chart is analyzed. The statistical performance of AEWMA t control diagram and EWMA t control chart is compared by simulation, and two The inertia size of the control graph is.2, and the economic statistical design of the AEWMA t control chart is studied. The traditional economic design will reduce the statistical performance of the control chart. The economic statistics design is a more comprehensive design method to consider the performance of the control chart. On the basis of the in-depth study of the design method of the AEWMA t control chart, two kinds of classics are given. The economic performance and statistical performance of the AEWMA t control chart under the two models are analyzed, and the sensitivity analysis of the key parameters is analyzed.3. The statistical design of the AEWMAt control chart under the short cycle production environment is studied, and the Q M frequency agent dead arkov chain is used to obtain the performance index TARL (Truncat) of the short period AEWMA t control chart. The algorithm of ED ARL, TARL) and alarm probability q. Based on the TARL index, a statistical design of the short period AEWMA t control graph is designed, and the statistical performance of the AEWMAt control diagram in short period is studied. The statistical performance of the short period AEWMA t control graph and EWAM t control chart is compared by simulation. The economic design problem of the short period control chart is studied. On the basis of the existing economic design model, the Taguchi loss function is introduced to make the economic design model more consistent with the actual situation. The algorithm of calculating the loss size of the AEWMA t control graph using the two-dimensional Markov chain is derived. The economic performance of the short period AEWMA t control chart is analyzed by simulation. The results show that the loss of the AEWMA t control diagram is less than the EWMA t control. The robustness of the other is obviously stronger than the AEWMA X control chart, and the sensitivity analysis of the key parameters is made, and the influence of the change of the parameters on the decision variables and the loss size of the short period AEWMA t control diagram is analyzed.
【學位授予單位】：南京理工大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O213.1

【參考文獻】

相關期刊論文 前1條

1 ;Economic Design of & S Control Charts Based on Taguchi's Loss Function and Its Optimization[J];Chinese Journal of Mechanical Engineering;2012年03期

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本文編號：1919479