统计过程控制中参数自适应型控制图的研究

发布时间：2018-05-21 14:03

本文选题：统计过程控制 + 自适应EWMA　；参考：《南京理工大学》2016年博士论文

【摘要】：质量是产品的核心竞争力,产品之间的竞争最终归结为产品质量的竞争。21世纪将是质量的世纪,如何提高产品质量是学术界与工业界研究的焦点。控制图作为统计质量控制的重要工具之一,通过在线监测可以有效地保证产品质量符合要求。Shewhart 型控制图对小偏移不敏感与 EWMA(Exponentially Weighted Moving Average,EWMA)控制图惯性较大的问题,一直以来是控制图研究的重点之一。针对该问题,早期的研究直接将Shewhart控制限加入EWMA控制图中,这种做法逐渐被更有效方法所取代。其中,通过自适应EWMA滤波方法将Shewhart控制图与EWMA控制图相结合而形成的AEWMA(Adaptive EWMA,AEWMA)控制图具有更加优越的性能与更大的研究价值。此外,为了更好地适应市场竞争的需求,越来越多的生产厂商趋向于小批量生产。传统的控制图要求有足够大的样本空间以精确地估计过程均值与方差,小批量生产模式下的样本空间往往是受限的,这使得传统控制图在小批量生产过程中的应用受到了限制。为了解决该问题学者们提出了新的统计量,其中基于T统计量的t控制图以其良好的性能而受到广泛的关注。然而,Shewhart控制图与EWMA控制图本身的缺点限制了其与t控制图相结合后整体性能的发挥。鉴于AEWMA控制图与t控制图优越的性能,将二者相结合而构成的AEWMA t控制图是值得研究的。综合以上分析,本文考虑不同的生产环境,对AEWMA t控制图的性能做了相应研究。本文的主要研究成果如下:1、研究了方差未知情况下AEWMA t控制图的统计设计问题。推导了利用Markov 链求取 AEWMA t 控制图性能指标 ARL(Average Run Length,ARL)与 SDRL(Standard Deviation of Run Length,SDRL)的算法。考虑到实际生产过程中方差未知这一普遍情况,研究了方差未知时AEWMA t控制图的统计性能,分析了方差不确定对AEWMAt控制图统计性能的影响。通过仿真比较了 AEWMA t控制图与EWMA t控制图的统计性能,以及两种控制图的惯性大小。2、研究了 AEWMA t控制图的经济统计设计问题。传统的经济设计会降低控制图的统计性能,经济统计设计是较为全面的考虑控制图性能的设计方法。在深入研究AEWMA t控制图经济统计设计方法的基础上,给出了两种经济统计设计模型。分析了两种模型下优化设计的AEWMA t控制图的经济性能与统计性能,并对关键参数做了灵敏度分析。3、研究了短周期生产环境下AEWMAt控制图的统计设计Q嬏狻Ｍ频剂死肕arkov链求取短周期AEWMA t控制图性能指标TARL(Truncated ARL,TARL)与报警概率q的算法。基于TARL指标对短周期下AEWMA t控制图进行了统计设计,研究了短周期下AEWMAt控制图的统计性能。通过仿真比较了短周期AEWMA t控制图与EWAM t控制图的统计性能。4、研究了短周期AEWMAt控制图的经济设计问题。在已有的经济设计模型基础上引入Taguchi损失函数,使得经济设计模型更加符合实际情况。推导了利用二维Markov链计算AEWMA t控制图损失大小的算法。通过仿真分析了短周期AEWMA t控制图的经济性能,结果表明AEWMA t控制图损失小于EWMA t控制图,对方差不确定的鲁棒性明显强于AEWMA X控制图。并对关键参数做了灵敏度分析,分析了参数的改变对短周期AEWMA t控制图决策变量与损失大小的影响。
[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.
【学位授予单位】：南京理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O213.1

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