基于Metrics统计量的非线性Profile控制图

发布时间：2018-03-11 08:07

本文选题：Profile监控　切入点：Metrics统计量　出处：《华东师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：传统控制图在统计过程控制方面发挥着重要的作用,而现代工业领域由于技术的革新,传统控制图已经满足不了实际监控的需要。相比于过去单一地监控某个或某几个质量特性,现在的生产过程通常需要准确地刻画响应变量与解释变量之间的函数关系才能更好地把握过程稳定性。对这类回归曲线的研究就被称为Profile监控问题。本文在Metrics统计量的基础上引入CUSUM设计思想,提出了一类非线性Profile的控制图方法,对Phase II阶段进行监控并及时对异常报警。为了满足传统CUSUM控制图的正态性假设,我们首先对Metrics统计量作一步正态性变换并利用Shapiro-Wilk检验证明变换后的统计量近似服从正态分布。基于正态变换的Metrics-CUSUM控制图(NM-CUSUM)是在固定参考值下计算对应的控制限,较小参考值在监控小漂移时表现较好,较大参考值在监控中大漂移时表现较好。为了进一步提高控制图监控效果,我们接着设计了自适应的Metrics-CUSUM控制图(AM-CUSUM),预先估计Profile的漂移量后自适应地选取最优参考值,根据控制限拟合函数计算对应的控制限。最后我们利用bootstrap技术,设计了一个不依赖于分布的动态控制限的Metrics-CUSUM控制图(BM-CUSUM),计算出一系列控制限替代原来的单值控制限。这三个控制图都有效改进了传统Metrics控制图的监控效果。结合数值模拟可知,监控小漂移时我们推荐较小参考值的NM-CUSUM和AM-CUSUM控制图,监控中大漂移时我们推荐较大参考值的BM-CUSUM控制图。另外,若监控系数漂移则优先考虑积分形式的Metrics统计量设计控制图,若监控方差漂移则优先考虑其它三个形式的Metrics统计量设计控制图。
[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.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O213.1

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