【作者】 张健；

【导师】 施亮星； 王新风；

【作者基本信息】 天津大学 ， 工业工程， 2019， 硕士

【摘要】 统计过程控制方法被广泛应用到工业领域,以监控生产过程中的质量问题。其中控制图扮演着非常重要的角色。随着科技的进步,越来越多的传感器被应用到生产过程中使得过程数据越加丰富且复杂,这对传统控制图带来了巨大的挑战,特别是以过程服从正态分布为假设前提的休哈特控制图。由于在实际中过程分布通常是未知且难以估计的,故而使传统控制图发生更多误判。本文以数据量丰富的过程为研究对象,提出了基于1范数的连续等级概率评分（CRPS₁）的控制图。首先,本文对CRPS₁的基本理论和性质进行研究,通过理论证明和实验仿真都能够表明该统计量服从正态分布,特别是在样本容量较大时。然后将CRPS₁与休哈特控制图相结合,具体地阐述SRS控制图的构建方式,以及在不同的样本容量下的控制限的确定方法。之后通过仿真实验给出了SRS控制图的受控性能和失控性能,并以运行链长的相关参数来阐述。同时对1范数和2范数的CRPS所构建的休哈特控制图进行比较,表明该控制图具有更加稳健的受控性能。其次,本文又将RS统计量与EWMA控制图相结合,进一步探讨了该控制图监控中小偏移的能力,并通过仿真与实际案例来说明该控制图的监控性能。其中仿真实验分别采用了正态分布和拉普拉斯分布,仿真实验说明该控制图要优于其他两种控制图,特别是在监控位置参数的偏移上更加具有优势。最后将该控制图应用于室内噪音案例中,结果表明该控制图能够很快地检测到过程的偏移,从而更加证明了该控制图在实践中有着重大意义。更多还原

【Abstract】 Statistical process control are widely used in the industrial field,it aims to monitor quality issues in the production process.Control charts play a very important role.With the advancement of technology,more and more sensors are applied to the production process,making the process data richer and more complex,which brings great challenges to the traditional control chart,especially the Shewhart control chart that assumes the process obeys normal distribution.Since the process distribution is usually unknown and difficult to estimate in practice,the traditional control chart is more misjudged.In this thesis,the process of data-rich process is taken as the research object,and the control chart based on 1-norm continuous ranked probability score is proposed.Firstly,this thesis studies the basic theory and properties of 1-norm CRPS.Both theoretical proof and experimental simulation can show that the statistic subjects to normal distribution,especially when the sample size is large.Then,the CRPS₁ is combined with Shewhart control chart,and the construction method of the SRS chart and the determination of the control limit under different sample size are specifically explained.Both in-control and out-of-control performance of the SRS control chart are given by simulation,and the relevant parameters of the run length are discussed.At the same time,we compare SRS chart with Shewhart chart based on 2-norm CRPS.It shows that the proposed chart has more robust in-control performance.Secondly,this thesis combines the CRPS₁ with the EWMA control chart to further explore the ability of ERS chart to monitor small and medium shifts,and demonstrates the monitoring performance through simulation and actual cases.The simulation experiment uses the normal distribution and the Laplace distribution respectively.The simulation shows that ERS chart is superior to the other two control charts,especially the ability of monitoring scale parameter.Finally,the control chart is applied to the indoor noise case.The results show that ERS chart can quickly monitor the process shifts,which proves that ERS chart is of great significance in practice.更多还原