标题: 二维随机效应剖面资料之监控方法
Monitoring Schemes for Two-dimensional Profiles with Random Effects
作者: 林思涵
洪志真
Lin, Szu-Han
Horng Shiau Jyh-Jen
统计学研究所
关键字: 二维剖面资料之监控;多线性主成份分析;随机效应;无母数回归;平均连串长度;高斯过程;无分配假设;two-dimensional profile monitoring;multilinear principal component analysis;random effects;nonparametric regression;average run length;Gaussian process;distribution-free
公开日期: 2017
摘要: 在科技高度发展之下,工业的生产线亦越来越复杂,对这些复杂的制程发展适当的监控方法在品质管制上是重要的议题。近年来剖面资料监控方法之研究已成为统计品质管制(SPC)上大幅成长且相当热门之研究领域,而现今许多工业制程已经复杂到必须监控曲面型的二维剖面资料,然而目前似乎尚无着墨于二维剖面资料监控之文献。本研究考虑具随机效应之二维剖面资料,采用无母数回归模型让剖面的函数形式更具弹性,可应用的范围更广。在此模型下,我们利用二阶(second order)多线性主成份分析(multilinear principal component analysis, 简称MPCA)来剖析管制中二维剖面资料的特性,然后由此提出监控方法。我们利用多线性主成份得到二维剖面资料的多线性主成份分数,并利用该分数来发展管制图。第二阶段中,在实际作业时管制图的平均连串长度(ARL)绩效表现会随着不同应用中第一阶段分析所估计的制程参数不同而有所变异,称作“从业人员之间”的变异,因此可将ARL视为一随机变数;所以我们探讨二维剖面资料在第二阶段下根据管制中ARL的分配来修正监控统计量的管制界限。在第一阶段中,若是资料来自常态分配,我们根据常态特色发展一套管制方法;若是资料并非来自常态分配,我们亦发展无分配假设的第一阶段管制方法;并利用伪阳性率与伪阴性率来当作衡量准则。最后使用真实的二维剖面资料来示范我们所提出的方法之适用性。
As high-tech advances rapidly, industrial production lines are getting more and more complicated. Developing suitable monitoring schemes for complicated processes as such has drawn much attention in the area of quality control. Among them, profile monitoring has been a growing and promising area of research in statistical process control (SPC) in recent years. Most research work in the literature focused on one-dimensional profiles. As technologies are advancing, two-dimensional profiles have become key quality characteristics for more and more processes; however, no monitoring schemes have been developed in the literature at the present time. Consider nonlinear two-dimensional profiles with random effects. Under a random-effect model and adopting the nonparametric regression approach, we propose using second-order multilinear principal component analysis (MPCA) to develop profile monitoring schemes. The multilinear principal component scores of two-dimensional profiles obtained from the multilinear principal component analysis are utilized to construct control charts. In Phase II, the average run length (ARL) performance of a control chart varies as the process parameter estimates from the Phase I analysis vary in each application. Consequently, the ARL becomes a random variable due to the so-called “practitioner-to-practitioner” variation. We develop an algorithm to construct a control limit with which practitioners would have a high “confidence” that the actual in-control ARL will exceed the nominal in-control ARL level. In Phase I, if two-dimensional profiles come from a normal distribution, we develop a control chart based on the distribution of the in-control ARL. If two-dimensional profiles violate the normal assumption, we develop a distribution-free control chart. The false-positive rate and false-negative rate are considered as the performance measures for Phase I analysis. Some real data analyses are provided to demonstrate the applicability of the proposed control charts.
URI: http://etd.lib.nctu.edu.tw/cdrfb3/record/nctu/#GT079926508
http://hdl.handle.net/11536/142514
显示于类别:Thesis