Statistical Adjustment for Short-Run Manufacturing: Parametric Optimization, Robustness Analysis, and Ensemble Control Using Gibbs Sampling

位于统计过程控制（SPC）领域的基础的问题是如何调整被怀疑在故障模式下操作的制造过程。当设置操作有缺陷时，快速调整制造过程尤其重要。本研究的目的是开发最佳顺序调整方法的设置和运行中的控制问题。摆位调整问题首先由F. Grubbs推导出了一个简单的序列方案。一个贝叶斯公式的过程调整将制定基于卡尔曼滤波器。该公式统一了几种调整规则，包括Grubbs方案，随机逼近，和经典的控制方法，如线性二次高斯（LQG）控制。本论文的主要研究方向为：（a）现有平差规则的参数优化和鲁棒性评估;（B）新的整体最优平差规则的开发。建议利用马尔可夫链蒙特卡罗技术，特别是吉布斯抽样，适用于估计的平均值的顺序调整的过程中，根据一些稳定的分布的设置中的经验错误的问题。这项研究的主要成果将是一套新的工艺调整工具，将提供有效的设置和运行内控制在短期内运行的制造过程。该配方的主要优点是，在生产几次运行或几批产品后，它允许在获得批次中的第一次测量之前开始调整新批次。这显然是一个灵活的，短期运行的制造系统的类型的优势，这项研究预计将受益。宾夕法尼亚州立大学的FAME制造实验室的使用将为该项目中开发的技术提供一个现实的测试平台。与工业研究人员合作（Eli Lilly和SAS Institute Inc.）将提供专业知识，在现实生活中应用的技术开发在这项研究和指导有关软件的实施。为了允许技术转让，将编写软件工具，并将在宾夕法尼亚州立大学的应用统计实验室网站上免费分发。

A problem located at the foundations of the Statistical Process Control (SPC) field is how to adjust a manufacturing process that is suspected to be operating in a malfunctioning mode. Rapidly adjusting a manufacturing process when the setup operation is defective is particularly important. The object of this research is to develop optimal sequential adjustment methods for the setup and within-run control problems. The setup adjustment problem was first analyzed by F. Grubbs who derived a simple sequential scheme. A Bayesian formulation for process adjustment will be developed based on Kalman filters. The formulation unifies several adjustment rules including Grubbs' scheme, Stochastic Approximation, and classical control methods such as Linear Quadratic Gaussian (LQG) control. The proposed work will follow two main research thrusts: a) parametric optimization and robustness assessment of existing adjustment rules; b) development of a new ensemble-optimal adjustment rule. It is proposed to utilize Markov Chain Monte Carlo techniques, and in particular, Gibbs Sampling, applied to the problem of estimating the mean of a sequentially-adjusted process that experiences errors in the setups according to some stable distribution. The main outcome of this research will be a new set of process adjustment tools that will provide efficient setup and within-run control in short-run manufacturing processes. This formulation has the major advantage that after a few runs or lots are produced, it allows to start adjusting a new lot prior to obtaining the first measurement in the lot. This is clearly an advantage for the type of flexible, short-run manufacturing systems this research is expected to benefit. Use of Penn State's FAME manufacturing laboratory will provide a realistic testbed for the techniques developed in this project. Collaboration with industrial researchers (Eli Lilly and SAS Institute Inc.) will provide expertise in the real-life application of the techniques developed in this research and guidance about software implementation. To allow technology transfer, software tools will be written and will be freely distributed at Penn State's Applied Statistics laboratory web site.