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

统计过程控制（SPC）领域的基础问题是如何调整被怀疑在故障模式下运行的制造过程。当设置操作有缺陷时，快速调整制造过程尤为重要。本研究的目的是开发最优顺序调整方法，以解决设置和运行内控制问题。F. Grubbs首先分析了设置调整问题，他推导了一个简单的顺序方案。基于卡尔曼滤波的过程调整贝叶斯公式将得到发展。该公式统一了几种调节规则，包括Grubbs方案，随机逼近和经典控制方法，如线性二次高斯（LQG）控制。建议的工作将遵循两个主要的研究重点：a)参数优化和现有调整规则的鲁棒性评估；B)发展一个新的集合最优调整规则。提出利用马尔可夫链蒙特卡罗技术，特别是吉布斯抽样，来估计一个顺序调整过程的均值问题，该过程在一些稳定分布的设置中经历误差。本研究的主要成果将是一套新的工艺调整工具，它将在短期制造过程中提供有效的设置和运行控制。这种配方的主要优点是，在生产了几次或几批产品后，它允许在获得第一批产品之前开始调整新的产品。这显然是柔性、短期制造系统的优势，这项研究有望从中受益。宾夕法尼亚州立大学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（Eli Lilly和SAS Institute Inc.）的合作将为本研究中开发的技术的实际应用提供专业知识，并指导软件实现。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.