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

统计过程控制(SPC)领域的一个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，快速调整制造工艺尤为重要。这项研究的目的是发展最优序贯调节方法来解决整定和运行中的控制问题。F·格拉布斯首先分析了设置调整问题，他推导出了一个简单的顺序方案。将基于卡尔曼滤波建立工艺调整的贝叶斯公式。该公式统一了几种调整规则，包括格拉布斯方案、随机逼近和经典控制方法，如线性二次型高斯(LQG)控制。拟议的工作将遵循两个主要研究方向：a)现有平差规则的参数优化和稳健性评估；b)开发新的集合最优平差规则。本文提出利用马尔可夫链蒙特卡罗技术，特别是Gibbs抽样技术，来估计按某种稳定分布在设置中经历误差的序贯调整过程的均值问题。这项研究的主要成果将是一套新的工艺调整工具，将在短期制造过程中提供有效的设置和内部运行控制。该配方的主要优点在于，在生产了几批或几批之后，它允许在获得批次中的第一个测量之前开始调整新的批次。对于这项研究有望受益的灵活、短期的制造系统来说，这显然是一种优势。使用宾夕法尼亚州立大学的FAME制造实验室将为该项目开发的技术提供现实的试验台。与行业研究人员合作(礼来公司和SAS研究所公司)将提供在本研究中开发的技术的实际应用方面的专业知识和关于软件实施的指导。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.