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

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.