A Unifying View of Some Process Adjustment Methods

Abstract

We consider the problem of adjusting a machine that starts production after an off-target setup operation. This setup adjustment problem was first studied by Grubbs (1954, 1983). A general formulation for setup adjustment problems is presented in this paper. The formulation unifies some well-known process adjustment schemes, including Grubbs' harmonic and extended rules, adjustment methods based on stochastic approximation and recursive least squares, and a recent method on adaptive EWMA feedback controllers. The proposed formulation is Bayesian and based on a Kalman filter. The formulation allows us to show the equivalence of the setup process adjustment problem with a simple instance of what is called a Linear Quadratic Gaussian (LQG) controller in the control engineering literature. As an important byproduct, the LQG model allows us to solve more complicated setup adjustment problems with readily available techniques. Extensions to cases in which there are quadratic adjustment costs and in which the problem is multivariate are discussed. The multivariate setup adjustment solution is illustrated with a multihead filling machine example.

• Engineering Process Control
• Kalman Filtering
• Linear Quadratic Control
• Setup Adjustment
• Stochastic Approximation

Additional information

Notes on contributors

Enrique del Castillo

Dr. Del Castillo is an Associate Professor in the Department of Industrial & Manufacturing Engineering. His email address is [email protected].

Rong Pan

Dr. Rong Pan is an Assistant Professor in the Mechanical and Industrial Engineering Department. His email address is [email protected].

Bianca M. Colosimo

Dr. Colosimo is an Assistant Professor in the Dipartimento di Meccanica. Her email address is [email protected].