Statistical process adjustment methods for quality control in short-run manufacturing

by Pan, Rong.

iii Process adjustment techniques based on the feedback control principle have become popular among quality control researchers and practitioners, due to the recent interest on integrating Statistical Process Control (SPC) and Engineering Process Control (EPC) techniques. Traditionally, quality engineers, who are more familiar with SPC methods, avoid using process adjustment methods because of process tampering concerns. This has resulted in very few systematic studies on how to apply process adjustment strategies for continuous quality improvement. Most of the work in this area concentrates on chemical processes which typically have long production runs. This thesis focuses on studying sequential adjustment methods, closely related to well-known Stochastic Approximation procedures, for the purpose of quality control of a short-run manufacturing process. First, the problem of adjusting a machine that starts production after a defective setup operation is considered. A general solution based on a Kalman Filter estimator is presented. This solution unifies some well-known process adjustment rules, and is a particular case of Linear Quadratic (LQ) control methods. In essence, this solution calls for a sequential adjustment strategy which recursively calculates the value of an adjustable variable according to the prior knowledge of this variable and the most recent observation from the process. Next, the integration of sequential adjustments with SPC control charts are investigated for controlling an abrupt step-type process disturbance on a manufacturing iv process. The performance of this type of integrated methods depends on the sensitivity of the control chart to detect shifts in the process mean, on the accuracy of the initial estimate of shift size, and on the number of sequential adjustments that are made. It is found that sequential adjustments are superior to single adjustment strategies for almost all types of process shifts and shift sizes considered. A combined CUSUM chart plus sequential adjustments approach has better performance than other methods when the shift size is not very large. If there are different costs associated with a higher-than-target quality characteristic compared to a lower-than-target quality characteristic, that is, an asymmetric cost function, the adjustment rule needs to be modified to avoid the quality characteristic falling into the higher cost side. For this case, a sequential adjustment rule with an additional bias term is proposed. A method to determine these bias terms is developed. Furthermore, the effect of process measurement and adjustment costs on the decision of whether or not to apply adjustment actions at each sampling instant is investigated. A modified Silver-Meal scheduling algorithm is found to be good at providing robust and close-to-optimal adjustment schedules for this problem. Finally, methods for identifying and fine-tuning a manufacturing system operating in closed-loop are studied. When a process is operated under a linear feedback control rule, the cross-correlation function between the process input and output has no information on the process transfer function, and open-loop system identification techniques cannot be used. In this research, it is shown that under certain general assumptions on the controller and process disturbance structure, it is possible to identify the process disturbance models from data obtained under closed-loop operation. After v identification, it is proposed to tune the controller to a near-optimal setting according to a performance criterion that considers both the variance of the output and the variance of the adjustments. In summary, a collection of mathematical models for short-run manufacturing processes are proposed and studied systematically in this thesis. It is demonstrated that by implementing proper adjustment strategies the stability of the process can be better maintained; thus, significant economic benefits obtained from the consistent quality of products will be achieved. This research contributes directly to the quality improvement program of the manufacturing industry and to the field of applied statistics.