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Most Statistical Process Control (SPC) research has focused on the development of charting techniques for process monitoring. Unfortunately, little attention has been paid to the importance of bringing the process in control automatically via these charting techniques. This thesis shows that by drawing upon concepts from Automatic Process Control (APC), it is possible to devise schemes whereby the process is monitored and automatically controlled via SPC procedures. It is shown that Partial Correlation Analysis (PCorrA) or Principal Component Analysis (PCA) can be used to determine the variables that have to be monitored and manipulated as well as the corresponding control laws. We call this proposed procedure Active SPC and the capabilities of various strategies that arise are demonstrated by application to a simulated reaction process. Reactor product concentration was controlled using different manipulated input configurations e.g. manipulating all input variables, manipulating only two input variables, and manipulating only a single input variable. The last two manipulating schemes consider the cases when all input variables can be measured on-line but not all can be manipulated on-line. Different types of control charts are also tested with the new Active SPC method e.g. Shewhart chart with action limits; Shewhart chart with action and warning limits for individual observations, and lastly the Exponentially Weighted Moving Average control chart. The effects of calculating control limits on-line to accommodate possible changes in process characteristics were also studied. The results indicate that the use of the Exponentially Weighted Moving Average control chart, with limits calculated using Partial Correlations, showed the best promise for further development. It is also shown that this particular combination could provide better performance than the common Proportional Integral (PI) controller when manipulations incur costs.

Due to uncertainty in manufacturing processes, applied probability and statistics have been widely applied for quality and productivity improvement. In spite of significant achievements made in causality modeling for control of process variations, there exists a lack of understanding on error equivalence phenomenon, which concerns the mechanism that different error sources result in identical variation patterns on part features. This so called error equivalence phenomenon could have dual effects on dimensional control: significantly increasing the complexity of root cause identification, and providing an opportunity to use one error source to counteract or compensate the others. Most of previous research has focused on analyses of individual errors, process modeling of variation propagation, process diagnosis, reduction of sensing noise, and error compensation for machine tool. This dissertation presents a mathematical formulation of the error equivalence to achieve a better, insightful understanding, and control of manufacturing process. The first issue to be studied is mathematical modeling of the error equivalence phenomenon in manufacturing to predict product variation. Using kinematic analysis and analytical geometry, the research derives an error equivalence model that can transform different types of errors to the equivalent amount of one base error. A causal process model is then developed to predict the joint impact of multiple process errors on product features. Second, error equivalence analysis is conducted for root cause identification. Based on the error equivalence modeling, this study proposes a sequential root cause identification procedure to detect and pinpoint the error sources. Comparing with the conventional measurement strategy, the proposed sequential procedure identifies the potential error sources more effectively. Finally, an error-canceling-error compensation strategy with integration of statistical quality control is proposed. A novel error compensation approach has been proposed to compensate for process errors by controlling the base error. The adjustment process and product quality will be monitored by quality control charts. Based on the monitoring results, an updating scheme is developed to enhance the stability and sensitivity of the compensation algorithm. These aspects constitute the "Error Equivalence Theory". The research will lead to new analytical tools and algorithms for continuous variation reduction and quality improvement in manufacturing.

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