Compensability of errors in product quality in multistage manufacturing processes

Recent advances in model-based feedforward control of quality in multistage manufacturing processes (MMPs) are used to introduce the concept of compensability of errors in product quality. It is defined as the system-level ability to automatically eliminate quality errors accumulated in the product, given the allocation of measurements and controllable tooling. Significant similarities are observed with the control theory concepts of controllability and observability. In addition, just like in control theory, it is shown that relatively simple matrix rank tests can be used to determine the compensability of a MMP and are related with the previously introduced notion of diagnosability. The theory introduced in this paper enables rapid quantitative analysis of one's ability to actively control the quality in a manufacturing system, which is crucial for optimal allocation of measurements and controllable tooling in an MMP. Compensability studies based on the newly introduced methods are conducted using models of the flow of errors in product quality in two automotive cylinder head machining lines and a multi-layer semiconductor lithography process.