In certain run-to-run (R2R) processes, timely accurate measurements are difficult to obtain due to slow laboratory measurement operations. Instead, only low-resolution categorical observations are observed online for important quality variables; continuous measurements for the same variables are provided after a specific amount of delay. Currently, most conventional R2R controllers cannot be applied if no continuous observations are available. It is therefore important to develop online algorithms for R2R process control based on mixed-resolution information that is partially timely and partially delayed. In this study, we take the lapping process in semiconductor manufacturing as an example and propose parameter estimation models with these mixed-resolution data for processes with the first-order autoregressive, AR(1), disturbance series. We also derive control strategies to generate recipes between production runs for better process control. The computational results of a performance evaluation show that the control performance of the proposed method is competitive compared to existing methods that are based on accurate measurements.

In certain manufacturing processes, accurate numerical readings are difficult to collect due to time or resource constraints. Alternatively, low-resolution categorical observations can be obtained that can act as feasible and low-cost surrogates. Under such situations, all classic statistical quality control activities, such as model building, parameter estimation, and feedback adjustment, have to be done on the basis of these categorical observations. However, most existing statistical quality control methods are developed based on numerical observations and cannot be directly applied if only categorical observations are available. In this research, a new online approach for parameter estimation and run-to-run process control using categorical observations is developed. The new approach is built in the Bayesian framework; it provides a convenient way to update parameter estimates when categorical observations arrive gradually in a real production scenario. Studies of performance reveal that the new method can provide stable estimates of unknown parameters and achieve effective control performance for maintaining quality.

Categorical observations are frequently observed in run-to-run processes where obtaining accurate measurements of quality characteristics is difficult. In such circumstances, the use of categorical observations to estimate a process model and generate an adjustment recipe becomes inevitable. However, most conventional run-to-run controllers cannot be applied if no continuous observations are available; some parameter estimation methods that can handle categorical data only use historical dataset in an offline manner. In practice, it is common to see observations collected following a time sequence in a run-to-run process. Taking the lapping process in semiconductor manufacturing as an example, this paper develops an online approach for parameters estimation and run-to-run process adjustment using categorical observations. The proposed method optimises a penalised Maximum Likelihood (ML) function and updates parameters step by step when new categorical observations become available. A control strategy is also derived to generate receipts for process update between runs. The computational results of performance evaluation show that the proposed method is capable of estimating unknown parameters and control output quality online when initial bias exists.