Online parameter estimation and run-to-run process adjustment using categorical observations

Abstract

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.

Keywords:

• categorical observations
• cut-points estimation
• parameter estimation
• statistical process adjustment
• statistical process control

Acknowledgements

The authors are grateful to the editor and the referees for carefully reading this manuscript and giving valuable comments, which have helped improve this work greatly. This research was supported by the National Natural Science Foundation of China (NSFC) under grant No. 70802034.