A Bayesian framework for online parameter estimation and process adjustment using categorical observations

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.