Multimode Geometric-Profile Monitoring with Correlated Image Data and Its Application to Nanoparticle Self-Assembly Processes

We propose a new method for monitoring changes in geometric profiles of objects, where the geometric profiles may change through various modes in a dynamic process. This work is motivated by the need for monitoring changes in geometric shape and sizes of nanoparticles during their chemical self-assembly process; the changes often occur through many different modes before converging to the final state. The proposed multimode geometric-profile monitoring method addresses three issues specific to this process, all of which have never been addressed together by existing process-monitoring methods profiling of functional data, monitoring of multimode processes, and monitoring of time-correlated processes. The new profile-monitoring method consists of two phases. In phase I, we characterize multiple modes of geometric shape changes under in-control process conditions given a sequence of geometric observations on products. We propose using a mixture of time-series models for this characterization and present an exact Gibbs sampling procedure for Bayesian estimation of model parameters. In phase II, we test whether a new observation of product geometries sampled at a certain time in the current process run exhibits significant out-of-control symptoms. We propose a Bayes factor score-based criteria for this testing. The proposed method is empirically verified using simulated datasets and a real dataset from a nanoparticle self-assembly process.