Adaptive monitoring of multimodal data

Multimodal process data that include several subpopulations appear frequently in many complex applications due to process heterogeneity. Different from the most existing control charts that are only applicable to unimodal data, a new adaptive monitoring method is proposed in this paper for multimodal data from heterogeneous processes. Specifically, a Gaussian mixture model is first employed for data modeling. Considering the number of subpopulations that may change in Phase II, a penalized likelihood function is devised to infer the true number of subpopulations by shrinking any insignificant or redundant Gaussian components. Our proposed control chart, is thus not only sensitive to process changes in subpopulation parameters, but also adaptive to changes in the number of subpopulations. A diagnostic procedure is also followed to classify the changes in multimodal data. The superiority of our chart is fully demonstrated through numerical Monte Carlo simulations and a real industrial example in the production process of a 3D printing nylon powder material.