Online profile monitoring of functional data using Markov random field approximations

Music City Center 

In this talk, we will present a new methodology for conducting online profile monitoring of functional data response using Markov random field approximations to detect when the process shifts from an in-control state to an out-of-control state. Functional profile monitoring problems typically assume a fixed functional form for an in-control process. Novel to our approach is a relaxation of this assumption, which allows for random functional processes that incorporate both randomness in the underlying function and error in the observation of the function. Such constructs will result in non-zero and potentially strong correlations between response values at different points in the functional domain, violating common assumptions of independent errors found in much of the literature. Markov random fields provide a means of modeling dependence among observations of the functional response as well as a framework for detecting when the observed functional behavior of a process deviates from the typical behavior of the in-control process. We outline a learning and monitoring methodology that shows promise toward a wide range of functional profile monitoring problems under weak assumptions. We discuss the theoretical properties of our methodology and showcase its empirical performance in both simulation studies and through an application.

statistical process control

online profile monitoring

Markov random fields

undirected graphical models