Multi-function radars (MFRs) are sophisticated types of sensors with the capabilities of complex agile inter-pulse modulation implementation and dynamic work mode scheduling. The developments in MFRs pose great challenges to modern electronic reconnaissance systems or radar warning receivers for recognition and inference of MFR work modes. To address this issue, this paper proposes an online processing framework for parameter estimation and change point detection of MFR work modes. At first this paper designed a fully-conjugate Bayesian non-parametric hidden Markov model with a designed prior (agile BNP-HMM) to represent the MFR pulse agility characteristics. The proposed model allows fully-variational Bayesian inference. Then, the proposed framework is constructed by two main parts. The first part is the agile BNP-HMM model for automatically inferring data on pulse parameter clusters and corresponding number of clusters from input pulse sequence. The second part utilizes the streaming Bayesian updating to facilitate computation, and designed a online work mode change detection framework based upon a family of one-ended sequential probability ratio test. We demonstrate that the proposed framework is consistently highly effective and robust to baseline methods on diverse simulated data-sets.