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Mobile notifications have become a major communication channel for social networking services to keep users informed and engaged. As more mobile applications push notifications to users, they constantly face decisions on what to send, when and how. A lack of research and methodology commonly leads to heuristic decision making. Many notifications arrive at an inappropriate moment or introduce too many interruptions, failing to provide value to users and spurring users' complaints. In this paper we explore unique features of interactions between mobile notifications and user engagement. We propose a state transition framework to quantitatively evaluate the effectiveness of notifications. Within this framework, we develop a survival model for badging notifications assuming a log-linear structure and a Weibull distribution. Our results show that this model achieves more flexibility for applications and superior prediction accuracy than a logistic regression model. In particular, we provide an online use case on notification delivery time optimization to show how we make better decisions, drive more user engagement, and provide more value to users.