The increasing popularity of cell phones has made them the most personal and ubiquitous communication devices nowadays. Typically, the ringing notifications of mobile phones are used to inform the users about the incoming calls. However, the notifications of inappropriate incoming calls sometimes cause interruptions not only for the users but also the surrounding people. In this paper, we present a data-driven approach to infer the opportune moments for such phone call interruptions based on user's unavailability, i.e., when a user is unable to answer the incoming phone calls, by analyzing individual's past phone log data, and to discover the corresponding phone silent mode configuring rules for the purpose of minimizing call interruptions in an automated intelligent system. Experiments on the real mobile phone datasets show that our approach is able to identify the opportune moments for call interruptions and generates corresponding silent mode configuring rules by capturing the dominant behavior of individual users' at various times-of-the-day and days-of-the week.