In the last decade, the effects of interruptions through mobile notifications have been extensively researched in the field of Human-Computer Interaction. Breakpoints in tasks and activities, cognitive load, and personality traits have all been shown to correlate with individuals' interruptibility. However, concepts that explain interruptibility in a broader sense are needed to provide a holistic understanding of its characteristics. In this paper, we build upon the theory of social roles to conceptualize and investigate the correlation between individuals' private and work-related smartphone usage and their interruptibility. Through our preliminary study with four participants over 11 weeks, we found that application sequences on smartphones correlate with individuals' private and work roles. We observed that participants engaged in these roles tend to follow specific interruptibility strategies - integrating, combining, or segmenting private and work-related engagements. Understanding these strategies breaks new ground for attention and interruption management systems in ubiquitous computing.