"On my own responsibility" is a phrase that means that someone is acting independently without relying on others. There are a number of synonyms for this phrase, each with their unique connotations. For example, "taking charge" implies a sense of control and leadership. "Being self-sufficient" acknowledges the individual's ability to operate independently without assistance. "Assuming responsibility" conveys a sense of accountability and ownership for a task or undertaking. "Self-governing" speaks to a person's ability to regulate their own behavior and actions. Regardless of the phrase used, taking on responsibility and acting independently can be empowering, but it comes with the obligation to ensure that the task is successfully completed.