The R in FRBM stands for Responsibility. The full form of FRBM is Fiscal Responsibility and Budget Management (FRBM). You can read about the Fiscal Responsibility & Budget Management (FRBM) Act in the given link.

The Bill was introduced in the parliament of India in the year 2000 by Atal Bihari Vajpayee Government.

Further readings:

1. Previous Years Economic Mains Questions for UPSC GS-3
2. Indian Economy Notes For UPSC