Heterogeneous multiprocessor systems are becoming more common and scheduling real-time tasks on them is an extremely challenging research problem. While the stringent functional and timing requirements are to be met, this problem becomes even more difficult in dynamic environments, for example, caused by processor failures. Furthermore, in safety critical applications having tasks with mixed criticality levels, guaranteeing adaptive fault tolerance to meet the reliability requirements adds another complex dimension. The key contribution of our research is a framework for task allocation and scheduling in the above context, which has a generic task model enabling task-level redundancy, a range of reconfiguration/task migration options during processor failures and definition of a set of performance metrics. We have addressed the issues of both timeliness and reliability under three different allocation strategies for a multiprocessor system with the feasibility check being performed using the well-known Rate Monotonic (RM) schedulability test. The algorithm presented in this paper, ensures that all required deadlines are met with efficient processor utilization under normal conditions and guarantees essential operations even during processor failures. In real-time multiprocessor systems used in safety critical applications, the proposed approach is expected to provide better utilization of resources and guarantees with respect to the system reliability. We demonstrate as well as evaluate the performance of our approach by simulation studies on task scheduling in heterogeneous multiprocessor environments.