Previous studies have shown that the best way to achieve high throughput/Watt of a single threaded application is by running it on an asymmetric multicore processor (AMP). AMPs feature cores that are tuned for specific workload characteristics. To increase efficiency, the core that offers the best power-performance trade-off for the executing thread is chosen. To reduce the overhead of thread migration, we have previously proposed a morphable core that can morph into multiple core types. In this study, apart from power-performance efficiency, we also consider the reliability of the different core types as indicated by their vulnerability to soft-errors. We show that the best core type for power-efficiency may not be the best for reliability. Accordingly, we develop a multi-objective thread migration strategy to determine the best core type considering power efficiency and reliability. To support runtime decision making, we have developed online estimators for reliability and power efficiency based on performance monitoring counters. In keeping with the existing literature, we use the architectural vulnerability factor (AVF) as the metric for reliability and instructions-per-second 2 /Watt as the metric for power efficiency. For the multi-objective optimization we use a Cobb-Douglas production function. Our results indicate that the proposed runtime mechanism for reliability and power-efficiency improves, on the average, the throughput/Watt of applications by 24% and reduces the Soft-Error Rate (SER) by 12% compared to the best static execution.