A simple and efficient approach is proposed to improve the reliability and availability of SIMD (single instruction, multiple data stream) parallel processor systems (PPSs) with N equals 2**n PEs (processing elements), interconnected by multistage interconnection networks or crossbar networks. This approach requires slight modifications of the system. A particular running fashion, called the dual running fashion, is provided, in which the whole PPS can be viewed as two duplicated PPSs with half the processors (PEs) in each PPS. The modified PPS can still operate with half the original processors for up to n faulty processors in the system. An efficient self-diagnosis method to detect all faulty PEs is given. The dual running fashion can also be used to provide a redundant configuration for certain computations that require high accuracy.