Reliability and mean-time-to-failure (MTTF) models of different fault-tolerant processor arrays (FTPAs) are introduced. On the basis of these models, approaches which allow for the analytical estimate of the necessary number of spares (NNS) and the optimal number of spares (ONS) are proposed. Knowledge of the NNS is suited to FTPAs where nonredundant hardware (hardware for which no redundancy is provided) is considered nearly fault free. Knowledge of the ONS is useful when faults can affect the nonredundant hardware, because in this case overall array reliability may actually decrease when the number of spares increases beyond some value. The quick estimates provided here can be used to help designers in the early design phases of an FTPA. >