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A large number of microprocessors (μPs) have been widely used in many practical fields and the demand for improvement of their reliabilities have recently increased. Watchdog processors (WDPs) are small and simple coprocessors that can detect errors by monitoring the behavior of μPs. This paper formulates three reliability models of μP systems with WDPs: model 1 considers the system where a main processor (MPu) has n WDPs with self checking. Next, model 2 considers the system with upper limit number of resets. Further, model 3 discusses the system with limit processing time. The expected costs of each model are derived and the optimal policies which minimize them are discussed analytically. Finally, the numerical examples are given.