In this paper, a formal system is proposed based on beta reputation for the development of trustworthy wireless sensor networks （FRS-TWSN）. Following this approach, key concepts related to reputation are formal described step by step for wireless sensor networks where sensor nodes maintain reputation for other sensors and use it to evaluate their trustworthiness. By proving some properties of beta reputation system, the beta distribution is founded to fit well to describe reputation system. Also, a case system is developed within this framework for reputation representation, updates and integration. Simulation results show this scheme not only can keep stable reputation but also can prevent the system from some attacks as bad mouthing and reputation cheating.
