A Wireless Sensor Network (WSN) is composed of a large number of distributed tiny sensor nodes which report data from an environmental phenomenon. Each sensor node consists of measurement devices, computational resources, a communications component, and a finite power source. Typically, the sensor nodes are densely deployed, prone to failure, and limited in power. In centralized data processing, all of the sensor nodes data's and their geography locations are sent to a central processor. But because of requirements in communication bandwidth usage reducing, reliability increasing and cost decreasing in WSN application, employing of this structure is not suitable. As a result a distributed data processing scheme is considered in WSN applications. In this scheme, some local processing is done on each sensor nodes then only condensed information sent to central processors. Event region detection and faulty sensor recognition are two major research issues in WSN. In this thesis, a distributed processing scheme is proposed to detect two simultaneous events in WSN area. This procedure consists of two processing layers, local detection layer and final detection layer. This detection procedure is designed based on hypothesis tests and Bayesian detection criteria. By applying three hypothesis including normal, first event, and second event, the risk function in the Bayesian detection criteria is defined based on the priori probability of each hypothesis and probability of each option may be happened in decision making. Then decision rules are obtained via minimization of the risk function. In chapter 4, a fault- tolerant algorithm is proposed to improve the precision of detection of two events in presence of sensor fault. By proposing all the sensor faults that may be occurred in decision making layers, and in occurrence of specific probability of sensors fault, computation of the optimal thresholds used in first layer of decision making will be attainable. By using a numerical method, the optimal values of thresholds are calculated such that the overall risk function is minimized. Sensor networks are usually deployed in uncontrolled and harsh environments and observations are associated with noises by excessive variance which may corrupt the observations. Since the probability of sensor fault not been determined before detection of two events, it is necessary to recognize the faulty sensors. On the next step of this thesis, improved distributed fault detection has been employed to recognize the sensor nodes which have a noise with excessive variance. Therefore, the error probability of the two events detection is reduced by elimination of faulty nodes decisions in the second processing layer. To show the accuracy and efficiency of the proposed methods, numerical examples are presented in all chapters and the simulation results are compared. Keywords: Two Simultaneous events detection; Distributed data processing; Wireless Sensor Network; Bayesian criteria; Fault- tolerant; Improved distributed fault detection