One of the important concerns in wireless sensor networks is network lifetime, which is defined as the time span that all targets can be thoroughly covered. Random and dense deployment of sensors in many applications may impose some coverage redundancy in the network. Under these conditions, judicious power management and sensor scheduling can considerably extend network lifetime. One way to reduce energy consumption is to divide sensors into disjoint groups, called covers, each of which can cover all targets and to activate them iteratively in a round robin fashion. At each time interval, only the sensors from the current active set are responsible for monitoring the targets, while all other nodes are in sleep or power-saving mode. The more covers can be found, the longer sensor network can be prolonged. Obtaining the maximum number of such covers is known as DSC problem which is proved to be NP-hard. Existing heuristic algorithms either get unsatisfactory solutions in some cases or take unacceptable computation time, which makes them inapplicable in medium (large) dimensions. The aim of this research is finding an effective method to improve lifetime and reliability of wireless sensor networks. We first propose an optimal method to solve this optimization problem; that is to split the set of sensors into maximum number of covers. The proposed method is based on the transformation of the problem into the well known Boolean satisfiability (SAT) problem. Simulation results show that this method can lead to a large reduction in computation time meanwhile produces optimal solutions. We then investigate the sensor scheduling for K-coverage problem, in which targets are required to be monitored by at least K sensors throughout the whole network lifetime. Based on the proposed method, we extend this approach to a reliable coverage problem and evaluate its performance through several simulations. The algorithm is simple, fast, and according to the simulations, significantly increases the longevity of sensor network in scenarios which require stronger monitoring and fault-tolerant capability. Key words: Boolean Satisfiability, Disjoint Set Cover, Life Time, NP-hard, Wireless Sensor Networks.