Energy efficiency and fault tolerance are two important features required for sustained and reliable operations of wireless sensor networks deployed in unstructured environments. This paper investigates an approach to prolonging network lifetime and ensuring sensing reliability by organizing the sensors into several disjoint subsets, each of which takes shift to cover the entire region. This strategy is made possible by the enormous redundancy in large-scale sensor network applications where many small and inexpensive sensors are deployed to achieve quality through quantity. However, such energy savings through shift taking in time and fault tolerance via redundant coverage require an appropriate network partition in space: each on-duty subset must (i) cover the entire region, (ii) maintain its own connectivity, and (iii) cover every point with multiple sensors. Based on a general sensor network model, we formulate this problem as an NP-complete Connected M-SET k-Coverage problem. We rigorously derive a necessary and sufficient condition for checking the sensor coverage of a continuous two-dimensional space based on geometric reasoning, and analytically derive the upper bounds on both M and k for any given sensor network. We further propose a heuristic approach to this problem and evaluate its performance through extensive simulations.