An important challenge facing many large-scale surveillance applications is how to schedule sensors into disjoint subsets to maximize the coverage time span. Due to its NP-hard complexity, the problem of finding the largest number of disjoint set covers (DSC) of sensors has been addressed by many researchers. Majority of these studies employs the Boolean sensing model where a sensor covers a target if it lies within its sensing range. In reality, however, the sensing reliability may be affected by several parameters, e.g., strength of the generated signals, environmental conditions and the sensor's hardware. To the best of our knowledge, improving coverage reliability of Wireless Sensor Networks (WSNs) has not been explored while solving DSC problem. This paper addresses the problem of improving coverage reliability of WSNs while simultaneously maximizing the number of DSC. Thus, in the context of WSNs design problem, our main contribution is to turn the definition of single-objective DSC problem into a multi-objective problem (MOP) by adopting an additional conflicting objective to be optimized. Specifically, we investigate the performance of two multi-objective evolutionary algorithms in terms of diversity and quality of the Pareto optimal set for the modeled MOP. The simulation results indicate that multi-objective approach results in achieving reliable coverage and large number of DSC compared to a single-objective approach.