Increasing the lifetime of energy constrained wireless sensor networks is one of the key challenges in sensor network research. In this paper we present a bottom-up approach to evaluating the lifetime performance of networks employing two basic sensor placement schemes: square-grid and hex-grid. Lifetimes of individual sensor node as well lifetimes of networks are modeled as random variables and their probability density functions (pdf) are obtained theoretically. Reliability theory is used for

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... the network lifetime analysis, and provides a methodology for similar studies. Simulation results show that the actual pdf's match very closely to those obtained theoretically. The theoretical results provided in this paper will serve as a basis for other related research such as analysis of other sensor placement schemes, lifetime and sensor density tradeoff study, and performance of energy efficiency related algorithms.