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The aim of this work is to evaluate the nth joined probability of three-dimensional wireless sensor networks, and to extend the lifetime of these networks. A Gaussian probability distribution function is assumed for the power coverage probability for each sensor in the 3-dimensional cartesian and spherical coordinates. The overall joint probability is evaluated from each sensor to a target in the network, and then the network lifetime of sensors power sensing a number of targets, is extended based on removing redundancies of powering all sensors at the same time. Proportional to the evaluated probabilities, sensors are energized during slots of periodic time. The formulated probabilities are assumed to be uncorrelated among each sensor to any target zone. A case study is introduced to demonstrate extending the lifetime of a network comprising 7 sensors targeting two uncorrelated zones, in which 8 different cases of subsets are formed, when a minimum threshold of overall power coverage probability of 35% is assumed. Network lifetime is extended more than 70%, with some sensors reaching more than 90% power saving. This work can be extended to deal with other types of probabilities, as well as with cases of correlated sensor-target coverages.

An Algorithm to extend sensor lifetime and energy is implemented for different scenarios of ad hoc and wireless sensor networks. The goal is to prolong the lifetimes of sensors, covering a number of targeted zones by creating subsets of sensors, in which each subset covers entirely the targeted zones. Probabilistic analysis is assumed in which each sensor covers one or more targets, according to their coverage failure probabilities. Case studies of different sensor subsets arrangements are considered such as load switching, variable target load demands as well as a perturbation in sensor planner locations.

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