A health care system (HCS) has promptly progressed owing to the increasing need for accurate reactions in seriously urgent situations of health, especially for elderly people. The well-being of patients throughout the curing time as well as observing and keeping excellent measurement with reduced power consumption and cost all together forms the nature of the HCS. To tackle these objectives, a remote online observing network system has been assembled here to afford reliable correct measurements using a reduced amount of energy utilization. In this paper, the required measurements are provided by a simulated healthcare measuring device. A Quality of inference QoIn f function is optimized via an intelligent Brute Force algorithm in order to choose most acceptable set of sensors that will provide high accuracy but also the lowest cost. Moreover, to maintain the least power consumption within a group of monitored HCSs, a theoretical framework of consensus algorithms has been proposed. The analysis of the framework is based on algebraic graph theory. Simulation results show the effectiveness of the proposed approach. It has been noticed that the consensus application comprises the need for low power when dealing with a network of wireless sensors used for health care monitoring.