  With the development of IoT, the sensor usage has been elevated to a new
level, and it becomes more crucial to maintain reliable sensor networks. In
this paper, we provide how to efficiently and reliably manage the sensor
monitoring system for securing fresh data at the data center (DC). A sensor
transmits its sensing information regularly to the DC, and the freshness of the
information at the DC is characterized by the age of information (AoI) that
quantifies the timeliness of information. By considering the effect of the AoI
and the spatial distance from the sensor on the information error at the DC, we
newly define an error-tolerable sensing (ETS) coverage as the area that the
estimated information is with smaller error than the target value. We then
derive the average AoI and the AoI violation probability of the sensor
monitoring system, and finally present the {\eta}-coverage probability, which
is the probability that the ETS coverage is greater than {\eta} ratio of the
maximum sensor coverage. We also provide the optimal transmission power of the
sensor, which minimizes the average energy consumption while guaranteeing
certain level of the {\eta}-coverage probability. Numerical results validate
the theoretical analysis and show the tendency of the optimal transmission
power according to the maximum number of retransmissions. This paper can pave
the way to efficient design of the AoI-sensitive sensor networks for IoT.
