The notion of weighted Renyi's entropy for truncated random variables has recently been proposed in the information-theoretic literature. In this paper, we introduce a generalized measure of it for double truncated distribution, namely weighted generalized interval entropy (WGIE), and study it in the context of reliability analysis. Several properties, including monotonicity, bounds and uniqueness of WGIE are investigated. Moreover, a simulation study is carried out to demonstrate the performance of the estimates of the proposed measure using simulated and real data sets. The role of WGIE in reliability modeling has also been investigated for a real-life problem.