In this paper we consider the estimation of the mean time to failure using a weighted loss function that reflects fit and precision of estimation. The weighted loss function we propose here is an extension of weighted balanced loss function used in Rodrigues and Zellner [7] and a special case of the one used in Chung et al [1]. As in the previously mentioned article, we will prove that optimal point estimates relative to our weighted loss function are linear combination between Bayesian and non-Bayesian estimates. Examples based on non-informative and informative priors for evaluating posterior expected loss associated to alternative estimates are given. The results obtained generalize the results from Ciumara et al. [3].