Studying the reliability concepts of the components of a system or a device based on conditional random variables are important and usual, because, most of the real observations are left, right or doubly truncated censored data. In many situations, we only have information about between two lifetime points, so we should study the reliability measures under the condition of doubly truncated random variables. One of the important and applicable reliability concepts, that recently has gathered the most attention of the researchers, is the variance residual life. In this paper, we try to study some of the reliability properties of the variance residual life based on doubly censored data which has not been studied precisely yet. Its monotonicity properties and relation with doubly truncated mean residual life and doubly truncated residual coefficient of variation are discussed. Furthermore, the lower (upper) bound for it under some conditions is obtained. Finally, some examples due to this subject are mentioned.

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