Variance residual life function based on double truncation

Since, most of the real observations in industrial and reliability studies, are left, right or doubly truncated data, studying the reliability concepts of the components of a system or a device based on conditional random variables, are important and usual. One of the important and applicable reliability concepts, that recently has gathered the 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 truncated data. Its monotonicity properties and relations 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. We also discuss and find the similar results for discrete random ageing which its differences with the continuous case, are noticeable. Finally, some examples due to this subject are mentioned.